Slowing with age as an explanation for age changes in fluid intelligence

MISSING IMAGE

Material Information

Title:
Slowing with age as an explanation for age changes in fluid intelligence
Physical Description:
vi, 148 leaves : ill. ; 28 cm.
Language:
English
Creator:
Tomer, Adrian, 1944-
Publication Date:

Subjects

Subjects / Keywords:
Age and intelligence   ( lcsh )
Psychometrics   ( lcsh )
Psychology thesis Ph. D
Dissertations, Academic -- Psychology -- UF
Genre:
bibliography   ( marcgt )
non-fiction   ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1989.
Bibliography:
Includes bibliographical references (leaves 139-147)
Statement of Responsibility:
by Adrian Tomer.
General Note:
Typescript.
General Note:
Vita.

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 001485771
oclc - 21107724
notis - AGZ7886
System ID:
AA00002135:00001

Full Text


















SLOWING
AN EXPLANATION
FLUID ]


WITH AGE AS
FOR AGE CHANGES
INTELLIGENCE


ADRIAN


TOMER


A DISSERTATION PRESENTED TO T
OF THE UNIVERSITY O
IN PARTIAL FULFILLMENT OF
FOR THE DEGREE OF DOCTOR


'HE GRADUATE SCHC
F FLORIDA
THE REQUIREMENTS
OF PHILOSOPHY


UNIVERSITY


OF FLORIDA


)OL















ACKNOWLEDGMENTS


I would


like


express


deep


gratitude


the


chairman


supervisory


committee


and


academic


advisor,


Walter


Cunningham.


The


present


study


conception


approach


relies


heavily


on his


work


as well


as on


innumerable


talks


have


had


with


him


on the


subj ects


treated


here.


guidance,


continuous


encouragement


and


openness


constituted


a vital


support


this


major


endeavor.


I would


like


also


to thank


and


express


appreciation


supervisory


committee


members:


James


Algina,


Richard


Griggs,


Patricia


Miller


Robin


West


their


continuous


support


assistance


different


stages


the


dissertation.


Thanks


are


extended


Christopher


Hertzog


from


Georgia


Tech


whose


help


the


design


and


analysis


this


study


was


extremely


important.


Appreciation


also


extended


fellow


graduate


students


whose


support


helped


me all


along


the


way


achieving


a difficult


task.


Finally,


wife


who


was


patient


and


supportive


A~~~~~~~~~~~~~~~ at seA fll -1 ar a 4.aaaS .. A~ --ni 'nab.4.1


AnC 4 ~1 hrJ


LI


CIL YIA II ~I ClIf


C rrwni
















TABLE OF CONTENTS

page

ACKNOWLEDGMENTS .............. .......... ............i i

ABSTRACT..............................................v

CHAPTERS

1 INTRODUCTION AND OVERVIEW.......................1

The Speed Hypothesis............................ 3
Alternative Views and Criticisms................7
The Present Study..............................10

2 LITERATURE REVIEW.............................. 13

Cerella's Approach.............................14
Factor Analytical Studies......................15
Tentative Conclusions on the Dimensionality
of Slowing.............. .....................21
Slowing in Relation to Psychometric Abilities..22
Speed and Memory Abilities...................32
Alternative Interpretations....................34
Summary................... . . ....... . 39

3 THE PROPOSED MODELS............................42

4 METHOD........ ...... .. .. . .. .... ........ ..58

Subjects.............. . . ....... . . .58
Tasks and Tests................................59
Speed Tasks...................... ...........59
Fluid and Crystallized Intelligence.........64
Other Variables...................... .......65
Procedure............. ...... ... ................ 66


RESULTS.... ..... ... .. . . ... ....... . ... 68


Confirmatory Factor analysis of Speed
Mea n r s - - - s - - - -


......- - -7









Models with
Speed....
Models with


Multiple


Second


First


Order


Order


Speed
Speed


Factors


Factors.
Factors.


S. .99
.....102


DISCUSSION..................... ...... ......... 108


The Speed Hypothesis..
Fluid and Crystallized
Integration and Future


Intelligence
Directions..


APPENDICES


GOODNESS


OF FIT


INDICES ..... ........... .....


The Normed
The LISREL'
The Adjuste
The LISREL'
Chi-Square
Diagnostics
Other Indic
Relationshi
Indices of


Fixed Index.
s Goodness-o
d Goodness-o
s Root-Mean-
and Chi-Squa
of Fit.....
es of Fit...


ps
Fit


between
for the


*
f-Fit
f Fit
Squar
re/df


Indices
User of


Index (G.I
Index (AGF
e-Residual


.......
of Fit..
LISREL.


;FI)..... 1
. (RMR)..1
* ..... .1
* .4....1
* .. .. .1

. . .1

e 1



RAW


REFERENCES..

BIOGRAPHICAL


...SKETCH...... . . . .. ........ .148


.00....


. .... ...109
..... .. ... 118
...........120


DATA......................................133















Abstract


the


Dissertation


University


Requirements


Presented


Florida


the


Degree


the


Partial F
of Doctor


Graduate


School


fulfillment


of Phil


osophy


SLOWING


WITH


AGE


AN EXPLANATION


FOR


AGE


CHANGES


FLUID


INTELLIGENCE


ADRIAN

August


TOMER

1989


Chairman:


Major


Walter


Department


R. Cunningham
: Psychology


Ph.D.


The


speed


hypothesis


attempts


to explain


changes


intellectual


functioning


with


increased


postulating


mechanism


level


of the


central


nervous


system


decline


thi


mechanism


with


age


assumed


to affect


speed


of performance


of various


tasks


and


cognitive


functioning


in general.


Correlational


anal


yses


measures


of speed


suggest


that


more


than


one


mechanism


may


involved


. Correlational


or regres


sion


analyses


relationship


between


speed


and


fluid


intelligence


were


general


consistent


with


the


speed


hypothesis.


In thi


study


the


issue


of structure


measures


speed


was


addressed


conducting


confirmatory


factor


analy


ses


of fi rmt


1 avel


order


then


the


level


of second


S. R-


nL


n.l l









crystallized


intelligence


(Gc)


were


estimated


several


path


models


which


included


age,


education


subjective


health


as exogenous


variables.


Speed,


a mediating


variable,


was


modeled


as a first


order


factor


or as a second


order


factor,


agreement


with


the


confirmatory


analysis.


The


analyses


were


performed


a sample


elderly


adults


aged


73 and


a sample


of 147


young


adults


aged


Confirmatory


factor


analyses


found


, as hypothesized,


five


first


second


order


order


factors


speed


of speed


factors


both


were


age


necessary


groups.


Three


to account


the


relationships


between


the


first


order


speed


factors.


The


path


models


investigated


supported,


general,


a speed


hypothesis


the


older


sample.


The


evidence


this


young


subjects


was


weaker.


Also,


the


analysis


indicated


that,


old


subjects,


two


factors


of speed


mediated


independently


the


effect


age


on Gf,


suggesting


the


existence


of a multitude


of speed


mechanisms.















CHAPTER


INTRODUCTION


AND


OVERVIEW


Intellectual


abilities,


as amply


documented


cross-


sectional


, longitudinal


and


sequential


approaches


Botwinick


, 1977;


Cunningham


1987


Schaie,


1983;


Schaie


Hertzog,


1983)


vary


among


adults


as a function


age.


Sequential


analyses


show


that


beyond


certain


ages,


which


might


be different


different


abiliti


there


steady


decline


differences


with

the


increased

respective


independent


abiliti


of cohort


(Schaie


& Hertzog,


1983).


There


also


evidence,


most


cross


sectional,


suggesting


a decline


problem


solving


ability


with


Reese


& Rodeheaver


, 1985)


secondary


memory


with


increased


, Poon,


1985)


Convergent


evidence


indicates


that


a decline


with


larger


and


seen


earlier


speeded


than


unspeeded


intellectual


tasks


, Cunningham,


1988)


. Thus,


Schai


and


Strother


(1968)


found


steep


longitudinal


declines


two


highly


speeded


abilities--Verbal


Fluency


and


Psychomotor


Speed.


Cunningham


(1988,


1989)


found


pronounced


declines


negligible


cohort


differences


the


longitudinal


Florida











Expressional


Fluency--also


decreased


with


but


showed


larger


cohort


differences


. In


a subsequent


study


Cunningham


and


White


(1984)


found


the


factor


scores


of Figural


Perceptual


two


Speed


samples


to correlate


old


higher


(ages


than


and


.7 with


young


age


(ages


across


to 33)


adults


. Symbolic


sensitive


Perceptual


. Thi


Speed


pattern


appeared


of relatively


to be 1

y steep


ess

declines


with


age


speeded


tasks


consis


tent


with


the


pattern


a steeper


between


increase


unspeeded


covariances


intellectual


between


factors


speeded


which


than


been


demonstrated


cross


sectional


(Cunningham,


1980)


longitudinal


analy


ses


(Cunningham,


Smook,


Tomer,


1985)


The


pattern


of pronounced


decline


speeded


intellectual


factors


consistent


with


a large


body


studi


showing


slowing


with


reaction


times


responses


to different


stimuli


times


exe


cution


almost


any


activity


which


has been


tested


, Birren,


Woods,


& Williams,


1980;


Salthouse,


1985a)


. A few


exceptions


pattern,


however,


have


been


found


. Vocal


suggested


at least


part


of the


evidence


does


not


slow


with


increased


Salthouse,


1985a)


. Lexical


access


time


as shown


priming


studi


Cerella


& Foza


1984


. Salthouse,


1985b)


affected


systematically


age.











forming


sentences


which


incorporate


a given


pair


nouns


(Nebes


& Andrews-Kulis


, 1976)


. Finally


no age


differences


were


found


Waugh


(1980)


the


rate


of reading


words.


The


Soeed


Hypothesis


A major


attempt


to explain


the


decline


cognitive


functioning


Birren


s hypothesis


(e.g. ,


Birren,


1964,


1965;


Birren,


Woods,


& Williams,


1980)


. According


to this


hypothesis:


There


a decline


central


nervous


system


with


increased


age,


and


As a result


there


decline


intellectual


functioning.


The


hypothesis


was


first


conceived


Birren


the


late

and


forties


his


and


colleague


inspired

s in the


many


research


fifties


projects


sixties


of Birren


(Cunningham,


press).


It reflects,


part


a realization


Birren


the


importance


of the


evidence


showing


that


the


well-known


finding


slowing


with


cannot


be attributed


peripheral--input


or output--slowing.


In fact,


had


become


clear


that


slowing


of encoding


processes


and


of movements


executed


response


to stimuli


explain


only


a small


part


the


overall


slowing


a variety


tasks


(Birren,


1964,


1965).

factors


To the

than


extent


that


periphera


slowing

1 ones


was


attributed


was


treated


to other

as a


dependent


variable,


a result


of cognitive


adaptations o











behavior


and


can


used


as an explanatory


variable.


The


computer


metaphor


used


Birren


(Birren,


1965)


according


which


speed


of behavior


similar


to operation


speed


computers


and


may


be similarly


used


as a "primary


descriptive


characteristic"


(Birren,


1965,


195)


has


been


proved


to be a fruitful


model


describing


changes


cognitive


The


seventies


functioning


speed


and


ever


hypothesis


eighties


since


has


from


(e.g.,


received


several


Salthouse,


new


1985b).


impetus


developments


the


field


of intelligence


the


field


information


processing.


A first


development


refers


to what


Eysenck


called


"a Kuhnian


revolution


the


theory


and


the


measurement


of intelligence"


(Eysenck,


1986,


731).


It is


related


the


work


of Jensen


(e.g.,


Jensen,


1982)


the


United


States


and,


quite


independently,


to the


work


others


Europe,


especially


Germany


. Eysenck,


1987)


and


represents


a large


degree


a return


the


ideas


Sir


Francis


Galton.


The


main


concept


that


intelligence


a biologically


determined


cognitive


ability


. The


experimental


work


supportive


this


notion


indicated


substantive


correlations


between


scores


reaction


times.


was


also


observed


that,


when


the


number


of choices


the


amount


of information)


increases


a multiple











intelligence


resulted


in several


similar


models


being


proposed


(Eysenck,


1987;


Jensen,


1982;


Vernon,


1987).


Thus,


Vernon


the


"neural-efficiency"


model


(Vernon,


1987,


assumed


that


brain


or short-term


or working


memory


has


limited


capacity


to store


process


information.


addition,


there


are


processes


of decay


of information


absence


of rehearsal.


speediness


these


easy


circumstances


understand

. In the m


the


odel


advantage

put


forward


Eysenck


(1967,


1987)


he asserts


that


there


are


three


components


to the


concept


of IQ:


mental


speed,


persistence/ and


error


checking,


first


one


being


more


fundamental


accounting


individual


differences


intelligence


(Eysenck,


1967


Eysenck,


1987,


27).


The


first


factor


supposed


to be biological


while


the


other


two


are


personality


factors.


A similar


approach


was


adopted


Hunt


and


his


colleagues


(e.g.,


Hunt,


1978,


1983).


Studying


individual


differences


long-term


memory


access


they


found


(Hunt,


Davidson,


& Lansman,


1981)


that


reaction


times


from


several


verification


tasks


correlated


with


verbal


ability.


Moreover,


reaction


the


time


reading


measures


and


formed


vocabulary


a factor


measures.


which


Other


was


evidence


related


reviewed


Hunt


(1978)


has


shown


that


encoding


processes


(measured











individual


differences


cognition


are


based


on three


factors:


knowledge,


individual


s ability


manipulate


information


(the


"mechanics


of information


proce


ssing"--


Hunt,


1978,


128) ,


and


strategies.


Verbal


ability


according

Cattell,


Cattell


1987;


Horn,


1978;


Horn

Horn


distinction


Cattell,


(e.g.,


1966),


crystallized


ability


supposedly


determined


to a considerable


degree


make


cultural


inferences,


factors.


draw


Fluid


relations,


intelligence--the


develop


ability


hypotheses--


on the


other


hand,


assumed


to be


essentially


genetically


determined.


Hunt


sugge


sted


that


fluid


intelligence


and


mechanistic


information


processing


show


conceptual


empirical


affinities


which


make


study


of their


relationship


Given


promising


a speed


intelligence,


(Hunt,


1978,


of information


natural


125).


processing


propose


theory


a processing


rate


theory


aging


as has


been


done


Salthouse


(1980,


1985b)


elaborating


on the


ideas


Birren.


The


first


inclination


was


assume


an aging


organism


which


like


the


young


organism


but


slower


than


(Salthouse,


1985b,


296).


However,


this


simplified


view


does


not


take


into


consideration


possibility


of interactions


the


information


processing


system.


In fact,


the


same


chapter











to thi


model,


given


task


memorize


words,


old


people


rehearse


words


more


slowly


than


young


people


rehearse.


There


also


a process


decay


memory


traces


proceeding


the


same


speed


the


young


and


the


old


. Assuming


a slow


enough


rehearsal


rate


older


people,


possible


reach


a point


where


a trace


completely


lost


before


next


rehearsal,


making


strategy


no longer


a viable


option


the


elderly.


A distinction


between


a strong


and


a weak


version


speed


hypothesis


was


made


Cerella,


Poon


Fozard


(1981)


. In


the


strong


form


hypothesis


a single


age-


related


mechanism


the


level


of the


central


nervous


system


slows


down


the


same


extent


mental


processes.


A weaker


version


allows


multiple


mechanisms


which


are


age-


dependent


different


degrees


and


which


affect


different


sets


cognitive


variable


(Salthouse,


1985b).


Finally,


a realistic


model


of cognitive


change


based


the


concept


of processing


rate


should


include


also


adjustments


slowing,


and


as well


adaptations

as other v


which


may


ariabl


happen


such


as a result


as strategy


information


which


may


affect


cognitive


performance


and


may


affected


(Salthouse,


1985b,


. 295


-319)


Alternative


Views


Criticisms











cognitive


changes


aging


have


met


with


various


criticisms.


Sternberg


(1985,


301-304)


argued


against


the


view


that


speed


emphasized


a critical


that


what


aspect


critical


intelligence


is resource


. He


allocation


speed


selection


rather


than


speed


per


se.


Thus,


more


intelligent


persons


tend


to spend


relatively


more


time


than


less


less


intelligent


on lower-order


persons

planning


on higher-order


(Sternberg,


planning


1981).


and


Similarly,


more


intelligent


tend


spend


relatively


more


time


encoding


the


terms


of a problem


(Sternberg,


1977)


and


tend


to spend


more


time


trying


to solve


insight


problems


(Sternberg


& Davidson,


1982)


conditions


of unlimited


time


than


less


intelligent


persons


While


these


other


examples


advanced


Sternberg


highlight


importance


"metacomponent"


intelligent


(Sternberg,


allocation


1985)


dealing


resources,


with


not


issue


clear


that


they


conclusively


show


that


"sheer


speed"


not


important


at all.


when


First,


performing


the


ability


simple


tasks


to respond


such


quickly


as reaction


important


time


perceptual


speed


tasks.


Second,


and


poss


ibly


more


important,


Sternberg


s argument


seems


to confound


two


distinct


issues:


the


speed


answer


issue


and


the


speed


information











individual


faster


than


they


are


executed


a slower


individual.


The


speed


hypothesis


as an explanation


of cognitive


change


with


increased


has


also


been


criti


cized


on the


basis


of the


exceptions


the


phenomenon


of slowing,


on the


basis


of the


existence


of a multitude


of slowing


models


(Botwinick,


1984),


and


also


reason


that


the


opposite


approach


basis


which


on other


tries


to explain


cognitive


changes


changes


makes


speed


more


on the


sense


(e.g


., Arenberg,


1980)


Kausler


a speed


(1982,


mechanism


. 258),

truly u


example,


Universal


then


mentioned


there


that


should


exceptions


to the


phenomenon


of slowing


. There


are,


however,


notable


(1984),


exceptions


reviewing


which


the


were


mentioned


evidence


diff


above.


erent


Botwinick


models


slowing


(additive,


multiplicative,


exponential),


concluded


that


some


functions


may


described


better


models


one


type


while


other


functions


are


best


described


models


different


kind.


This


suggested


the


existence


more


than


one


mechanism


slowing.


Botwinick


maintained


that


this


weaker


form


the


speed


hypothesis


loses


much


value


239).


Also,


Arenberg


(1980)


suggested


that


more


plausible


to consider


speed


a result


of effi


cient


cognitive











Other


authors


tended


to play


down


significance


exceptions


or the


significance


of having


many


possible


models


competing


to explain


data.


Part


these


results


may


prove


not


to be genuine


(Salthouse,


1985b)


. Should


they


stand


scrutiny


of additional


and


more


powerful


tests


still


seems


that


most


them


may


be subsumed


under


the


general


category


automatic


processing


(e.g


lexical


access


a very


well


trained


function).


might


well


the


case


that


automatic


processing,


because


does


not


require


many


information


resources,


qualitatively


different


from


active


processing


(Hasher


& Zachs,


1979;


Salthouse,

unaffected

1985b). In


"consequence


1985b).


aging


addition


view"


automatic


processes


there


(Botwinick,


(Cerella,

no strong


1984,


processing


1985; S

evidence

230) ac


might


althouse,


cording


which


slowing


of behavior


with


a consequence


changes


declines


the


perceptual


and


cognitive


systems


(Salthouse,


1985b,


302).


The


Present


Study


The


present


study


was


conceived


as an investigation


two


main


aspects


speed


hypothesis:


An examination


the


issue


of the


structure


measures


of speed


and


examination,


the


context


of a causal


model,











testing


a longitudinal


study


on memory


and


intelligence


(White


& Cunningham,


1987).


Several


first


order


and


one


or more


second


order


factors


of speed


are


assumed


to subsume


the


intercorrelations


among


scores


on various


tasks


and


tests


which


were


administered


a group


old


and


a group


young


adults.


These


include


reaction


time


and


card


sorting


tasks


as well


as perceptual


speed


tests.


Confirmatory


factor


analyses (

hypotheses


Gorsuch, 1983)

regarding the


were


undertaken


structure


of the


test


the


measures


of speed


and


make


comparisons


between


the


two


groups.


LISREL


(Joreskog


& Sorbom,


1984)


the


maximum


likelihood


estimation


method


(Hayduck,


1988


Mulaik,


1972


were


used


these


analyses.


The


second


part


of the


study


uses


structural


equation


models


(Hertzog,


1987)


order


to evaluate


models


pertinent


to a speed


hypothesis.


these


models


several


independent


variables


such


as age


and


level


of education


are


assumed


affect


fluid


and


crystallized


intelligence


either


directly


or indirectly


through


a speed


factor.


A speed


hypothesis


would


predict


that


most


of the


decline


fluid


intelligence


mediated


through


a decline


speed


. The


inclusion


theoretical


variable


crystallized


intelligence


makes











Again,


LISREL


procedure


were


and

the


maximum


method


likelihood


of choice


estimation


estimation


these


models


with


multiple


indicators.


The


following


chapters


provide


a detailed


literature


review


as well


as a description


of the


methodology,


analyses,


results


and


interpretations.


Chapter


presents


literature


review


the


main


findings


regarding


the


two


general


issues


this


study:


the


dimensionality


measures


of speed


and


explanation


of declines


cognitive


abilities


on the


basis


of declines


speed


information


investigated


processing


the


. Chapter


hypotheses


depicts


examined.


models


A description


sample


of the


tasks


and


procedure


provided


Chapter


Chapter


5 presents


the


main


analyses


and


findings


which


are


later


interpreted


discussed


Chapter


addition,


reader


may


find


Appendices


a general


presentation


variance-covariance


topic


matrices


indices


of fit


on which


as well


analyses


are


based.















CHAPTER


LITERATURE


REVIEW


The


speed


hypothesis


explains


parsimoniously


the


fact


that


behaviors


mediated


the


central


nervous


system,


almost


without


exception,


slow


down


the


aging


organism


and


that


covariances


between


speed


factors


increase


with


age.


Thi


chapter


surveys


the


literature


relevant


the


issue


of change


in the


structure


of speed


measures


with


increased


possibility


. The


that


speed


a general


hypothesis


slowing


makes


mechanism


plausible


evidenced


a general


factor


speed


. The


ques


t after


such


factor


has


been


conducted


on young


mainly


subjects


regressing


scores


and


old


factor


subjects


analyze


' scores


speed


and


other


measures


. The


literature


relevant


to this


reviewed


chapter


. In


addition,


speed


hypothesis


may


explain


changes


intellectual


functioning


with


increased


age.


Given


that


there


are


individual


differences


rates


of age-related


change


and


that


these


changes


have


common


cause


(slowing),


one


can


expect


increased


covariances


on the cc

(Hertzog,


,gnitive

1985,


variable


1987)


influenced


. Moreover,


this


partialling


cause

or parting-out











(Salthouse,


1985b).


The


body


of literature


relevant


these


issues


also


reviewed


here


Cerella


s Approach


Cerella


attempted


answer


question


"How


many


slowing


processes


are


there?"


using


a method


proposed


Salthouse


(cf.


Salthouse,


1985b)


assess


the


impact


age


on reaction


time.


Young


subj ects


' reaction


times


on a given


task


and


older


subjects


' reaction


time


on the


same


task


may


be considered


determine


a point


a two-dimensional


space.


Various


tasks


within


a given


experiment


or across


experiments


determine


a multitude


of points


and


linear


models


relating


young


and


older


subjects


' reaction


times


may


evaluated


as to their


accuracy


in reproducing


points


the


space.


Cerella,


Poon,


and


Williams


(1980)


used


information


processing


conditions


(points


the


two-


dimensional


space)


taken


from


35 studies.


They


found


that


simple


regression


Old=1.36*Young-


accounted


the


variance


subject


data.


Further


refinements


are


possible


based


on a distinction


between


sensorimotor


and


mental


each


tasks.


one


Two


of these


regressions


were


categories.


constructed


The


results


the


indicated


tasks


that


regression


coefficient


sensorimotor


tasks


was


much


lower


than


regression


coefficient


the


mental


tasks--











operating


at a peripheral


level,


and


a second


one


central


level.


These


results


are


basic


agreement


with


Birren's


hypothesis.


In a subsequent


article


Cerella


(1985)


considered


more


general


terms


the


topic


of fitting


models


to points


a two-dimensional


space


relation


the


issue


of how


many


factors


or mechanisms


of slowing


should


postulated


order


to account


the


data.


Instead


using


a one-factor


or a


two-factor


linear


model,


one


can


increase


number


of parameters


or factors


the


model


and


gain


power.


One


can


assume,


example,


a distinct


regression


line


each


experiment


. The


number


parameters


this


case


two


multiplied


the


number


studies.


Conducting


this


kind


of analysis


Cerella


was


able


to predict


the


variance


old


subjects'


scores.


However,


as Cerella


has


shown,


this


result


may


be reproduced


assuming

mental D


that


different


processes


experiments


different


contain


proportions


sensorimotor


and


that


these


processes


slow


with


age


to different


degrees.


Different


proportions,


in addition


to sampling


error,


produce


different


regression


lines.


Cerella


s conclusion


that,


reasons


parsimony,


one


should


adopt


simple


two-


factor


model


involving


one


central


mechanism


of slowing.


Factor


Analytical


Studies











of other


measures


as well.


Given


a multiplicity


of speed


factors,


an assumption


of multiple


slowing


mechanisms


plausible.


regarding


A speed


the


hypothesis


structure


also


of these


enables


factors


some


with


predictions


increased


these


predictions


are


somewhat


different


the


case


a single


slowing


mechanism


than


the


case


of multiple


mechanisms.


Given


that


individuals


slow


down


with


increased


at different


rates


and


given


that


a central


mechanism


slowing


responsible


this


phenomenon


with


increased


age,


several


predictions


are


possible


(Hertzog,


1985


, 1987).


Factor


Similarly,


covariances


may


increased


be expected


factorial


to increase


variances


should


with


age.


result.


More


comprehensive


and/or


higher


order


factors


are


also


more


likely


multiple

variances


appear


slowing

and c


with


increased


mechanisms


ovariances


are

with


age.


on the


at work,

increased


the

age


other


hand,


change

should


rather


nonuniform


across


different


factors--for


example


existent


some


cases


and


others


(Hertzog,


Raskind,


& Cannon,


1986)


one


the


earlier


factor


analytical


studies,


Birren


and Morrison

on 11 tests


(1961)

of WAIS


performed

including,


a principal


component


addition,


analysis


and


education.


A sample


about


subjects,


aged


25-64


was











second


component


associated


positively


with


several


verbal


scores


and


negatively


with


several


performance


scores.


The


performance


tests


associated


with


the


second


component,


especially


the


digit


symbol


subtest,


may


be considered


reflect


speed.


This


analysis,


therefore,


has


demonstrated


the


existence


a pure


speed


factor.


Possible


reasons


this


are


the


fact


that


unrotated


solutions


tend


to produce


bipolar


factors


as well


as the


fact


that


WAIS


a test


that


does


not


emphasize


speed.


Birren,


Riegel,


and


Morrison


(1962)


performed


a study


which


measured


reaction


times


stimuli


of varying


complexity


a group


young


and


a group


of old


subjects.


The


study


used


22 stimuli


conditions


including


tasks


of varying


complexity


as different


as choice


reaction


time


versus


word


association.


In all


cases


subjects


had


press


a button


according


to instructions.


A principal


components


analysis


the


data


demonstrated


the


existence


of a general


speed


factor


old


but


not


the


young


subjects.


The


general


factor


had


high


loadings


on tasks


varying


complexity


and


character


and


explained


variance.


The


existence


of a general


factor


of speed


was


also


examined


Salthouse


(1985b).


Two


studies


conducted











tachistoscopic


tasks.


A second


study


included


same


types


tasks


with


the


exception


of the


perceptual


speed


tasks.


The


median


correlations


were


low


both


cases:


first


and


the


second


study.


The


modest


intercorrelations


suggest


a multitude


of speed


factors,


least


the


young


ages


represented


these


studies.


These


results


highly


should


selected


qualified


samples


however


as those


the


used


observation


Salthouse


that


s studies


are


likely


to be accompanied


restrictions


range


and,


as a result,


reduced


correlations.


White


factor


and


analysis,


:unningham

found a


(1987),


multitude


using


an exploratory


of speed


factors


group


young


and


a group


of old


subj ects


who


were


tested


(among


other


tasks)


on simple


, choice


Sternberg


and


card


sorting


. In


both


groups


card


sorting


was


a separate


factor.


the


young


group


Sternberg


tasks


loaded


on the


same


factor


and


simple


RT and


choi


on another


factor.


The


factorial


structure


was


more


complicated


elderly


subjects.


Most


important,


Sternberg


RT tasks


including


spatial


stimuli


and


Sternberg


RT tasks


including


verbal


stimuli


formed


two


distinct


factors.


A multitude


of speed


factors


was


also


reported











adults.


A two-group


confirmatory


factor


analysis


established


the


existence


of a semantic


memory


access


speed


factor


distinct


single


from


reaction


a choice


time


reaction


factor.


time


Moreover,


factor


this


and


from


factor


showed


similar


pattern


both


age


groups


. The


correlation


between


this


factor


and


the


choice


reaction


time


factor


was


greater


the


old


group


than


young


group.


However


the


semantic


speed


factor


correlated


less


with


simple


RT in


the


older


group.


This


lack


of uniformity


the


behavior


the


matrix


factor


covariances


(excluding


some


kind


selection


effects)


not


consistent


with


the


existence


single


mechanism


of slowing.


an additional


study


to be


reviewed


in some


detail


the


next


section,


Hertzog


press)

measure


found

and


measures


an answer


shee


of speed--a

t measure--t


perceptual

o be highly


speed

correlated


suggesting


the


existence


a second


order


factor


of speed.


Cunningham


and


White


(1983)


analyzed


a battery


tests


including


measures


of fluid


and


crystallized


intelligence


figural


symbolic


perceptual


speed


abilities


group


subjects.


young


The


to 33 years)


confirmatory


and


factor


in a group


analysis


old


indicated


equal


number


of factors


with


a similar


pattern


across


groups.


More


important


present


context,


the











In the


White


and


Cunningham


(1987)


study


factorial


covariances


were


relatively


large


the


young


subjects.


However,


the


different


factor


structure


the


two


age


groups


(see


above)


precludes


a significant


comparison.


Longitudinal


data


collected


over


a period


seven


years


showed


also


increase


the


covariances


between


highly


speeded


tests.


Cunningham,


Smook,


and


Tomer


(1985)


presented


data


based


on 100


older


subjects


who


had


taken


battery


speeded


tests


twice


over


interval


of 7


years.


The


factors


analyzed


this


paper


were


Symbolic


Perceptual


Speed,


Figural


Perceptual


Speed,


Expressional


Fluency


and


Word

based


Fluency.

on tests


Each

from


factor


had


the


three


indicators,


of Factor


most


Referenced


of them

Tests


(Ekstrom,


French,


& Harman,


1976).


A longitudinal


confirmatory


factor


analysis


has


been


performed


using


LISREL.


A model,


restricting


the


factor


loadings


but


not


factor


variances


and


covariances,


was


significantly


better


(p<.o1)


than


a model


that


restricted


both


to be equal


but


only


marginally


.05)


worse


than


a model


that


allowed


both


factor

free.


loadings


The


changes


factor

the m


variances


agnitude


and


covarlances


of factor


to be


covariances


and


intercorrelations


confirmed


the


results


obtained


the


earlier


cross


sectional


analysis


(Cunningham,


1980)


: factor











covariance


Perceptual


between


Speed.


Figural


Another


Perceptual


result


Speed


and


of interest


Symbolic


this


study


refers


to the


magnitude


of stability


coefficients


(correlations


stability


within


coefficients


factors


were


across


occasion)


high


.90) ,


. While


figural


perceptual


speed


had


a relative


stability


.73)


indicating


that


this


variable


interindividual


differences


intraindividual


rate


change


are


maximal.


Tentative


Conclusions


on the


Dimensionality


Slowina


While


Cerella's


approach


produced


one


single


central


factor


slowing,


evidence


suggested


the


factor


analytical


studies


more


congenial


to the


hypothesis


multiple


speed


mechanisms,


other


words


to a weak


form


(Cerella,


Poon,


Fozard,


1981)


of Birren


s hypothesis.


The


reasons


this


discrepancy


need


still


to be explored.


Several


observations


on this


point


seem


pertinent


. It


possible


that


the


regression


method


used


Cerella


and


his


colleagues


not


very


sensitive


the


existence


more


than


one


central


mechanism


of slowing,


especially


when


there


onei


predominant


central


factor,


or when


speed


factors


(processes)


are


represented


different


tasks


comparable


proportions


and/or


change


with


age


to a similar


degree.


the


other


hand


is not


impossible


that


behind


the











higher


order


factor


rather


than


a first


order


factor.


The


magnitude


intercorrelations


among


different


speed


factors


important


judging


the


plausibility


general


(second


order)


speed


factor.


In White


and


Cunningham


s study


the


correlations


were


about


.6 for


young


subjects


and


the


older


subjects.


High


but


"imperfect"


correlations


between


a perceptual


speed


factor


and


a Thurstone


PMA


Answer


Sheet


speed


factor


are


reported


unpublished


Hertzog


results.


press),


In Salthouse


referring


s studies


some


in young


subjects


(1985a)


intercorrelations


between


the


speed


variables


were


relatively


low.


Together


these


findings


suggest

exist,


that


a general


although,


higher


given


order


great


speed


factor


variability


might


of speed


tasks,


abstraction


Slowin'a


difficult


Relation


. Salthouse


Psychometric


, 1985b).


Abilities


Several


groups


of findings


make


a causal


relationship


between


a reduction


speed


a decline


intellectual


functioning


plausible.


First


, as shown


many


cross


sectional


studies,


there


are


positive


correlations


between


measures


1985b).


speed


While


measures


magnitude


of intelligence


of these


(Salthouse,


correlations


generally


very


high,


and


while


there


are


large


differences











Another


of relevant


findings


regards


the


fact


that,


general, a r

intellectual


education


functioning


speed t

. Thus,


:ends


to precede


Schaie


& Stroth


declines

er (1968)


using


sequential


different


cohorts


data

for


found

those


longitudinal


variables


age


(word


changes

fluency


across

and


psychomotor

Subsequent


speed) where

analyses have


response

confirmed


speed

this


was


important.


pattern


(Schaie,


1983)


Some


other


results


come


closer


the


examination


causal


model


of relationships


. Witt


and


Cunningham


(1979),


analyzing


data


from


second


author'


master'


thesis


(Cunningham,


1974;


Cunningham


Birren,


1976) ,


showed


that


pattern


of intercorrelations


between


a highly


speeded


relations


factor


and


two


unspeeded


factors


verbal


and


numerical


consistent


factor


with


from


the


Army


assumption


Alpha


Examination)


of a causal


relationship


between


speeded


factor


an early


time


and


the


unspeeded


factors


at a later


time.


The


subj ects


were


males


and


females


tested


when


they


were


young


and


then


retested


years


later.


The


speeded


factor


time


one


was


highly co

abilities


related


time


(about


two


.65)


whereas


with

each


the

one


verbal

of the


and

two


numerical

abilities


at time


one


was


only


weakly


correlated


(about


.25)


with











The


assumption


a causal


relationship


implies


increased


covariances


between


speed


factors


and


other


factors


of psychometric


intelligence


with


increased


age.


This


between


increase


different


similar


speed


to the


variables


increase


or factors


covariances


which


already


been


discussed.


However,


the


focus


this


section


on the


relationship


between


speed


variables


and


other


intelligence


factors


which


have


no direct


or evident


connection


to speed.


There


are


several


pieces


of evidence


suggesting


that


there


indeed


an increase


covariances


correlations)


with


increased


age.


Birren


(1965)


reported


that


Wechsler


Memory


Scale


the


speed


of writing


digits


young


group


showed


adults


of old


essentially


but


no correlation


a significant


adults.


.01)


correlation


longitudinal


a group


.52)


comparisons


with


Army


Alpha


Examination


(Cunningham


& Birren,


1980)


showed


increased


intercorrelations


between


a highly


speeded


relations


factor


and


a verbal


factor.


The


increase


was


particularly


dramatic--from


independence


to 50%


of the


variance


results


shared


based


the


two


on the


factors.


factor


Other,


system


cross


showed


that


sectional


the


covariances


between


symbolic


perceptual


speed


and


figural


perceptual


speed


on one


hand


fluid


intelligence


on the











were


smaller.


Additional


longitudinal


results


showed


also


increased


covariances


between


these


two


factors


perceptual


speed


and


expressional


fluency


and


word


fluency


factors


(Cunningham,


Smook,


& Tomer,


1985).


The


last


group


of findings


to be reported


this


section


relates


to the


prediction


that,


given


a causal


relationship

relationship


between

between


speed


and


and


fluid


intelligence,


intelligence


should


be weaker


after


controlling


speed.


The


rationale


behind


this


approach


was


presented


Salthouse


(1985b)


. Salthouse


argued


that


the


best


method


to control


statistically


speed


partial


correlation


which


enables


an examination


the


relationship


between


a cognitive


variable


after


removing


speed


related


variance


from


both.


Other


authors,


however


(e.g.,


Horn,


Donaldson,


Engstrom,


1981) ,


argued


that


artificial


remove


variance


from


and


that


part


semipartial)


correlation


that


removes


speed-related


variance


The


only


location


from


cognitive


processes


which


variable


mediates


should


changes


used.


fluid


crystallized


intelligence


one


of the


main


interests


work


Horn


and


his


colleagues


(Horn,


Donaldson,


Engstrom,


1981;


Horn,


1982).


They


tested


three


samples


middle-aged


and


older


adults


aged


20 to 60,


residents











apprehension,


short-term


memory,


encoding


organization,


attentiveness,


concentration,


hypothesis


generation,


speediness,


carefulness


persistence.


The


speed


measures


included


perceptual


speed


measures


(two


measures


symbolic


speed


and


one


measure


of figural


perceptual


speed)


and


also


measures


based


on the


time


spent


providing


(correct


or incorrect)


responses


to items.


Fluid


intelligence


was


measured


using


the


Raven


Progressive


Matri


ces


Test,


a letter


series


test,


a paper


folding


test


one


study


only)


visual


organization.


Crystallized


intelligence


was


measured


with


vocabulary


tasks,


analogies


and


remote


assoc


iations.


Variables


factor


level


were


defined


as simple


unweighted


linear


combinations


of the


relevant


scores.


The


method


of analysis


was


based


on part


correlational


procedures:


the


linear


component


predicted


one


or several


removed


from


process


the


variable


relationship


(e.g.,


between


perceptual


age


speed)


and


intelligence.


If the


process


variable


which


parted-out


mediates


entirely


relationship


between


and


fluid


intelligence,


a nonsignificant


part


correlation


can


expected.


however,


the


part


correlation


different


from


zero


but


significantly


lower


than


bivariate


correlation


between


intelligence,


the


conclusion











intelligence:


was


found


to decline


some


analyses


(Horn,


1982


75 IQ


points


per


decade.


Controlling


perceptual


speed


reduced


this


rate


points.


Interestingly,


speed


to correct


or to incorrect


answer


was


not


found


to have


same


effect.


Thi


kind


of speed


correlated


also


at a low


level


with


the


perceptual


speed.


Horn


indicated


that


relation


between


perceptual


speed


and


fluid


intelligence


might


be mediated


an attentional


factor


of concentration.


This


factor


accounted


a similar


decline


Gf and


also


much


decline


perceptual


speed.


Other


processes


were


also


found


to contribute


to the


decline


Gf--the


ability


to eliminate


irrelevancies


concept


attainment,


and


also


processes


involved


hypothesis


formation.


similar


finding


was


obtained


Hertzog


press)


using


tests


from


the


Educational


Testing


Services


Reference


and


Thurstone


Thurstone


Primary


Mental


Abilities


(PMA)


test


a group


of older


adults,


ranging


in age


from


through


years.


The


speed


factors


included


were


Perceptual


test


Besides


Speed


figural

speed,


(based


on two


perceptual


the


tests


speed)


psychometric


and


batter


of symbolic


and


Answer-Sheet

y provided m


one


Speed.


multiple


measures


Verbal


Comprehension,


Inductive


Reasoning,










variables


re-standardization.


The


two


measures


of speed


correlated


highly


with


each


other


supporting


the


existence


a higher


order


factor


speed.


Regression


analyses


have


been


conducted


variables


and


using

speed


ability

factor


factor


scores


scores


as dependent


as independent


variables.


Age


(and


age


squared)


have


been


entered


a second


step,


sex

the


a third,


regression


and


interactions


analysis.


Both


the


Perceptual


last


two


Speed


steps


and


Answer


Sheet


ability


Speed


predicted


factor.


Although


significantly


and


adding


independently


the


speed


the


predictors


resulted


a significant


improvements


magnitudes


of this


improvements


were


minimal.


Of special


interest


are


the


results


Induction.


unadjusted


age


differences


(based


on the


regression


analysis)


Induction


were


about


standard


deviation


from


age


Adjusted


speed,


the


age


differences


were


only


half


a standard


deviation.


Numerical


Facility


and


Verbal


Comprehension


showed


when


levelling

consistent


adjusted


off


with


old

the


for sp

age. I

results


eed


a positive


n general

obtained


age


these


Horn


gradient


results


and


are


his


colleagues.


A detailed


comparison


difficult


because


methodological


differences


between


two


studies


. It


seems,


however,


that


the


relationship


remaining


between











The


results


are


interpreted


Hertzog


as supportive


general


position


that


cognitive


slowing


associated


with


declines


of intellectual


abilities.


However,


independent


contribution


of the


speed


factors


the


variance


cognitive


variables


suggests


that


more


than


one


mechanism


of slowing


involved.


Hertzog


also


mentions


unpublished


factor


analytical


work


showing


that


while


Answer


Sheet


factor


correlated


highly


with


Perceptual


Speed


factor


these


two


factors


had


different


pattern


correlations

strengthens


with

the c


other


onclusi


cognitiv

on that


abilities.


multiple


This


processing


finding

g speed


factors


are


involved


an explanation


of slowing.


Schaie


press)


analyzed


cross-sectional


and


longitudinal


data


from


Seattle


Longitudinal


Study


with


respect


primary


to Perceptual


mental


Speed


abilities:


and


Verbal


relationship


Meaning,


the


Spatial


Orientation,


Inductive


Reasoning


, Number


and


Word


Fluency.


The


subjects


included


two


large


samples


more


than


1600


adults.


Longitudinal


data


were


available


over


adults


from


first


sample.


The


ages


represented


were


to 91.


Perceptual


speed


was


measured


using


two


indicators:


Identical


Pictures


test


and


Finding


test.


Partial


correlations


between


age


and


the


five


abilities


were











reduced


also


the


correlations


but


to a lesser


extent.


additional


analysis


the


author


examined


the


behavior


residuals


abilities


after


regressing


them


on speed.


the


case


Inductive


Reasoning


the


trend


of decline


with


age


which


had


been


found


with


usual


measure


of Inductive


Reasoning


was


found


with


residualized


measures


but


reduced


degree.


Moreover,


this


trend


of reduced


decline


with


was


apparent


both


longitudinal


and


the


cross-


sectional


analysis.


An examination


of the


figure


presented


author


shows


that


the


range


about


to 80


years


the


longitudinal


the


cross-sectional


curves


are


virtually


identical


show


almost


no decline.


Schaie


interpreted


Salthouse's


data


slowing


as providing


of processing


"limited


speed


support"


model.


Stankov


(1988)


has


examined


relationship


between


fluid


and


crystallized


intelligence


and


attentional


abilities


a group


subj ects


aged


One


attentional


factors


Perceptual/Clerical


Speed


this


with


study


salient


was


Search


loadings


from


Number


Comparison,


Letter


Comparison,


And


Search


Time


tests.


Other


attentional


Flexibility.


factors

author f


were


ound


Concentration

a correlation


and


of -.31


Attentional


between


fluid


intelligence,


indicating


a loss


of about











particular,


parting-out


Search


reduced


the


correlation


from


-.31


-.08


decline


-.08


points


per


decade).


even


greater


effect


was


obtained


when


Flexibility


was


parted-out.


Parting-out


three


attentional


factors


to a positive


relationship


between


age


and


The


results


obtained


using


same


technique


examine


the


relationship


between


and


crystallized


intelligence


showed


of about


a different


.7 IQ


trend.


points


Gc evidenced


of crystallized


an increase


intelligence


with


per


decade

Search


which

and C


increased


to 3


concentration


anm


.6 and

d to 4


.7 after

after p


parting-out


arting-out


Flexibility

indicating


. These


that


results


changes


are


interpreted


in attentional


Stankov


processes


mediate


changes


in fluid


and


crystallized


intelligence.


Salthouse


(1985b)


examined


the


relationship


between


age,


speed,


perceptual-spatial


abilities.


Two


tasks


were


selected


this


purpose:


the


Gestalt


Closure


Test


from


a task


involving


the


identification


of computer-


generated


incomplete


figures.


In both


cases


subject


had


to identify


the


object


represented


a distorting


drawing.


Two


groups


and


point-biserial


correlations


were


used.


Speed


was


measured


a digit


symbol


substitution


test


. The


findings


showed


no major


reduction


magnitude


the











indicating


that


closure


ability


dependent


on speed


but


an independent


correlate


(Salthouse,


51).


Soeed


and


Memory


Abilities


As is


case


with


psychometric


abilities,


the


speed


hypothesis


predicts


that


controlling


speed


should


reduce


substantially


correlation


between


age


and


memory.


the


same


time,


controlling


should


affect


much


the


correlation


between


speed


and


memory


performance.


Salthouse


(1985)


reviewed


relevant


research


regarding


these


predictions


providing


also


data


from


a number


of studies


performed


own


laboratory


. Salthouse'


work


was


based


on samples


of 16


young


adults


aged


to 30 and


comparable


numbers


of older


adults


aged


to 84. The


digit


symbol


substitution


test,


a reasonable


indicator


of symbolic


perceptual


speed,


served


as the


speed


measure.


Different


memory


tasks


were


used:


digit


span,


letter


span,


dual


span


(including


both


digits


and


consonants),


supra


span


(involving


the


pre


sentation


seven


pairs


of letters


and


seven


pairs


digits


several


trials),


free


recall,


paired


associates


and


spatial


recall.


The


analysis


based


on a comparison


the


correlations


between


age


and


performance

correlations


on the

between


various

n the s


tasks


ame


with


variables


partial


after


partialling











The


results


showed


that,


general,


the


span


measures


are


consistent


consistent


Morrison


with


(1961)


with


similar


and


predictions.


findings


Goldfarb


These


obtained


(1941).


The


results


Birren


are


and


results


regarding


free


recall


were


less


convincing,


possibly


because


increased


importance


of strategies


mediation


this


task.


The


spatial


recall


performance


the


paired


associate


performance


were


inconsistent


with


the


processing


rate


hypothesis.


Salthouse


attempted


to explain


the


first


inconsistency


on the


basis


the


assumption


that


spatial


recall


a pass


task


whereas


measure


speed


(digit


symbol)


a measure


active


processing.


satisfactory


explanation


was


found


second


inconsistency.


The


fact


that


age


still


accounted


substantial

performance


part

after


the


variance


controlling


the


speed


paired

(about


ociate

versus


about


the


zero


order


correlation)


but


only


much


lower


percentages


the


span


measures


was


attributed


Salthouse


relative


complexity


first


versus


the


simplicity


the


latter.


In free


recall


strategies


mediation,


elaboration


and


organization


may


play


important


role


and


may


overshadow


some


extent


the


effects


of speed.


This


interpretation


fits


the


rate


processing


model











section.


They


included


measures


of primary


memory,


secondary


memory,


free


recall


and


incidental


memory.


In general


these


measures


behaved


as predicted


the


speed


hypothesis.


Alternative


Interpretations


The


findings


reviewed


here,


while


supporting


general


a speed


hypothesis


(especially


the


area


of fluid


intelligence),


possible


do not

to view


exclude


alternative


a reduction


spee


interpretations.

d as a consequence


rather


than


as a cause


of cognitive


changes


(e.g


Botwinick,


1984;


Salthouse,


1985a,


1985b).


Cognitive


factors


that


are


frequently


mentioned


this


context


are


strategy


changes,


differential


motivations


and


age


differences


familiarity


with


tasks


(Salthouse,


1985b).


While


this


kind


hypothesis


between


can


a reduction


account


positive


speed


a decline


correlations


intelligence,


cannot


easily


account


the


large


reductions


the


correlations


between


and


intelligence


after


controlling


for

one


speed.

should


Moreover,

be able t


make


:o provide


such


an hypothesis


evidence


showing


plausible

a drastic


reduction


the


correlation


between


age


and


intelligence


after


controlling


for,


say,


strategy.


However


studi


this


topic


are


lacking


(Salthouse,


1985a,


1985b)


Another


possible


interpretation


begins


with


the











confound


of two


phenomena:


chronological


time


and


cohort.


Accordingly,


possible


that


the


relationship


age--fluid


intelligence


reflected


the


first


place


mainly


cohort


differences


which


were


reduced


after


controlling


speed


because


a possible


relationship


between


speed


and


cohort.


Semipartial


correlations


equivalent


statistics)


which


have


been


often


used


these


studies


seem


particularly


susceptible


this


criticism.


The


reason


that


(the


square


a semipartial


correlation


this


context


represents


proportion


of variance


in Gf


accounted


beyond


that


accounted


speed


this


necessity


Gf without

necessarily


smaller


the

the


than


statistical


case


the


proportion


control


partial


accounted


of speed.


correlations


This

(or


age


path


coefficients)


partialled


from


are


from


both


used.


age,


and


In this


only


still


latter


from


leaves


case


speed


. Partialling


substantial


speed


portions


variance


unaccounted


and


one


can


expect,


given


that


cohort


explanation


correlation


should


true,


obtain.


that a

In other


substantial


words


(partial)


an explanation


based


exclusively


on cohort


differences


seems


unlikely


partial


correlation


between


small.


It is


also


possible


to consider


the


lationship











problems


may


determined


a test


that


measures


how


fast


one


can


solve


simple


problems.


According


to this


argument,


speed


of processing


information


may


be not


a good


predictor


of the


may


ability

a good


relatively


solve


very


predictor


trivial


difficult


the


problems.


problems


intelligence


Such


an argument


shown


may


although


solving


rely


Horn


s finding


that


speed


to correct


answer


a poor


predictor


of ability


level


(Horn,


1981,


1985)


and


that


part


of the


psychometric


tests


are


of low


difficulty


. However,


some


tests


contain


items


of increasing


difficulty


to high


levels


difficulty.


As Cunningham


(1987)


indicated,


what


stops


subjects


timed


tests


of this


nature


the


difficulty


of the


items


rather


than


time


itself.


These


later


items


place


greater


information


processing


demands


on the


person


attempting


them


and,


as a result,


success


on them


more


likely


at increased


speeds


information


processing


(Vernon,


1987).


Some


empirical


results


confirm


this


interpretation:


The


correlations


of RTs


with


untimed


scores


have


been


shown


(with


exception


of performance


tests)


to be


of a similar


magnitude


as the


correlations


RTs


with


timed


scores


(Vernon,


1987;


Vernon,


Nador,


Kantor,


relevant


1985;


Vernon


research


may


& Kantor,


be criti


1986)


cized


. While


part


Sternberg,


the


1986) ,


the











intelligence:


tests


may


emphasize


speed


too


much


and,


as a


result,


may


penalize


older


subj ects


(Lorge,


1936;


Cunningham,


1989).


seems


that


Cunningham'


counterargument


holds


this


case


as well.


The


empirical


evidence


on this


point


rather


scant.


Hertzog


press)


obtained


an interaction


between


age


and


Answer


Sheet


Speed


analyzing


PMA


Verbal


Meaning


subtest


indicating


that


the


speed


marking


the


answer


sheets


become


increasingly


more


important


with


increased


age


determining


the


score.


However


such


an interaction


was


found


other


and


subtests.


Also,


as Hertz


remarks,


the


invariance


number


and


pattern


of intellectual


factors


across


adult


ages


(Cunningham,


1981,


Hertzog


& Schaie,


1986)


rather


inconsistent


with


this


type


of interaction.


Another


possibility


that


both


speed


of information


processing


cognitive


abilities,


such


as fluid


intelligence,


decline


with


increased


age


because


both


are


influenced


the


same


age-related


mechanism.


A candidate


this


attention


(Horn,


1982,


1985;


Horn


et al.,


1981).


Some


other


findings


are


rather


inconsi


stent


with


such


possibility.


(1983)


Cornelius,


performed


Willis,


a confirmatory


Nessellroade,


factor


and


analysis


Baltes


on data


obtained


from


a group


older


people.


The


analysis


was











variables


have


been


measured


using


tests.


Other


tests


measured


attention


attention

attention


factors:

switchin


decoding

g and co


processes,


ncentration.


selective

The


loadings


were


fixed


the


ability


factors


the


levels


indicated


a previous


analysis


while


the


attention


variables


were


allowed


load


freely


on these


four


factors.


The


expectation


was


that


they


will


load


mainly


on fluid


intelligence


on short


term


acquisition-retrieval.


However,


three


of the


four


attentional


factors


loaded


highly


on the


perceptual


speed


factor.


The


authors


interpreted


these


findings


as showing


that


changes


in attention


with


age


occur


independently


of changes


fluid


intelligence,


crystallized


intelligence


or memory.


Finally,


the


results


reviewed


this


chapter


are


compatible


with


more


complex


models


relating


age,


speed


information


processing


and


additional


variables.


The


additional


variables


complexity


(age,


may


etc.)


be at


allowing


level


variables


of the


other


independent


than


per


se to affect


Birren


s notion


speed


of information


of a secondary


processing.


factor


reflecting


An example


disease


processes


(Birren,


1965)


. Also


variables


reflecting


strategy,


motivation,


adjustments,


etc.


may


affect


and/or


mediate


the


relationship


between


speed


and


cognitive











considered


more


comprehensive


models.


Indeed


one


should


explain


why,


example,


there


are


declines


fluid


intelligence


corresponding


to reductions


speed


but


apparently


there


are


no analogous


declines


crystallized


intelligence


with


(e.g. ,


Horn


al.,


1981).


Finally,


even


an influence


of cognitive


declines


on speed


information


processing,


possibly


via


additional


variables


such


as depression,


not


incompatible


with


the


claim


that


main


path


of causality


goes


the


opposite


direction.


Obviously


the


scientific


community


still


away


from


being


able


to construct


evaluate


properly


complex


models


this


type.


Summarv


The


studies


reviewed


this


chapter


allow


several


tentative


conclusions


regard


to the


two


main


issues


discussed


: the


dimensionality


of the


speed


measures


relation


plausibility


an explanation


cognitive


change


based


on a reduction


the


speed


processing


information.


Most


speed


the


measures


evidence


(e.g.,


favors


White


a multidimensional


Cunningham,


view


1987).


addition,

measures


while


the


covariances


factor


level


between


typically


different

increase w


speed


ith











multidimensionality


of speed


measures


and


lack


homogeneity


the


rate


change


with


suggest


the


existence


of multiple


mechanisms


of slowing


possibly


mediating


relationship


age


with


other


cognitive


variables


(Hertzog,


press).


. Other


evidence,


however,


favors


a more


parsimonious


view.


Cerella


s results,


particular,


are


consistent


with


existence


one


central


mechanism


slowing


addition


to a peripheral


mechanism


explaining


slowing


at the


input-output


level).


Cerella


s results


may


conceivably


reconciled


with


other


results


obtained


with


factor


analytical


procedure


at a higher


level


of analysis:


possible


that


a higher


order


factor


of speed


represents


captures


the


central


mechanism


of speed.


Although


difficult


from


the


perspective


one


higher


order


factor


interpret


nonuniform


changes


in factorial


covariances


those


obtained


Hertzog,


parsimony


considerations


require


examination


the


possibility


that


higher


order


speed


factors


are


better


measures


of information


processing.


There


of the


evidence


intercorrelations


(most


between


of it


age,


based


speed


on the


and


analysis


cognitive


abilities)


suggesting


that


a reduction


in speed


processing


information


mediates


the


decline


cognitive











relationship


are


possible.


In particular,


arguable


that


other


factors


than


speed,


possibly


attentional


factors,


explain


both


the


decline


speed


and


the


change


cognitive


abilities


with


increased


age


(Horn,


1982;


Horn


al.,


1981).















CHAPTER
PROPOSED


MODELS


The


approach


described


a general


way


the


introductory


chapter


is a two-stage


approach.


the


first


stage


the


factorial


structure


the


speed


measures


considered.


Of particular


importance


in this


stage


is the


stence


of a higher


order


speed


factor


. The


prediction


based


on the


speed


hypothesis


of increased


covariances


with


increased


may


be examined


the


level


of first


order


factors


and


also


the


level


of second


order


factors.


In the


second


stage


a model


based


on the


speed


hypothes


and


on the


theory


of crystallized


and


fluid


intelligence


(Cattell,


1987)


examined.


A basic


question


addressed


part


whether


a model


that


assumes


that


speed


mediates


intelligence


the


and


relationship


that


fluid


between


intelligence


fluid


mediates


relationship


between


speed


crystalli


intelligence


fits


the


data


reasonably


well


. Given


that


further


important


question


refers


to the


magnitude


path


relating


processing


age


rate


directly


theory


to fluid


as well


intelligence.


as empirical


The


findings


suggest











bulk


the


influence


age


on fluid


intelligence


passes


through


a speed


variable.


Figure


depicts


the


model


defining


five


first


order


factors


speed


: Symbolic


Perceptual


Speed


(SPS),


Figural


Perceptual


Speed


(FPS),


Choice


Reaction


Time


(CRT),


Sternberg


Reaction


Time


(STRT),


and


Card


Sorting


(CS).


Four


factors


have


three


indicators


each.


Sternberg


Reaction


Time


has


four


indicators


. The


tests


on which


these


indicators


are


based


are


described


Chapter


The


model


assumes


a simple


structure

loading f


: each


ixed


variable


zero


loads


on the


on one


other


factor


factors.


and

This


model


suggested


the


previous


analyses


of these


data


(Cunningham


& White,


1983;


White


& Cunningham,


1987).


Confirmatory


factor


analyses


using


LISREL


(Joreskog


& Sorbom,


1984)


can


be conducted


both


groups


order


to estimate


free


parameters


of the


model


(factor


loadings,


specific


variances


corresponding


the


error


terms


of each


observed


variable,


correlations


between


factors)


as well


as to obtain


an evaluation


correlations


the


or covariances


model


between


to the


the


data


observed


(matrix


variables)


on which


model


based


. Correlation


matrices


are


used


input


and


the


scale


the


latent


variables


(factors)


established


fixing


variances


the


factors


to unity











44





Ct 0

H 0



-4 *~
I a r



, (0 PC
00 )

c I 0
r .C VO
^ PU #




S C 0 C-

*H ..C O
I IIH
H C E- 0 r-
P 040 1 'a
**n 0
) C U3
>-lQ .4 C

C oQC 0
*HM r-4 -l


C0 I S

00 CO 0 0
r- ** 9t-4

0) S
03 0)0
0)a 0

DQ ) fO O

0 I 5P0 4
S04 0I 0


000I I *
kW UI P -
n.-dir


















e -s
c
fO 4


II


P S
a) n3
we


I I0 a
IU O


WIU
0 0
W041)
- I*

UCO
C #CM
* <0 C
~0E.4.r4

WH40
T3C 0 Vt
*r4'OC
(H 0 V
II I
I I rBl
11r40
4 c 0
40 I
Wv *- r


>Q *O C
O) C E^r 0


'CO
00 13
.0 r't0)
-r^ n r-^


C< I e
POI
C 03I 04
tU MI
> *. r U








0~0
S4J W )
'too




fP r-1
0 I U2 r4Q4


C I f -P



M i
4.4) 0)idE



MI -^ Q>
0 IJJW


^ C PI PI
CI ) 0 I
































II
IS6


a

.I 04
I





I 0)

U O
CQ &

0 0 C


SI I P1
> 0 E-H*.


I I k
I II






. I.E-1 H
OC ** .











a)
.0 C 0





IO I

r E-* .


S4 O 0 I




S** 0 04
4-lW I(0




-> -- 3
-H -*(
CI V1 I;











program.


The


LISREL


program


supplies


a Chi-square


statistic


which

model


can


be used


to the


data


as a test

(Hayduck,


the


1988;


correspondence


Joreskog


& Sorbom


of the

, 1984).


This


Chi-square


may


be also


related


to the


degrees


freedom


the


model


to obtain


an index


of goodness-of-fit


and


other


indices


of goodness


are


provided


the


program


or may


be computed


(see


Appendix


Moreover,


possible


to perform


simultaneous


confirmatory


factor


analyses


both


groups


test


the


hypothesis


increased


covariances


the


older


subjects.


This


hypothesis


may


be considered


versus


a null


hypothesis


of equal


variances-covariances.


more


general


terms,


models


with


constraints


on their


parameters


across


the


two


groups


may


be compared


with


models


without


or part


these


constraints.


Previous


anal


yses


this


kind


(Cunningham,


Smook,


& Tomer,


1985)


have


shown


that


very


restricted


model


which


assumes


equality


of factor


loadings,


as well


as equality


of factor


variances-covariances


and


equality


specificities


the


observed


variables


across


two


groups


does


not


data


well.


Moreover,


such


model


may


be improved


relaxing


some


constraints.


Thus,


a model


which


does


assume


equality


specificities


may


be expected


to fit


data


better.











Chi-squares


This


reported


difference


the


itself


LISREL


program


a Chi-square


as a statistic.


distribution


with


number


of degrees


of freedom


equal


the


difference


between


number


of degrees


freedom


of the


compared


models.


repeating


this


operation


a series


of models


nested


one


within


another


obtained.


According


to previous


results


is expected


that


a model


may


be sequentially


improved


relaxing


first


the


constraint


on specificities


and


next


the


constraint


on equality


of variances-covariances.


No further


significant


improvement


expected


as a result


of relaxing


the


constraint


on factor


loadings.


The


comparative


analyses


are


based


on variance-covariance


matrices


which


have


been


rescaled


using


the


pooled


mean


variances


age


groups


(Cunningham,


1978).


Figure


depicts


a model


based


on a second


order


factor


of speed.


In this


simple


model


the


second


order


factor


explains


intercorrelations


covariances)


between


the


first


order


factors.


In the


LISREL


notation


second


order


factor


an exogenous,


variable


determining


first


order


factors


which


are


endogenous


Eta


variables.


One


path


coefficients


from


the


second


order


factor


to the


first


order


factors


fixed


one


order


to determine


the


scale


the


second


order


factor.











Speed


than


to other


factors


and


Choice


Reaction


Time


more


similar


to Sternberg


Reaction


Time


than


to other


factors.


possible


conceive


a model


where


there


a second


order


factor


explaining


only


part


of the


relationships


between


factors.


In this


more


complicated


model


there


are


specific


intercorrelations


between


the


residual


terms


"similar"


factors:


between


Figural


and


Symbolic


Perceptual


Speed


and


between


Choice


RT and


Sternberg


Formally,


this


model


equivalent


to a model


postulating


three


second


order


factors


(Figure


3-3) .


A second


order


factor--


Perceptual


Speed--has


as corresponding


first


order


factors


Figural


Perceptual


Speed


and


Symbolic


Perceptual


Speed.


Another


second


order


factor


correspond


to Choice


Rt and


Sternberg


as first


order


factors.


Finally,


this


case


the


"second


order"


factor--Card


Sorting


identical


with


the


first


order


factor.


In this


model


three


second


order


factors


"explain"


the


correlations


between


the


first


order


factors


and


the


off-diagonal


covariances


between


the


residuals


(specificities)


the


first


order


factors


are


zero


the


matrix.


A second


order


factor


model


may


considered


nested


a first


order


factor


model


therefore


can


be evaluated


relation


to it


the


usual


way.


Moreover,


the


first,


more











factors


are


correlated.


The


model


with


three


second


order


factors,


being


equivalent


to the


less


restricted


model


with


one


second


order


factor,


may


not


be considered


explanation


of this


latter


model


and


cannot


be validated


the


usual


way


showing


that


fits


the


data


as well


the


single-factor


model.


However,


this


model


presents


some


interest


since


allows


use


of alternative


latent


variables


speed


path


models.


The


basic


path


models


relating


to fluid


intelligence


(Gf)


and


cry


stallized


intelligence


are


illustrated


Figures


3-4,


3-5.


They


may


be described


terms


the


model


of their


paths


components:


between


referring


the


latent


to the


structural


variables


relationships


model


the


between


referring


measurement


the


latent


variables


the


observed


variable


(Joreskog


& Sorbom,


1984).


the


model


depicted


Figure


(omitting


measurement


model)


and


education


are


independent,


exogenous


variables.


Gf and


variables.


Speed


mediates


education


are


Speed,


mediates


the


allowed


and


the


are


relationship


relationship


to relate


to GC.


to all


endogenous


between


In addition


three


latent


and


, age


latent


variables.


In a slightly


more


complicated


model


presented


Figure


(omitting


again


measurement


model)











51











U)

a H
|0 --------0 0 j
*rI






01

0
a4



*r4

4ir

/ I ( / \
0)



0)


C
0


0)




f Y/ \
^*r


ti
3
its
0












52





II)
0
0
Cn
0

0)
f \Jo \ S
0 In


ICI
0)
'C
a)


*In


C)





en
l (A

(U
'C
01
-H
4,
IC



a)



a)











with


subjective


health


of particular


importance


older


subjects.


The


two


basic


path


models


are


constructed


on the


basis


the


speed


hypothesis.


particular


interest,


explained


above,


is the


path


from


to Gf.


According


speed


hypothesis


this


path


should


be of modest


magnitude


such


that


most


of the


effect


to Gf


pas


ses


through


latent


variable


of speed.


A strong


version


speed


hypothesis


will


predict


fact


that


this


path


not


significantly


different


from


zero.


The


LISREL


program


provides


t-values


estimated


parameters


which


allows


us to confirm


or disconfirm


this


prediction.


An equivalent


formulation


the


strong


prediction


the


following:


The


nested


model


obtained


fixing


path


coefficient


path


age--Gf


zero


not


significantly


worse


then


the


more

speed


relaxed


model.


hypothesis


A somewhat


allows


for


weaker


a significant


interpretation


path


of the


coefficient


path


from


to Gf but


requires


that


most


of the


effect


age


on Gf will


through


mediation


one


more


speed


variables


measuring


speed


mechanisms.


The


latent


variable


of speed


these


models


may


any


first


order


speed


factors


or second


order


speed


factors


obtained


the


confirmatory


factor


analysis.


also


possible











The


models


also


integrate


elements


of the


theory


fluid


which


and


crystallized


predicts


intelligence


a relationship


between


(e.g.,


the


Cattell,


two


1987)


forms


intelligence


as well


as a causal


influence


from


education


crystallized


intelligence.


can


be expected


fact


that


the


effect


of education


on Gc is


larger


than


the


effect


The


paths


from


education


Gc and


were


allowed


be estimated


on speed


the


program.


information


process


A possible


sing


impact


suggested


of education


some


findings


(Botwinick


& Storandt,


1974),


and


this


path


coefficient


also


estimated


these


models.


One


the


two


basic


models


includes


health


based


self


assessment


as an exogenous


variable


(subjective


health).


There


evidence


indicating


that


impaired


health,


as indicated


cardiovascular


disorder


related


to slower


reaction


times


(Birren,


Wood


& Williams,


1980).


Since


subjective


health


was


found


to be a valid


predictor


mortality

Shapiro,

variable


health


(LaRue,

1982), w

in these


and


Banks,


re can

model


intellectual


Jarvik,


expect


. Although


Hetland


to affect


the


functioning


1979;


the


Mossey


speed


relationship


yet


clear,


between


there


evidence


suggesting


that


physical


health


predictive


maintenance


of intellectual


functioning


(Schaie


& Hertzog,











In LISREL'


terminology


path


coefficients


going


from


exogenous


the


endogenous


variables


are


included


the


Gamma


matrix.


The


Beta


matrix


includes


relationships


among


endogenous


variables.


these


terms


Gamma


matrix


was


specified


to be


free


and


allowed


to be


estimated


. In


Beta


matrix


were


estimated


the


paths


from


speed


to Gf


and


from


Gf to Gc.


Other


coefficients


were


fixed


this


matrix


zero.


error

between


The


terms.

n these


endogenous

To obtain

residuals


variables

identified

should be


also

model


fixed


have

s the

to z


residuals


covariances


ero.


In LISREL


this


done


using


matrix


which


includes


the


variances-covariances


of these


residuals.


Accordingly,


diagonal


elements


this


matrix


were


fixed


zero.


The


diagonal


elements


representing


residual


variances


were


allowed


to be


estimated.


The


structural


models


with


second


order


factors


speed


are


somewhat


more


complicated.


A second


order


factor--


itself


an endogenous,


variable--is


related


to Gf,


Gc and


to the


exogenous


variables


the


same


way


a first


order


factor


related.


However,


addition,


this


factor


determines


first


order


factors


speed


. The


paths


from


second


order


factor


to the


first


order


factors


are


represented


Beta


matrix.


The


residuals


of the


first


off-











the


level


of the


measurement


model


the


path


models


several


comments


are


necessary.


Age,


education


subjective


health


are


measured


on the


basis


of self


report


and


are


considered


be measured


without


error.


The


relationships


between


the


exogenous


latent


variables


and


their


indicators


are


expressed


the


Lambda


X matrix


variances-covariances


of the


residuals


the


exogenous


variables


latent


Theta


variables


Delta


are


matrix.


"identical"


our


with


case


the


in which


observed


variables


the


identity


realized


fixing


unit


diagonal


Lambda


X matrix


and


fixing


zero


elements


of the


Theta


Delta


matrix.


Multiple


indicators,


especially


case


of subjective


health


would


have


been


preferable.


However,


there


evidence


that


a single


self-


report


item


like


one


used


the


Memory


and


Intelligence


study


see


Chapter


has


good


validity


and


reliability


Mossey


& Shapiro,


1982


The


endogenous


variables


each


have


several


indicators.


The


relationships


between


these


indicators


endogenous


latent


variables


are


represented


the


Lambda


matrix.


The


observed


matrices


have


also


"specificities"


"whose"


variances-covariances


form


Theta


Epsilon


matrix.


measured


four


indicators,


and


Gc is


measured











Chapter


The


indicators


speed


(three


or four)


vary


according


the


speed


factor


used


the


model


are


also


well-established


measures.


A description


of them


provided


Chapter


The


indicators


speed


a first


order


factor)


allowed


Lambda


fixed


latent


and


fluid


to load


Y matrix


to unity


variables


and


freely


with


order


(Joreskog


crystallized


on the


appropriate


exception


to determine


& Sorbom,


intelligence


factors


loading


metrics


one


the


1984).


All


are


the


which


the


other


loadings


are


fixed


zero.


The


variances


the


specificities


the


observed


variables


are


estimated


assuming


that


the


specificities


are


intercorrelated.


The


Theta Epsilon

program. The


matrix


covariances


therefore

between


diagonal


these


and


free.


residuals


Theta


Epsilon


matrix


were


fixed


zero.


cases


where


a second


order


factor


was


used


this


factor


corresponds


to a column


zeros


the


Lambda


matrix


while


first


order


factors


correspond


to columns


defined


way


explained


above.


The


path


models


were


applied


to the


two


age


groups


However,


since


almost


no variability


subjective


health


was


found


among


young


subjects,


model


including


subjective


health


were


estimated


only


old


subjects.















CHAPTER 4
METHOD


Subi ects


The


subjects


were


young


adults


aged


old


subjects


aged


73 which


have


been


tested


the


Intelligence


Memory


study


(White


& Cunningham,


1987)


. Both


young


and


the


old


subjects


were


residents


Gainesville


area


who


responded


advertisements


local


newspapers


and


were


paid


their


partic


ipation


study


. Four


subjects,


three


young


and


one


old


with


ssing


data


on two


or more


variables


corresponding


given


factor


were


deleted


. For


eight


other


subjects


with


ssing


data,


corresponding


means


groups


have


been


used


. The


analyses


reported


here


are


based


on 147


young


subjects


(Mean


age=


24.9


SD=4


and


old


subjects


(Mean


age=65


SD=4


. The


young


group


included


69 mal


females


. The


group


include


50 mal


and


females.


The


young


subjects


had


a mean


education


15.3


years


school


SD=3


. Eighty


four


of them


.1%)


were


students


. Those


of them


who


were


attending


school


were


general


younger


than


the


others--the


average


was


about











(SD=3


.4) .


21 of them


.1%)


were


still


studying.


The


subjective


from


health


the


(excellent)


subjects


(poor).


was


The


evaluated


mean


on a scale


subjective


health


the


young


subjects


was


1.64


(SD=. 54)


while


corresponding


mean


older


subjects


was


(SD=.73).


difference


not


significant.


Subjects


were


asked


report


various


subjects


cardiovascular


reported


problems.


hypertension


About


versus


of the


of the


younger


older


subjects


who


reported


These


results


are


close


the


incidence


this


condition


the


general


population


U.S.,


1981


respective


groups:


the


age


category


to 44 and


37.9%


the


age


category


. Bureau


of the


Census,


1984).


Other


cardiovascular


conditions

respective


are

ages


also


typical


: less


than


the

(one


general ;

subject)


populationn


had


of the


a stroke,


no one


had


a heart


attack


about


suffered


from


angina.


The


corresponding


rounded


percentages


the


old


subj ects


are:


strokes,


heart


attacks


and


angina.


Tasks


and


Tests


Speed


Tasks


The


belong


speed


to five


measures

categories


included

s that r


the


present


present

distinc


analyses

t factors











Symbolic


Perceptual


Speed


represents


the


ability


scan


and


compare


quickly


patterns


of symbols.


Figural


Perceptual

comparisons


Speed


between


represents


patterns


the a

with


ability


to make


a figural


fast


content.


Tests


perceptual


speed


are


often


used


as measures


of speed


Horn


et al.,


1981)


but


are


considered


mark


also


intellectual


ability


(Ekstrom,


French,


& Harman,


1976).


Earlier


work


produced


equivocal


results


regarding


the


separation


Figural


and


Symbolic


Perceptual


Speed


(Ekstrom


et al.,


1976)


. Work


of Cunningham


and


his


assoc


iates


(Cunningham


Richardson,


1978;


Cunningham


& White,


1983)


demonstrated


existence


two


separate


factors


predicted


Guilford


(1967)


his


Structure


of Intellect


model.


This


conclusion


was


further


externally


validated


finding


of higher


correlations


between


and


Figural


Perceptual


Speed


(Cunningham,


1989;


Cunningham


& White,


1984;


Schaie,


press)


The


reaction


time


tasks


were


presented


on the


screen


a TRS-80


Radio


Shack


microcomputer.


They


included


simple


choice


reaction


times


which


were


assumed


load


on the


same


factor


(White


& Cunningham,


1987).


Sternberg


reaction


times


with


symbolic


content


were


assumed


to form


a different


factor.


The


Intelligence


and


Memory


Study


included


also


.g.,











structure


may


be different


the


old


contrast


the


young


adults


(White


& Cunningham,


1987).


The


reaction


time


tasks


are


often


used


the


study


of slowing


of behavior


with


increased


as well


as in


the


study


of speed


relation


to intellectual


functioning.


Card


sorting


tasks


were


considered


to define


additional


fifth


factor


(White


& Cunningham,


1987)


. These


tasks


are


also


used


the


study


of slowing


with


increased


and,


more


generally,


the


study


of selective


attention.


The


following


list


details


the


tasks


each


one


five


categories.


Symbolic


Perceptual


Speed


included:


Finding


s Test


(Pl) ,


(French,


Price,


Ekstrom,


1963).


The


subjects


had


to find


which


words


of a given


list


contain


the


letter


. Number


Comparison


Test


(P2)


from


the


Educational


Testing


Service


(ETS)


kit


of reference


tests


cognitive


factors


(French,


Price,


& Ekstrom,


1963)


involved


a comparison


pairs


of numbers


to establish


identity.


Letter


Comparison


Test


(P4).


This


an unpublished


test


developed


Walter


Cunningham


at the


University


of Florida.


The


test


requires


subjects


to make


comparisons


between


pairs











Identical


reference


Pictures


tests


Test--part


cognitive


(P31)


factors.


from


the


Subjects


had


decide


which


of five


possible


figures


are


identical


given


figure.


. Identical


Picture


Test--part


. This


part


from


the


test


referenced


above


was


used


as an indicator


of figural


perceptual


speed


addition


part


. Perceptual


Speed


Test


(PSC) ,


(Guilford


& Zimmerman,


1948).


The


test


requires


subjects


to match


objects


arranged


groups


of four


at the


left


of the


page


to identical


objects


arranged


groups


five


at the


right


of the


page.


Choice


included


Simple


Reaction


Time


(SRT).


Subjects


were


instructed


respond


to the


onset


of the


letter


which


appeared


on the


screen


on each


trial


one


second


after


a warning


signal


There


and

the


were

Sthe


depend:


five


practice


following s

nt variable


trials


imple

was


and

the


and


choice

median


test


trials.


reaction


time


time


this


tasks


to respond


the


onset


of the


stimulus


on the


screen.


Response


times


less


than


msec


were


not


included


the


computation


of median


reaction


times.


Choice


Reaction


Time


(CRT1).


Subj ects


were


instructed


press


a key


when


letter


was


presented


but


to refrain











Choice


Reaction


Time


(CRT2).


Subjects


were


instructed


press


a key


when


the


letter


or "J"


was


presented


but


refrain


from


pressing


the


key


when


the


letters


or "W"


were


presented.


There


were


7 practice


trials


and


test


trial


13 of


them


positive.


Sternberg


reaction


time


tasks


based


on a modified


version


of Sternberg's


(1975)


memory


scanning


tasks


included


four


tasks


with


a symbolic


content--two


with


a word


content,


one


with


a letter


content


and


one


with


a number


content.


these

of th


tasks


ree


subj ects


stimuli


which


were

h was


instructed

presented


to retain


twice


a memory


ensure


better


recall.


They


had


press


a "yes"


key


when


the


stimulus


the


screen


was


a positive


instance


the


memory


and


"no"


when


stimulus


was


not


included


memory


set.


Each


task


included


practice


trials


and


eighteen


test


trials,


nine


requiring


positive


responses


and


nine


requiring


negative


responses.


Median


times


were


recorded


correct


positive


and


negative


responses


as well


as for


incorrect


positive


negative


responses.


The


analyses


here


are


based


on the


positive


correct


responses.


The


four


tasks


were:


Sternberg


Reaction


Time


(MFW).


This


task


was


based


words


taken


from


the


Thorndike


and


Lorge


(1944)


word











. Sternberg


Reaction


Time


(HFW).


This


task


was


similar


MFW


but


lists


stimuli


the


were


Thorndike


selected


and


Lorge


from


word


high


frequency


frequency


norms.


Sternberg


Reaction


Time


(NPR).


In this


task


the


memory


included


number


pairs.


Sternberg


Reaction


Time


(LPR).


In this


task


the


memory


include


letter


pairs.


Card


sorting.


The


tasks


involved


sorting


playing


cards


into


several


categories.


The


times


completion


was


measured


using


a stop


watch.


Three


tasks


were


included:


Card


Sorting


(CS1)


required


to sort


the


cards


into


two


piles


according


to color.


Card


Sorting


(CS2)


required


to sort


cards


into


four


piles


according


to suit.


Card


Sorting


(CS3)


required


to sort


the


cards


into


thirteen


piles


according


to rank.


Fluid


Crystallized


Several


of the


intelligence


tests


used


Intelligence


(Cattell,


and


1987;


Memory

Horn, 1


project


978)


between


the c

fluid


classic


distinction


intelligence


(Gf)


and


crystallized


intelligence


(Gc)


and


were


used


present


study


the


purpose


of measuring


these


two


dimensions


Intelligence











on time.


Subj ects


were


encouraged


however


not


to dawdle


too


long


on difficult


questions.


. Letter


Series


(LS)


from


Guilford


and


Hoepfner,


1971.


The


test


requested


subjects


solve


as many


series


letters


as they


could


a limited


amount


time.


Number


Series


Completion


(NS)


from


the


Army


Alpha


Examination


(Guilford,


1938).


The


subjects


had


to complete


several


series


of numbers


a limited


amount


time.


Figural


Relations


Diagnostic


Test


(FR),


(Plemons,


Willis,


& Baltes,


1978).


Subjects


were


given


sequences


of three


patterns


and,


each


one


were


requested


to select


out


five


possible


patterns


one


that


best


completed


the


sequence.


Crystallized


intelligence


was


measured


using


three


tests:


Vocabulary


Subtest


(VOC)


the


Wechsler


Adult


Intelligence


Scale,


(Wechsler,


1955).


Advanced


Vocabulary


Test


(V5)


from


the


Educational


Testing


Service


Kit


of Factor


Referenced


Tests


(French,


Ekstrom,


& Price,


1963)


Information


Subtest


(INF)


the


Wechsler


Adult


Intelligence


Other


Scale.


Variables











Education


was


measured


on the


basis


the


answer


the


question:


"How


many


years


did


you


to school"


. Subjective


health


was


determined


using


the


question:


general,


would


you


that


your


physical


health


has


been:


excellent,


good,


fair


poor,


very


bad? "


score


of 1


was


used


indicate


excellent


questions


health,


were


to indicate


asked


good


case


health,


education


etc.


and


Additional


subj ective


health


but


they


were


used


present


analyses.


Procedure


All


tasks


were


administered


individually


during


two


consecutive


days,


each


one


of about


three


hours


testing.


Several


testing


breaks


procedure


provided


subjects


included


opportunity


tasks


described


to rest.


above


The


as well


as additional


tasks


which


were


not


analyzed


here.


the


reaction


time


tasks


card


sorting


were


administered


during


the


first


day


testing.


The


reaction


times


tasks


and


the


card


sorting


tasks


were


administered


order


increasing


level


of complexity


ensure


gradual


familiarization


the


subjects


with


the


tasks.


Fixed


order


standard


procedure


in correlational


studies


(White


Cunningham,


1987).


The


perceptual


speed


tasks


and


crystallized


intelligence


tasks


were


administered


during


thoc


arrnr1


14mt,~~I n.F; Jr .ll Ci,


* -...


r^x ^f


1kjTr i4


rrC Ckn











other


Army


Alpha


tests


was


administered


during


the


first


day.















CHAPTER
RESULTS


This


chapter


presents


the


main


results


from


the


estimation


of the


structural


models


delineated


chapter


The


observed


variables


on which


the


analyses


are


based


have


been


presented


Chapter


All


reaction


time


and


other


variables


their


measured


reciprocals.


time


In this


units

way a


have


double


been


transformed


purpose


using


been


attained:


transformed


variables


have


a distributions


closer


to the


normal


distribution


and


speed


variables


are


measured


a similar


way.


An approximate


normality


variables


statistics


important


provided


one


LISREL


use


maximum


meaningfully


likelihood


estimates


(Mulaik,


1972).


path


models


with


first


order


factors


speed


and


comparative


analyses


are


based


covariances


matrices


as input.


In several


cases


which


second


order


factors


were


incorporated


a causal


model


use


of correlation


matrices


served


avoid


problems


encountered

Confirmatory


running


factor


the


analyse


models

s not


using co

including


variance


matrices.


comparisons


were


based


on correlation


matrices


(Tables


and


5-2).










































V
0

0
H
1 X
In -

0) -

(0
I C


69



) HNWANMO0WNHFO~cammoONCOW
ONO M rMit nowo^ Om m On In in eOmm rono
O OflnONfnu1UnmncnEcrs
r


0 # ONANOU~roNODnr4Hc1Oc
& 0^ ONONAMnnnM io~OWoWoWn'^'^owftccsoa
U * * * * * * *
I II H


C) Su S Su S3 SV( i ~O))C) t~ d V(
0 * * * * * *
SII I Hr

E NO^^D OO4 OimormnnOmnaocomo
Co SrlONM O M4 5 5 9 ma 9 6 5 5 S n5 n 5 4
A * * * * * *


U mO o or o 8 btfo iNo cu otor O I rin \o
04 5 5 5 4 5 5 5 4 4 5 5 5 4 5 4 S S S S S 9 5 4 6 5
i H i-i


NC r r ICo r iOn NInn
r) IV(VOUfl U t folnrnnnin nrrrln nnr innn nr


O N * a a a **
r( O 10I NMMM O O t Yb NMM MMMin cu MN
cu YICI. . . . . ..)V)V~dd~CV(r


SO cSnSo O m4oro4n4 5 S s oir5 4 m c5r 55m55i5o
OC(^ l U)0L o olc^^ r) o in In rFin rt 'ro 'i ^' 'iJrn n
UJ* * * *


ncMOnNOHMONfOrmNMno'inrt
0N M O OB nWr n oiSiIO oinnrr MMM wwwr wNr


Nlc r P) nc t dooi rcn o tn D SOfOQ) WC1 1ot^oo onio
rH OeNoi 0Uif OfMlUnnciq Q4in.4c nt
S* * * * * * *


NOON N H0Nr ( woinor- 4oio son <
7 NHONHsCrHH100rr rOOOOOH OHrrHOnMMrnrM ntO
M I 1 |


W oon onn O com-ucoa ti c'niooNNcHN
4. OOHHNc MnirMHHNN31fM r zc eS04HMH l HHH
ri* 5 6 5 5 4 4 5 9 5
SI i-l I I I I I I I I I I I I I I I I I I I I I I I I


0 Oi n fNNWHWfnC nNfrlC i rHNNiCOD*<(
' OONO HONr4NOOOOOr4OH MOH(OH-Hr
ni t f t f -f t















In ~(V~lo ~I ^*Mol tin o^'Vm r lo~roinDon'~~nri oHoot
F1400 fltAO HrOHOOH@OmO
2 HH1L MnMNNnnMnNOcnOnq O
1 4 * * * *


HWLAO >OOOCHOHrwumLAca
rO rl oi com r0 1o o Or0trorOrrrlcnooQr Uinino

I

U UNo H LAnr oO(o OoOr'coiOOO
03 HH nNHNcmnNnqMnNN^ nu @4n00oo
I WH


NH A mIO OHO4Hr io -cNor r0o0ocnO
* ri nc '* ^ nMNnMnnnn nLOcnino n
* * * * * * **


oNb i 1o O nc Ha b MNr) rcn cvtnobr4
c1 OMMn ^^^xo nnnMncs ^o itiM r
z * * * * * * *


H WH0DnWM oHNWH o OM~om

SII H



o II Hifinntn n c^' ^O oomn
U 1 I r^
I


I
HJ N N NH0WHLAHOOOOW OnH
I U

II H

l N ONHO I m Nn cnao iOm )mo c- 4^no
l l i ONHo V) Vm wS O wmmom
** U
C)9


H ifnOH o OMOM\ wrooooof mco o rmooHrN
co02mer jl orn mitn Uo rr t nfn
U * * * * * * *


coooiiwn oi~votomnNonooM in Stnr^m
tf Or-!o na* ^^c ^' \o \o rzo o r, nr^ 'nrhoocu
II

^*OaflOtnooinLAnO n 4 O9HH9m0 9M 9 9 9 9 9n N Mn99
ft ........... *


~NWNZONnLANnu MMtHt
O O 3 93 3 9) 9) 9 9r 9 6O 0nil 9 9I 99OC N 9M
C * * * *


'dHU





S0 dH 0 I
*I I



o ENW




r00 I t

rI0 Qa0 0 W
- 0 0 I (0


01 UC023







w I0


oCO04
r ll *HU XI



COI 0)



*r eaCI


HZ C
HiPt
rO I T(


0) H ,
OIC



-3 -







.1I IH0X
C C
0- O< L



0J m
3 *r P
984 b,


I


-a
Ed

0,
(0

>
-H
rn
















































k
0
(N 4-I
I
In x
-H-
0 $4

I0 0

ca
02

0
-H


r-t
4)
0

O
0
C'


~ONONOhqOfWoOwMw~NommMme
S Nr***% *O*fnooo .cv) mNNo cMOru
EC 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


Ot HO r ONNNO n oHoWDin^ mroorQf
2l O * o o * *
E ............


N OHOOinM nOomin-4ioa unior
(0 * * *0 * 9 0 0 9 0 0 0
I H
i-((


CI) 0 0 0 9 0 0 0 O9 9 000o 0 0 0 0m o0o o
0 * * * * *


E- rMcoMNSONHOMWinr-~orWfmnr-r~isoir o
A OrHr Hclr%4Ir Mrruoa^InNNrM NNoortH
Ca * * *0* *


U NN NCO'%OOHOIOtOflOr. H CO rO1nMe r^oo
02 OHm mONHnno m inin inn 'nMcn
& * * 0 0 0 0


N MO1 OMHOONmms ewaem
0 H0 0 m 0 M0 0 0 nM 0 0M o 0 0me 0 0 0 00a
(ij *. .. .. *. *IJ *I *. *3 *1 *. * *


rH fnNOio~r-ioornNnNHior-to~r^or^Oaut
m rl r-(m dlno co vor nn) r> \n Vomic r rS mnrl ci
04 *0 0 0 6 0 0 0 0 0 9 0 0 0 6 0 0 0 0 0 0 0.
I H

^' ocN e Norri ooa m mcci nr co^ co 'oom cu
4 OrmiomsonHMANNjM^xn^nywN
* * * **0*4* *


N OCN ONiON f lrmmH nonAioHWHocoNin
040 *o* * * *** *n e a go3e
0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 6 0 0 0 0 0 0 0 0


r-iV o or( rV o rle ) r mcoMur-i rlco 'inr^^n ^
04 ONOMiM flrMr4MNNeMNvrIMNN

I u


1 r-IOCM^ cOr Ol^CQr ^O ^' O cCO cV(Vrl U) r-l CU CJ
0 ONN c NH Nr OHNrl-I HHlHOr4-NNHN rInrmw
GE *0** *.. ...
H(


1 O r0
' oMo


-a


OOH tHO HHrl l r1NH NaCHN ar- r-Il nH




















Er r-in t ir)CM- o oorcrtu 2 ONNMHHNHNHNOrfl'.tOO

H

U, flMflOmoNwamwocNW~ om
> nC)NNNHHNHOOHOrIOOrnoHaoo
* * * * 0* 0 0


N
mV
04C
(0
V,

'0
4 -
ia



M n
g g

C U H
4"
* C
HOW
4'oW<-
f0 (Q -
0)*^


9-
*0



04
SOH
COG)


90 9) 0 0 0V D 9O t 9O 0 0 r 10 9t 9t 9) 0D 0O 9 0 0 0
O iaN omi'cm^'^ocotnooa e m woionoom r or



ErNONo W Nc OWO OWo~enmom0er
0 r4tnoMMWoiNeaoain^'^n omor
S* * *0 0 0 0 0 0 4 0 9 0 9 9 0 0 0 0 0


N O OO 0 OO MWOO NO O NN o
'0 2N cu M c r mf oo un u, no homn^C
0* **)* * * *


*H
43 IND~f~tnNH0HOH'otoomnhoN
C 0M orttTNNmcoWNMnmoormne
0 *. * * * * *


N E rl O rl^ W Ho0 dN M r-OOOCOr OO
I 0 HNNM4 wwmtN c nnn nc ogo\Doinm o
LA 0* *0 * *94. 0. 0.. 4 0


O 0W 0O O OO O0 oOOOOOO0A
(0 .0 ** ** * * **o* *
I r


rH1 lOOr( COOC OONr o r o rOatnw HHO ifo
o o( /2 N cr inM oO r
0 * * * *


0 0O 4 4 nnM O9 0 0 in nOO 0, 0 0 S 0 M 4r)
M * * *. ...... *


# Or Vt voorre U I O vo r or vtO~omco ocu r( co cM it
A Hr NNtNNtAOyOlm0noo ocomq cmNmNn r%
04N MMOMVMMMN


'U-ri
8 I
01 I


U
k


03COrn.
9 $
V-a)
0Hc/)
002


OHE
0)


00(i)
0.02
VI a,







Aug
WFIG
O 0)
r-1a E^'


k C
Q Gk
Sag
PI Q) (0
I CO- -l
0I vl i
UIM
en I Q)
< c% e
MI
-i-l


QOWN
HZ C
OI0
9!g H


4
3


a a
- $

C'


C -


- 104
Ma -


*0
In
0
U
-H

<0

0)
>


-H
-











correlation

Hayduck, 19


matrices


87;


are


Joreskog


being


Sorbo


evaluated

m, 1984).


(Cudeck,


All


1989


models


estimated


here


using


correlation


matri


ces


were


scale- free


model


thus


assuring


that


estimated


model


has


been


modified


and


that


the


omnibus


test


statistic


corresponding


model


correct


(Cudeck,


1989).


The


with


chapter


confirmatory


divided


factor


into


analyses


two


sections,


and


other


one


with


dealing


path


analyses.


In both


cases


an additional


subdivision


has


been


made


between


analyses


involving


first


order


factors


and


analyses


involving


second


order


factors.


Confirmatory


Factor Analyses Snesri Maa ~ii mc
- - - -.--.-.----- .- .- ~ *-. a --- U --


First


Order


Factor


Analyses


Five


first


order


factors


of speed


were


hypothesized


account


variables


model


the


matrix


both


described


of intercorrelations


young


subjects


Chapter


Two


of the


speeded


accordance


confirmatory


with


factor


analyses


were


performed


each


age


group.


The


usual


method


which


treats


the


observed


variable


as X variables,


the


factors


as Ksi


variables


and


determines


the


sca


le by


fixing


diagonal


the


matrix


to unity


(Joreskog


& Sorbom,


1984)


was


adopted.


The


loadings


and


the


intercorrelations


;amnnnrr


fa rt-nr


n ra


nra a an4 aA


-Un~~~~I a-I.-- inani


Factor


Analyses


SCnpere


Measures


m~a'^ ^.^


EC)-


T.. ,.%.


L


Ir


1~











Table 5-3


LISREL Maximum Likelihood Estimates of Factor
Unique Variances and Factor Intercorrelations


Loadings,
in Old Ss


Factor


Loadings


Variable


Unique
Variances


Symbolic


Figural


Choice


Sternb.


Sort


.536
.295
.132


.333
.267
.262


.681
.839
.932


.816
.856
.859


SRT
CRT1
CRT2


.652
.491
.312


MFW
HFW
NPR
LPR


.590
.713
.830


.209
.230
.268
.400


.889
.878
.856
.775


.238
.182
.326


Factor


.873
.904
.821


Intercorrelations


Symbolic


Figural


Choice


Sternberg


Sort


Symbolic
Figural
Choice
Sternberg
Sort


1.00
.74
.46
.55
.61


1.00
.57
.56
.72


1.00
.88
.66


1.00
.68


1.00


.. - a











Table 5-4


LISREL Maximum Likelihood Estimates of Factor


Unique


Variances and Factor


Intercorrelations


Loadings,
n Young Ss


Factor


Loadings


Variable


Unique
Variances


Symbolic


Figural


Choice


Sternb.


Sort


.728
.356
.047


.522
.803
.976


.215
.172
.396


PSC

SRT


CRT1
CRT2


.886
.910
.777


.710
.473
.258


.539
.726
.862


MFW
HFW
NPR
LPR

CS1
CS2
CS3


.388
.357
.316
.399


.782
.802
.827
.775


.308
.286
.218


.832
.845
.884


Factor


Intercorrelations


Symbolic


Figural


Choice


Sternberg


Sort


Symbolic
Figural
Choice
Sternberg
Sort


1.00


1.00


1.00


1.00











constitutes


acceptable


fit.


The


loadings


are


general


high:


About


of them


are


above


each


the


two


groups.


In addition,


there


are


substantial


correlations


among


the


five


factors


young


group


.80)


and


the


old


group


(.46


.88).


It is


possible


on the


LISREL


output


to calculate


the


compound


reliabilities


factors


(Dillon


& Goldstein,


1984)


and


these


are


presented


subjects


Table


range


5-5.


The


from


reliabilities


young


old


subj ects


from


.89.


A comparative


hypothesis


factor


of relatively


analysis


high


was


undertaken


covariances


among


test


factors


the


older


group.


Specifically,


several


nested


models


were


compared. In the

covariances, the


most restricted

factor loadings


model


the


and


factor


unique


variances-


variances


were


assumed


to be equal


the


groups.


In a second


model


the


restriction


equal


unique


variances


was


dropped.


even


less


restricted


model


imposed


only


the


same


factor


loadings


but


not


equal


variances


and


covariances.


In the


most


relaxed


factorial


Model


pattern


only


was


an identical


assumed


without


simple


requiring


structure


equality


factor


loadings.


The


basis


this


comparative


analysis


was


matrices


variances-covariances


the


groups.










Table


Reliabiliti


of Speed


Factors


in Old


and


Young


Speed Factor Reliability--Old Reliability--Young


Symbolic Perc. Speed .86 .89
Figural Perc. Speed .88 .89
Choice RT .83 .76
Sternberg RT .91 .87
Card Sorting .90 .89










compared


using


the


differences


between


the


corresponding


Chi-squares


as a statistic


which


has


a Chi-square


distribution


with


a number


degrees


freedom


equal


the


difference


restrictive


restrictive


between


model


model


the

the


the


Degrees

degrees


comparison


of freedom


freedom


(Herting,


the


of the


1985)


most

less


. As


Table


shows,


Model


which


does


not


impose


equal


unique


variances


fits


the


data


better


than


the


most


restrictive


Model


However,


no further


significant


improvement


has


been


achieved


relaxing


Model


the


equality


condition


on factorial


variances


and


covariances.


A visual


inspection


of the


two


matrices


variances-covariances


obtained


the


most


relaxed


model


shows


(Table


5-7)


that


variances


and


8 covariances


are


higher


the


old


subjects,


a total


5 variances


10 covariances.


Second


Order


Factor


Analyses


Two


second


order


factor


models


have


been


hypothesized


and


tested.


the


most


simple


model


(Model


one


second


order

first


factor

order


of speed


speed


explains


factors.


the


In LISRE


correlations

L terminology


between the

the second


order


factor


a Ksi


variable


without


indicators


and


the


first


order


factors


are


Eta


variables


with


multiple


indicators.


The


scale


defined


the


second


order


factor


* a *


i ft


II


i


1





A











Table


The


Results


Simultaneous
in Young


Confirmatory
and Old Ss


Factor


Analyses


Model


Restrictions


Chi-sq.


GFI"


Same
Same
Same
Same

Same
Same
Same

Same
Same


factorial pattern
factor loadings
factor var./cov.
unique variances

factorial pattern
factor loadings
factor var./cov.

factorial pattern
factor loadings


347.45




281.83



271.09


.869




.887



.890


Same


factorial


pattern


257.19


.894


Model 2 offers a significant improvement i
Model 1, Chi-square=60.62, df=16, p<.001.
Goodness-of-fit index for the whole model.


over











Table 5-7


Variances and Covariances of


Speed Factors


Young and


Old Subjects


Factor Symbolic Figural Choice Sternberg Sort


Young


Symbolic
Figural
Choice
Sternberg
Sort


45.99


34.94


3.94
5.63


1.00
1.08


Old


Symbolic
Figural
Choice
Sternberg
Sort


45.33
5.20
9.94


3.27


30.44
3.22
5.05


1.48


1.91











more


complex


model


(Model


was


obtained


allowing


some


the


residuals


the


matrix


to correlate.


this


case


correlations


were


allowed


between


the


two


reaction


time


factors


and


between


two


perceptual


speed


factors.


All


other


correlations


remained


null.


Model


nested


Model


2 which


itself


nested


the


five


first


order


factors


model


which


has


been


examined


previous


section.


The


evaluation


of Models


and


the


old


and


the


young


subjects


presented


Tables


5-8,


5-9.


In both


cases al

resulted


lowing


factor


large


residuals t

significant


o correlate


improvements


Model


the


goodness


of fit.


the


subjects


the


goodness-of-fit


index


was


.89 and


young


subjects


. Root


mean


square


residuals


.043


the


old


and


.046


the


young


were


also


acceptable


as well


as ratios


below


the


Chi-


squares


respective


number


degrees


freedom.


The


difference


Chi-squares


between


Model


and


the


first


order


factors


model


both


younger


older


subjects


not


significant.


Table


5-10


presents


the


factor


loadings


the


specificities


(unique


variances)


first


order


factors


corresponding


to Model


loadings,


both


groups,


with


one


exception,


are


above


. On


the


other











Table


A Comparison


of First


Models


Order


Old


Second


Order


Factors


Subjects


Model Description Chi-square (df) Diff.(df)


1 One second order factor 203.85 (99) 53.30 (2)*
Null covariances in PSI

2 One second order factor 150.75 (97) 4.01 (3)
Free covariances in PSI"

3 Five first order factors 146.74 (94)


The
mode


Chi-square


1


Covariances
Speed, on o
RT, on the


difference


gnificant
between
ne hand,
other han


between


, p<.001.
Symbolic
and betwe


w


and


ere set


this


Figura
Choice


model


and


the


next


Perceptual


RT and


Sternberg


free.


&en


d,











Table-5-9


A Comparison


of First
Models


Order and Second
in Young Subjects


Order


Factors


Model Description Chi-square (df) Diff.(df)


One
Null


second order
covariances


factor
in PSI


164.49


(99)


53.26


(2)*


One
Free


second order
covariances


factor
in PS Ia


111.23


(97)


0.78


Five


first


order


factors


110.45


(94)


The Ch
model
Covari
Speed,
RT, on


i-s
is
anc
on
th


quare difference
significant, p<.
es between Symbo
one hand, and b
e other hand, we


be
001
lic
etw
re


twee

and
een
set


n


this


model


Figural
Choice RT
free.


the


next


Perceptual
and Sternberg











Table


5-10


Model


with


a Second
Subjects


Order


Speed


(Standardized


Factor


Old


and


Young


Solution)


First Order Factor Factor Loadings Unique Variances


Old

Symbolic Perc. Speed .679 .539
Figural Perc. Speed .780 .391
Choice RT .712 .494
Sternberg RT .744 .446
Card Sorting .912 .168

Chi-square=150.75 df=97 p=.000 GFI=.890


Young

Symbolic Perc. Speed .584 .659
Figural Perc. Speed .775 .399
Choice RT .624 .611
Sternberg RT .645 .584
Card Sorting .976 .047

Chi-square=111.23 df=97 p=.153 GFI=.918











Table


5-11


A Three
and


Second


Old


Order


Factors


(Standardized


Solution


in Young


Coefficients)


Second


Order


Factor


First


Order


Factor


Unique


Variances


Old


Symbolic
Figural
Choice R


Perc. Speed
Perc. Speed


Sternberg


Card


Sorting


.804
.924


.915
.957


1.00


.353
.146
.163
.084
.000


Young


Symbolic
Figural
Choice R


Perc. Speed
Perc. Speed


Sternberg


Card


Sorting


.717
.953


.883
.913


1.00


.486
.093
.221
.167
.000


Model
Model


for
for


old:
young


Chi
: Chi


-square=150.
-square=lll.


df=97
df=97


GFId=
GFId=


Perceptual
Reaction T


Card


Speed.
'ime.


Sorting.


Goodness-of-fit


index


(Joreskog


and


Sorbom,


1984)











valuable


theoretical


speed


variable


and


the


possibility


that


some


important


information


existent


first


order


level


may


be lost


at a higher


order.


An additional


model


(Model


with


three


second


order


factors


has


also


been


evaluated


. In


this


model


one


second


order


factor


explains


the


relationships


between


perceptual


speed


factors,


a second


factor


explains


the


relationships


between


reaction


time


factors


and


a third


factor


identical


with


the


first


order


factor--Card


Sorting.


Model


4 cannot


explain


Model


since


has


the


same


number


degrees


freedom


and


the


same


fit.


was


assessed


only


because


possibility


of using


the


three


second


order


factors


as latent


variables


general


model.


The


loadings


first


order


factors


on the


second


order


factors


and


the


correlations


between


the


three


second


order


factors


the


two


groups


are


presented


Table


5-11.


Both


the


loadings


and


the


coefficients


are


high,


first


are


above


the


last


are


the


range


Path


Analyses


Models


with


First


Order


Speed


Factors


The


models


presented


Chapter


were


first


evaluated


using


each


one


the


five


first


order


factors


of speed


*ha


anei Vana r 1 C


en ak a A 9


mI.... a


St


crrrnn~


C~A


m A ~L3 A 1










case


of older


subjects


the


exogenous


variables


were


age,


education


and


subjective


health.


the


case


young


subjects


there


was


almost


no variability


subjective


health


which


was


therefore


omitted


from


the


analysis.


For


purposes


of comparability


the


analyses


older


subjects


were


performed


twice,


once


without


subjective


health


and


once


including


assessed


subjective


these


subjects


health.


and


Ten


they


models


are


were


presented


thus


Tables


5-12,


5-13


and


Figures


5-1,


The


, 5-3.


five


models


assessed


Models


are


young


examined


subjects


here


presented

following


Table


order:


5-14.


five


The


models


without


health


older


subjects ;


five


models


including


health


older


subjects


and


five


models


(without


health)


young


subjects.


All


five


models


without


health


older


subjects


the


range


data


reasonably


from


well


. Two


: the


goodness-of-fit


models--with


Symbolic


indices

Perceptual


Speed


and


with


Sternberg


Perception


Speed--


have


Chi-squares


relatively


ratios


large


between


and


the


significant


Chi-squares


(p<.05).


the


However,


respective


the


number


degrees


of freedom


these


models


well


as for


other


three


models)


less


than


indicating


sati


factory


(Herting


& Costner,


1985;


see


also


Appendix


. In


only


one











Table


5-12


Standardized


Path


Coeffi


clients


Models


and
Old


Indices


of Fit


Five


Model


Path"

Speed--Gf
Gf--Gc
Age--Speed
Age--Gf
Age--Gc
Educ--Speed
Educ--Gf
Educ--Gc


Symbolic

.592
.585


.111)
.110)
.199
.253
.319
.294


Figural

.673
.585
-.328


.044)
.199
.260
.292
.294


Choice

.558
.598
-.199
-.063)
.201


.042
.444
.288


Sternberg

.451
.596


.064)
.146)
.200
.098)
.424
.289


Sort

.584
.599
-.162)
-.080)
.200
:.160)
.375
.287


Fitb


Chi-square
df
probc
GFId


63.19


.000
.916


.057
.937


81.39
58


.101
.941


61.78
47


.023
.926


.073
.938


: The


coefficients


Note
t<2.


parentheses


are


not


significant,


The


first


to fluid int
intelligence


and


education


paths


are


elligence


(Gc)


. The


(Educ)


Beta


(Gf)


paths


and


others
Speed,


from


are


from
Gf


Gamma


speed


factor


to crystallized


paths


from


age


Gf and


Summary


Probability


value


given


of goodness


for
that


Goodness-of-fit


the C
the
index


of fit


measures


rhi-square
model is


(Joreskog


each


to exceed


the


model.


specified


true.


and


Sorbom,


1984)











Table


5-13


Standardized


Path


Coefficients


Model


and
Old


Indi


ces


of Fit


Five


Model


Path'

Speed--Gf
Gf--Gc
Age--Speed
Age--Gf
Age--Gc
Educ--Speed
Educ--Gf
Educ--Gc
Hlth--Speed
Hlth--Gf


Hlth--Gc


Symbolic

.590
.603


-.129)
-.107)
.204
.226
.316
.244
-.314


.026)
.061)


Figural

.666
.604
-.338
'-.041)
.205
.235
.291
.245
-.281


.025)
.062)


Choice

.550
.617
-.212


.065
.206


(.013)
.442
.247
-.333


.029)
.065)


Sternberg

.426
.613


-.071)
-.152
.206
(.078)
.416
.243
-.219


.118)
.064)


Sort

.571
.617
-.172
-.083)
.206
(.135)
.373
.284
-.283


.050)
.064)


Fit"


-square


61.59


88.34


64.16
54


probc
GFId


.001
.918


.101
.938


.223
.944


.035
.925


.162
.941


The


coefficients


parentheses


are


not


significant,


t<2.


The
to


first
fluid


intelligence


paths


are


intelligence


(Gc)


age, education
Speed, Gf and


. The


Beta


(Gf)


paths


and


other


(Educ)


from


paths


subjective


from
Gf
are


the


speed


factor


to crystallized


Gamma


health


paths
(Hith)


from
to


Summary


Probability


value


given


of goodness


for
that


the
the


measures


Chi-square
model is


each


to exceed


the


model


specified


true.


Goodness-of


-fit


index


(Joreskog


Sorbom,


1984)











90










*9
*H
(0
3
-P
a




*4
0



cu u
SC)
s4






*4 0
-i *r-4







GOl
C 4









rd. lr
CO
*I~
-4 H

0 0
*H1


C 3
04 0
5.4 4 *
0 C
0 Co










OQ)
0U U
O) (f-l
r o r
2 0)
C 0
0 U
(0 P




& IP
(0
a 04

lr4

4 N
c -H
0) T3
U <0
Lw CU

0 C. T3
o rH
PC* 0
4.3 I"
a. 4g^










91









0
(4C4

( C <- 17 \
Q -CJ

IC C)

Cl \ \ \ /
Vt 0
CC

/ i \ / \ fs/ **-
I~~, \ \/ \/ w r-l
I~~c \ I I 'H- a)
44

/~~' '\H\- \ /I(

.'/ \/ ^^\ tr O
N ^ /\/^ 0 :3
w. 41 H

\C 0
o 4c)
0 C





0 /*\ / \\|(0 U)
o \\4 14J
to C

0 \
ct U)
I 5) -H-
a, 01 -4
C 0~


3 04





oP I i
*rn
'0j

: rl

C) ( U

oU C/
UC (
DC N
44 Ilx









92






0'.

tr

.617 44
----- o o
V sVd



I \r- / IC 43
C L
|~ ^\ \ / 5 H




'^ ^ o 0 C^

(V^/ .n1\\\
tr*r4





0 0\


X C 0H
K) 0) C)]



oo 1 I ^ 1-
Q) U
C 04r








*rII
U tn
0 44
o U)
U a
a ccit
10 I:-











Table


5-14


Standardized


Path


Coefficients


Model


and


Indices


of Fit


Five


Young


Model


Symbolic


Speed--Gf
Gf--Gc
Age--Speed
Age--Gf
Age--Gc
Educ--Speed
Educ--Gf
Educ--Gc


.464
.626


-.130)
-.293
.279
.341
.174
.244


Figural


.570
.623
-.220
-.226
.277
.261
.183
.245


Choi


.425
.616
-.328
-.212
.274
.320
.197
.247


Sternberg

.462
.627
-.320
-.203


.277
.297
.196
.243


Sort

.573
.608
-.396
[-.126)
.272


.311
.154
.250


Fitb


Chi-square


80.66


94.54


74.81


probc
GFId


.001
.916


.000
.913


.002
.918


.002
.915


.006
.925


The


coefficients


parentheses


Note
t<2.


are


not


significant,


The
to


first
fluid


intelligence


and


education


Summary


Probability


value


given


Goodness-of


paths


are


intelligence


(Gc)


. The


(Educ)


of goodness


for
that


-fit


the
the


index


Beta


(Gf)


paths


and


others


from


are


to Speed,


from
Gf


Gamma


speed


factor


crystallized


paths


from


age


and


measures


Chi-square


model


(Joreskog


each


to exceed


the


model


specified


true.


and


Sorbom,


1984)


Patha











greater


than


would


be expected


chance


alone,


given


that


the


model


true.


The


focus


the


examination


the


models


first


the


direct


indirect


paths


from


age


to fluid


intelligence


as well


as on the


path


from


fluid


to crystallized


intelligence.


Next


are


examined


the


paths


from


the


exogenous


variables--age,


education


(and


subjective


health


the


models


including


this


variable)


to fluid


and


crystallized


intelligence.


Symbolic


Perceptual


Speed:


In this


model


age


does


seem


to be related


indirectly


: The


to fluid


intelligence


coefficient


direct


directly


path


significant


the


path


from


to Symbolic


Perceptual


Speed


not


significant.


The


path


coefficients


the


path


from


fluid


crystallized


intelligence


high


significant.


Age


also


related


to crystallized


intelligence


but


this


case


positive,


significant


coefficient


indicates


an increase


crystallized


intelligence


with


increased


age.


Education


related


to all


three


endogenous


variables--speed,


fluid


and


crystallized


intelligence


and


the


corresponding


standardized


path


coefficients


are


of magnitude


.25--


.32.


Figural


Perceptual


Speed:


A direct


path


from


age