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Latent change score analysis of the impacts of memory training in the elderly from a randomized clinical trial

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Latent change score analysis of the impacts of memory training in the elderly from a randomized clinical trial

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LATENT CHANGE SCORE ANALYSIS OF THE IMPACTS OF MEMORY
TRAINING IN THE ELDERLY FROM A RANDOMIZED CLINICAL TRIAL

by

John Janson Prindle

A Thesis Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF ARTS
(PSYCHOLOGY)

December 2008

Copyright 2008 John Janson Prindle

ii
Dedication

To my parents and my brother.

iii
Acknowledgments
I would like to thank my advisor, Jack McArdle, for all of his help and
guidance. Also, to John Horn for giving me my first lesson in factor analysis.
Additionally, I would like to thank Kelly Kadlec and Archana Jajodia for their helpful
comments along the way.

December, 2008

iv
Table of Contents
Dedication ii
Acknowledgments iii
List of Tables v
List of Figures vi
Abstract vii
Chapter 1: Introduction 1
Chapter 2: Study Methods and Procedures 9
Chapter 3: Analysis 1 – Post Treatment Effects 20
Chapter 4: Analysis 2 – Pre-Post Treatment Effects 26
Chapter 5: Analysis 3 – Measurement Invariance Effects 32
Chapter 6: Analysis 4 – Bivariate Latent Change Scores 37
Chapter 7: Analysis 5 – Adding Covariates to the Models 41
Chapter 8: Discussion 45
Bibliography 49
Technical Appendix 53

v
List of Tables
Table 1: Outcome Variable and Demographic Statistics 10
Table 2: Two Group SEM with Nested ANOVA Models 25
Table 3: Two Group SEM with Pre-Post Scores 31
Table 4: Factorial Invariance Testing 36
Table 5: Bivariate Latent Change Factor Score Model 40
Table 6: Bivariate Latent Change Factor Score Models with Covariates 44

vi
List of Figures
Figure 1: Distributions and Plots of Outcome Scores on Near and Far Variables 11
Figure 2: Models for Training Experiments 22
Figure 3: A Bivariate Latent Change Score SEM for a Pre-Post Analysis 28
Figure 4: An Invariant Common Factor SEM with a Latent Change Score 33
Figure 5: A Bivariate Latent Change Score SEM with Invariant Common Factors 38
vii
Abstract
Latent Change Score models are used to examine training effects in a
randomized clinical trial on memory training (see McArdle & Prindle, 2008). Data are
taken from the Memory and Control groups of ACTIVE (Jobe, Smith, Ball, et al.,
2001). First, we examined mean differences in SEMs and find training effects within
the trained domain (memory) and transfer to everyday problem solving present for both
groups. Second, pre-post test latent change score models find mean training effects for
the memory variable with less transfer of training. Third, we use two common factor
models to test measurement. Standard likelihood ratio testing suggests invariant
loadings do not fit the Near factor but fit the Far factor. Fourth, a latent change score
model with common factors did not offer any new information over previous models.
Implications and ideas for future analyses are presented in the discussion section.
1
Chapter 1: Introduction
Cognitive Ability in Aging
Fluid Ability
Because we age, we are always looking to regain pieces of our youth by
whatever methods appear to yield promising results. The natural tendency in the
lifespan is a rise to peak performance by late youth and a leveling off in middle age,
with decline into old age. And we want to alter this.
Natural aging brings about a rising and falling of cognitive abilities which are
known broadly as fluid and crystallized intelligence, commonly referred to as Gf-Gc
Theory (Horn & Cattell, 1966, 1967). The elderly population experiences a decline,
particularly after the age of 65, in which an overall level of daily functioning is noted to
drop. We know from observational longitudinal studies that certain aspects of cognition
also decline as this overall level of functioning tapers off (Schaie & Gribbin, 1975;
Baltes, Reese, & Lipsitt, 1980; Salthouse, 2006). Many researchers are interested in the
kinds of intervention that seem most effective in boosting overall performance -- e.g.,
Speediness, Reasoning, Memory, or Knowledge. These areas have been shown in
smaller scale studies to respond positively to training interventions focused on a specific
ability (Baltes, Sowarka, & Kliegel, 1989). In this study, we examine the effect of
memory training specifically in this set of analyses because of its inherent use in
everyday functioning.
Much research has been done to examine which interventions could have a
positive effect on everyday functioning. Some such studies have looked at protective
2
factors that help to maintain cognitive function, including education, socioeconomic
status and baseline performance (Morrison-Bogorad, Cahan, & Wagster, 2007). Others
have looked at the role of exercise in maintaining cognitive prowess, with positive
results for moderate physical activity (Heyn, Abreu, & Ottenbacher, 2004). One of the
most researched areas of cognition and aging is that of cognitive training for older
adults (Schaie, Willis, Hertzog, & Schulenberg, 1987; Willis, 1987; Baltes, Dittman-
Kohli, & Kliegel, 1986; Willis, Blieszner, Baltes, 1981). These studies have focused on
targeting certain aspects of cognition to find some way to bolster everyday functioning
through transfer of training. They also give background to psychometric methods and
measurement tools for cognitive constructs of reasoning, speed of processing and
memory. In this way certain aspects of cognition can be targeted and the outcome on
everyday function is relatively easy to obtain and compare to previous performance.
Memory
The idea of participating in a cognitively stimulating activity is thought to
promote cognitive function and prevent decline (Wilson et al., 2003). A number of
studies have looked at the effects of Memory in an aging population. Yesavage (1985)
found in a review of literature that cognitive declines in 70 year old normal populations
ranged between 20% and 40% with Memory abilities. While there is this notable
performance difference between ages, there are still gains for both groups when given a
cognitive intervention. When compared to younger individuals older adults do not
perform as well but, both groups benefit from mnemonic training to improve memory
scores (Robek &Balcerak, 1989). Further research has found that a variety of training
3
techniques including loci mnemonics, face-name mnemonics, supportive environment
and slow pace can help to improve memory in a laboratory setting (Greenberg &
Powers, 1987). The scope of the research does not stop at simply asking if the trained
ability can be improved, but can these gains translate to improvements in everyday life.
This was the focus of the study from which the data comes. We want to see specifically
if the training program provides individuals a benefit in their memory abilities over
controls. And if this training will then transfer from Near benefits to Far benefits. Near
benefits would be those of memory and Far is everyday functioning. The gains realized
in memory should be positively associated with gains in the Far score for the
experimental group compared to the control group. So in addition to a higher Far
change score for the trained group, they may also show more transfer from Near change
to Far change.
Transfer of Training
Training of an individual on a specific task should transfer to the specific ability
and ideally create positive change in performance. This transfer is within the Near
domain, Memory, and indicates that there is shift due to the training. This transfer is
then separate from a transfer across domains which we will term, transfer of training.
Here the trained ability experiences a gain and this improvement may have an effect on
the overall everyday ability an individual is capable of. This transfer of training is the
result of gains in one domain being associated with gains realized in a broad set of
abilities to cope with everyday life. We have given this association a direction based on
hypothesizing that it is the basic abilities (e.g., memory) that make up the complete set
4
of cognitive abilities are the core of everyday abilities and improving these building
blocks leads to a detectable difference in every performance.
Previous Research on the ACTIVE Study
The Advanced Cognitive Training for Independent and Vital Elderly (ACTIVE)
study focused on enhancing cognitive performance in an aging population as it declines.
Three areas of cognition were targeted; Memory, Reasoning, and Speed of Processing
were chosen because of previous gains experienced in smaller scale studies on everyday
activities (Jobe et al., 2001; Ball et al., 2002; Willis et al., 2006). The three
experimental groups were contrasted with a No-Contact control group, and the focus of
this analysis is on the Memory group with the No-Contact control group.
The ACTIVE study was designed to provide evidence that training certain
aspects of cognition can translate into everyday gains. This is not a new idea and there
is previous evidence from smaller scale studies that certain regimens may be effective
(Baltes, Dittman-Kohli, & Kliegel, 1986; Willis, 1987).The ACTIVE study looked to
expand these efforts to a large-scale randomized clinical trial with multiple
experimental groups compared to a No-Contact control group. The hypotheses were
explicitly outlined in previous work by S. L. Willis (1987): (1) How can the course of
cognitive decline be altered in the elderly? (2) What procedures are effective in
improving cognitive performance? (3) Will these improvements transfer into everyday
abilities and not only improve the focused ability?
Specifically ACTIVE was designed as a randomized clinical trial in six sites
nationwide on elderly individuals aged 65 and older. Individuals at each site were
5
assigned as controls or to one of the experimental training programs. The training
programs focused on one of three possibilities (Speed of Processing, Memory, and
Reasoning) or participants were assigned to a No-Contact control group. The
participants were measured at baseline, then assigned to a group and underwent a ten
session intervention over a 2 to 6 week period. After the training a post-test assessment
was administered and then a year and two year follow-up were pursued.
Two comprehensive analytic reports have come out using the ACTIVE dataset.
The first uses the two-year dataset, applying mixed effects models to both the cognitive
outcomes and the everyday performance outcomes (Ball et al., 2002). This research
report finds that the training programs were effective in enhancing cognitive abilities
but these gains did not transfer to everyday activities. In the case of Memory, the
memory training provided a boost for the variables measuring memory, but no gains
were realized in everyday variables for individuals assigned this training program. The
second report includes a five year follow-up in addition to the previous data. The
researchers find that the Reasoning training resulted in significant gains in the
Instrumental Activities of Daily Living (IADL) compared to control performance
(Willis et al., 2006). The same enhanced within domain performance is observed even
at the five year follow-up, but overall there is no transfer of specific ability to everyday
functioning.
The previous analyses have used a traditional RCT analytic approach to estimate
training effects. Specifically repeated measures mixed effects models were fit with the
dependent variables being the cognitive outcomes, as well as the more broad everyday
6
outcomes (Jobe et al., 2001). The outcome variables were measured at each data
collection point and missing values were computed to compare against the complete
cases to see if there was selective attrition. The results for the imputed values
resembled those of the complete cases “suggesting that the results were not influenced
by selective attrition” (p. 2277; Ball et al., 2002). Both reports give compelling
evidence of trends towards positive benefits of cognitive training in an older population,
but these are not significant.
Current Research Plan
The current study investigates the possibility of new training results using more
contemporary Structural Equation Models (SEMs). The SEM used follow the work of
McArdle & Prindle (2008) where the Reasoning data of ACTIVE were used to examine
the training hypotheses described above. This report indicated that there is no
significant transfer of training as result of reasoning training. Latent Mixture Modeling
did show that there seems to be two identifiable groups within the Trained group that
have different trajectories depending on baseline performance levels.
In contrast, this is a SEM analysis of Memory training. Up to this point, there
has been no direct test of transfer of Near cognitive trained memory skills transferring
to Far everyday abilities. The path models used here follow the lead of McArdle &
Prindle (2008) on the Reasoning component of ACTIVE but here we focus on the
Memory component of ACTIVE. We build from the test of mean differences similar to
the ANOVA tests (Figure 2) to a bivariate factor analysis of latent change scores
(Figure 5). These models identify the effects of the specific training on the broad
7
everyday outcomes, something not tested in the mean difference comparisons done with
the repeated measures mixed effects models as presented before. The benefit of the
SEM design is outlined in a few ways.
1. Benefit of Randomized Clinical Trials.
First, the design of the study, being a randomized clinical trial allows us to make
certain assumptions that would not be possible otherwise. The work of Fisher (1928)
allows us to associate the size and casual direction with such random assignment to
groups. Because the initial time period is not influenced by training, there is the ability
to attribute dinfferences in individual changes between groups to the group assignment.
If one group experiences less change than another group on average, then the difference
is due to the experimental condition they were assigned.
2. Benefit of Latent Variables.
Secondly, the ability to model latent variables becomes possible, and with this
we can form factors with the outcome variables measured over time (Joreskog &
Sorbom, 1979; McArdle & Woodcock, 1997). In our framework this means that we can
form a factor for the cognitive measures that the participants were trained on (Memory)
and test for invariance in the factor structure over time. If this is the case we can
measure the change in performance that one may experience from one time to the next.
Likewise, testing of dynamic interactions between these latent constructs makes it
possible to examine the effects of training directly on the everyday outcomes (Ferrer &
McArdle, 2004; McArdle & Hamagami, 2004). The latent variable models provide a
8
value that is free of measurement error and yields the pure change in performance over
time.
3. Benefit of Multiple Group Design.
And third, Joreskog (1978) provides us with the tools to examine multiple
groups in an SEM structure. In this way we examine the means, variances, and
covariances to estimate a goodness of fit index for a given model. This follows from
work by Little & Rubin (2002) in which Maximum Likelihood Estimates (MLE) are
formed based on fitting the raw longitudinal data to a theoretical model that we specify.
We can compare nested models in which the shape of the model is held constant but
parameter constraints are progressively relaxed. The Chi-Square model fits are then
compared to choose a desirable fit for a given model.
This paper builds from a basic SEM representation of the ANOVA model to a
bivariate factor model of latent change where both the pre-test and post-test factor
scores are considered. From here we move to examining invariance in a change model
with factors for the Near and Far variables. With invariance established we can then
examine the bivariate factor SEM where the factors represent ability in the Near and Far
domains. Here we can see if the training affects the factors on the whole instead of
within focused variables as in the bivariate path model. In the last analyses we examine
the effects of covariates in the factor model.

9
Chapter 2: Study Methods and Procedures
Participants
The participants for the current analysis come from the ACTIVE study database
(Tennstedt, Morris, Unverzagt, et al., 2001). This sample is supposedly representative
of the population of the United States, sampling individuals from 6 locations throughout
the country. They were recruited through databases provided by local clinics, senior
centers, Department of Public Safety, etc. Information was disseminated to participants
through individual letters, newspaper advertisements, introductory letters, and follow-
up calls. The initial sample size of the study included 2,832 people, with 702 in the
memory training group and 704 in the no-contact control group.

10
Table 1: Outcome Variable and Demographic Statistics

The average age across the entire sample was 73.6 (65-94), 75.8% female
(which was effect-coded -.5/.5), 13.5 average years of education and 35.9% were
married. Additionally, the reported health was exceptionally good for the sample with
40.4% reporting good health and 43.9 reporting excellent or very good health. This
aspect is to be expected given the inclusion/exclusion criteria which limited
participation to individuals that were living without assistance and active during the
recruitment phase.

11
Figure 1: Distributions and Plots of Outcome Scores on Near and Far Variables

Figure Description. (a) Group distributions of post-test scores on Near and Far
variables; (b) Scatter plot of Near difference scores as a function of Near[0]; (c) Scatter
plot of Far difference scores as a function of Far[0]; (d) Far difference scores as a
function of Near difference scores.

12
The data of Figure (1a) indicate that there is a noticeable difference in the mean
scores of the Near[1] item, but this difference is not found in the Far[1] item based on
group assignment. This difference in group performance is realized when the change
scores are plotted as a function of the pre-test score as in (1b). There is a larger gain
experienced for those that start out lower and a linear trend of decline as the baseline
score increases for the Near item (Rivermead). The same is not true of the Far item
(EPT), which sees no group difference even over the range of pre-test scores (1c). The
Final part (1d), shows that there weak association of the difference in Near scores time
to time and the difference in Far scores time to time. So how much change you
experience in the Near ability does not necessarily correlate with an improvement in the
Far ability.
When the participants are randomly grouped by training program there is no
significant difference in means of gender levels, education, marriage, and health ratings.
Cognitive variables measured at baseline do not differ among groups because of the
randomization performed to group individuals. Randomization was performed after all
baseline measures were collected and directly before starting the training program in an
attempt to limit dropout numbers (Jobe et al, 2001). In this way we can be sure that the
groups should be similar to one another at the baseline, since the groupings are made
after the fact.
Procedures
After establishing eligibility of the participants, a baseline assessment provided
an overall picture of where all of the participants stood initially. This provided a
13
snapshot of both the near outcomes and the far outcomes, the achievement levels for the
participants of the study as a whole before any separations were made. This baseline
assessment took three sessions, two being individual assessment and the other being
group assessment. A take home psychosocial assessment was given to be completed at
home and returned at the third day of assessment. The total time commitment for the
baseline assessment lasted between 4 and 5 hours total. No indication is given of
whether this time commitment resulted in attrition and whether these individuals were
significantly different from those that completed the study. Informed consent was
provided according to each of the six institution’s (University of Alabama at
Birmingham, Boston Hebrew Rehabilitation Center for the Aged, Indiana University
School of Medicine, Johns Hopkins University, Pennsylvania State University, and
Wayne State University) human subjects review committee and was collected both
verbally and in written form (Jobe et al., 2001).
Next the sample was subdivided into four groups that made up the clinical trial.
This was done using a computer program to randomly assign individuals to one of the
four groups. As mentioned before the randomization took place after the baseline
assessment and directly before starting the intervention training. The given explanation
was to minimize dropouts in the sample (Jobe et al., 2001). The sample size was
targeted to produce a certain effect size (.25) for the training programs. Traditionally in
randomized clinical trials the randomization takes place at the outset and this seems to
be a more pure way to randomize individuals. The groups as they are all incredibly
14
close in all demographic variables and sample sizes being within 5 participants of one
another. The randomization should not yield results this perfect if it were truly random.
Booster sessions were administered at about eleven months after the baseline
assessment with four additional training sessions. These sessions were available to
participants that were labeled as compliant based on the above criteria. About 50% of
the sample underwent the booster training within each of the training program’s
compliant participant population.
In the follow-up assessments, there were three points of testing over a 24 month
period. The first follow-up testing occurred with 10 days of completion of the training
program. At this point the near cognitive outcomes and a select number of far everyday
outcomes were measured. This testing session averaged about 2.5 hours. The second
and third follow-up assessments took place at year intervals from baseline assessment.
In these sessions individual and group assessments included self-administered tasks and
health service and functioning indicators.
Memory Trained Group
The study designated that participants were divided into four groups with
differing goals. Each group theoretically started at the same level of ability at the
baseline time of measurement. The three training groups were designed to improve a
specific cognitive ability. The hope was that this specified training within a cognitive
domain would transfer to abilities in everyday activities.
Training programs lasted 6 weeks maximum but could be as short as 2 weeks
with 10 total training sessions carried out during this period. As long as eight of the
15
sessions were attended by the participant they were considered to be compliant with the
training program. Make-up sessions were organized for those that missed any portion
of a session in order to maximize participation and retention. Training sessions ranged
in size from 3 to 5 individuals and make-up sessions were done in small groups if
possible.
The memory training program was organized into several facets that were aimed
at promoting the use mnemonics in everyday activities (Jobe et al., 2001). These
strategies included organizing things into lists that had a theme, such as a grocery list.
Also, strategies for organizing ideas and details in text form, such as skills necessary for
reading medication. The last technique taught involved visualizing and grouping items
for later remembering, such as what is done when running errands.
The training sessions started by introducing participants to the method used to
target memory ability. After this they were given instruction in how to implement the
mnemonic rule given the opportunity to practice using the rule. The rule was associated
to one of the four memory principles (meaningfulness, organization, visualization, and
association) and after initial instruction the participants were given chances to practice
alone and in small groups (Jobe et al., 2001). Tasks included both laboratory and real
world applications.
No-Contact Control Group
Those assigned to the control group underwent no training activities during the
ten week experiment period. This group was tested at the baseline period along with the
other groups and then the randomization process sorted them to the no-contact control
16
category. These individuals underwent no intervention program and were only
contacted again to provide data at the follow-up assessment periods.
Outcome Measures – Near Transfer
Memory training effects were measured by three indicators. These indicators
were chosen by their relevance to the training program and their known association with
the memory construct. These include Hopkins Verbal Learning Test, Related Words
List (Bradnt, 1991), Rey Auditory-Verbal Learning Test, Unrelated Words List (Rey,
1941), and Rivermead Behavioral Memory Test Paragraph Recall task (Wilson,
Cockburn, & Baddeley, 1985). These tests are all self administered paper and pencil
tests where the number of correct responses in the allotted time makes up the score for
each test. The scores used are percentage scores obtained by dividing the obtained
score by the max score and then multiplying by 100. These three tests of the memory
ability as defined in cognitive studies allows us to combine these scores into a factor
score indicated by each of the individual test scores for each participant. Testing of
factor invariance between groups and over time is done to ensure that the same
construct is measured at each point between the two groupings.
Outcome Measures - Far Transfer
At each session three indicators of everyday problem solving tasks were used to
measure everyday functioning over time. These tests included Everyday Problems Test
(EPT; Willis & Marsiske, 1993), Observed Tasks of Daily Living (OTDL; Diehl,
Willis, & Schiae, 1995; Diehl, Marsiske, Horgas, & Saczynski, 1998), and Timed
Instrumental Activities of Daily Living (TIADL; Owsley, McGwin, Sloane, et al.,
17
2001). The EPT task was designed as indicating ones ability to identify normal things
one encounters during the course of a day. This task had 14 everyday household items
and participants had to provide responses to two questions about each item, with total
scores indicating how many questions they answered correctly. The highest raw score
was used a maximum bounds and all scores were divided by this score and multiplied
by 100 to give a percentage score. All scores were bounded between 0 and 100
subsequently. In the same fashion the OTDL measure presents participants with daily
tasks (balancing a checkbook, etc.). Scorers rate performance based on how they saw
the participant perform. And again a maximum score was used to get a percentage
score for this variable. The percentage score was used to provide a similar metric for of
performance across variables to better understand the parameters when interpreting the
results.
TIADL was supposed to be indicative of everyday speed in terms of everyday
cognitive functioning. The task presents subjects with five different everyday tasks that
are instrumental in daily life and records time taken to complete them. The task taps
more at how efficiently someone can carry out tasks with more efficient persons being
faster. This score was obtained by using the standardized scores from previous
analyses, adding one, and then taking a log transform of the new score. Though the
tasks appear to measure different aspects of everyday functioning, we contend that one
common factor is indicated by these three indicators. This common factor is Everyday
Performance and we follow the same line of analysis for factor invariance in the
everyday tasks as we do in the cognitive measures in the previous section. The TIADL,
18
EPT, and OTDL tasks should be related in performance in that those with high scores in
OTDL and EPT should have low times in TIADL and the opposite is true of those with
low scores in OTDL and EPT
The TIADL variable was coded as a normalized score in the dataset when
obtained. The variable is a timed score with penalties given for inaccuracies and has a
maximum cut-off that a person can obtain. This timed variable was highly skewed, with
a few scores in the tails and was thus rescaled with a log transformation. Once this was
done the maximum score was used produce a percentage score as was done in the
previous outcome variables.
Covariates
For consideration in the last few models various demographic covariates were
introduced. These variables included: age (centered at 75 and the unit of measurement
is decades), gender (half effect coded, towards females), education (centered at 12 in
yearly units), and Mini Mental State Examination (MMSE; Folstein, Folstein, &
McHugh, 1975) score (centered at 27).
The variables were chosen because of their availability and their supposed
importance in cognitive performance. Gender is introduced to account for differences
that may exist between the sexes. Age is included to see if there is a differential effect
based on participants’ age in years. Perhaps the training regimen would affect older
individuals differently from younger participants. MMSE is included to represent
current cognitive performance. This variable was used to exclude possible participants,
so one may conclude that the sample may not show any differences on this variable
19
since they are all high functioning. Education is another attempt to control for some
variation and we include it thinking that higher education will help the effects of the
training. The centering of the variables provides us with a simple way of interpreting
the results of the model output. The change score for a person with zero on all of the
covariates indicates that they are a 75 year old male, with a high school education, and
scored 27 on the MMSE.
20
Chapter 3: Analysis 1 – Post Treatment Effects
Post Treatment Analysis
The first set of analyses look at the scores obtained after the training program
has been completed. We use the post-test scores for the Rivermead task and the EPT
task to evaluate the effects of Near and Far Transfer as a result of the memory training
program. This strategy of investigation was developed in McArdle & Prindle (2008)
and is extended to examine memory training. This level of modeling mimics what is
typically done in RCT, with mean differences between groups examined. The added
benefit of these models is the regression from Near to Far indicating that there should
be a transfer from Near to Far abilities, especially when training on the Near abilities.
This specific hypothesis of directionality is not testable given the experiment design,
but is implemented because of our hypotheses of which variable affects the other.
The model presented in Figure 2 shows that the data is split into groups
depending on condition assignment and is represented by Eq. 1 in the technical
appendix. This SEM, as implied earlier features two groups, one Trained and the other
a no-contact Control. The g superscript marks parameters in the system of equations
that may be relaxed between groups. The intercept of the transfer scores is identified by
the Greek letter μ and the error of measurement for Near and Far are n[1] and f[1]
respectively. With these elements, we are able to test the hypothesis of equal means
and variances between the groups on both the near and far transfer outcomes measured.
The added element in the Far equation has a δ parameter multiplied by the Near
score at the post-test to indicate that Near performance may have a directional effect on
21
the Far outcome variable. This is based on specific hypotheses and the direction is not
testable with the experimental design. This regression effect from Near to Far could be
affected by the training, with this link being stronger in the Trained group versus the
Control.
We start with the completely invariant model in which all parameters are held
the same across the groups and add relaxations to test model fit. The form of the model
is not changed, just the parameters are not forced to be equal in a step by step sequence.
This idea of nested models allows us to compare Chi-Square model fits from previous
iterations of the models. We compare the difference in fit (Chi-Square) per degree of
freedom (with a p-value = 0.01) to other possible models to come up with a reasonable
set of models for the data.

22
Figure 2: Models for Training Experiments

(a) A path diagram of impacts in a two-group training experiment;
(b) An Alternative Two Group SEM for a Training Experiment

23
Results of the Memory Training on Post Treatment Scores
The results of the analyses for the two group SEM analyses are presented in
Table 2 with t-values in parentheses. The data from Table 1 were used to fit the SEM
models with the Rivermead task serving as the Near variable and EPT as the Far
variable.
In model 2a the simple invariant structure is assumed for Figure 2. The
expected means for the variables can be identified for Near ( μ
n
=39.9) and Far
( μ
f
=68.4=[38.0+.761*39.9]) and are the same for both groups of participants. The Chi-
Square misfit index is, χ
2
=46 on df = 5 and RMSEA ε
a
= .114, so this is not a
satisfactory fit. In model 2b the Near score is allowed to vary between the groups
which yields a fit of χ
2
=14.5 on df = 4 and RMSEA ε
a
= .064, within the acceptable
range. The expected means of this model yield μ
n
(c)
=37.5 for the control group and
μ
n
(t)
=42.4 for the those that underwent training. This 5 point difference in expected
Near scores will also result in a difference for Far scores because of the transfer
regression. The difference is ( μ
f
=66.5=[38.0+.761*37.5]) for controls and
( μ
f
=70.3=[38.0+.761*42.4]) for the trained, or a 4 pt difference in Far transfer scores.
In model 2c the Far transfer intercept is relaxed and this yields a 2 point difference in
this variable between groups with no difference in the Near transfer scores. The model
fits for this nested model provide an acceptable improvement but not to the degree of
model 2b, χ
2
=41 on df = 4 and RMSEA ε
a
= .121. In the next run (2d) both means are
allowed to vary between groups yielding a fit of χ
2
=9.3 on df = 3 and RMSEA ε
a
= .058.
This model is the best fitting so far and now we move to see if the regression indicating
24
Near Æ Far transfer differs between groups. Model 2e then provides an increase in fit
of d χ
2
=0.9 on ddf = 1, which is not sufficient to allow us to say that the regression
coefficients differ between the groups. The final model (2f) is a fully relaxed model in
which all parameters are freed across groups, but provides no increase in model fit.
From the sequence outlined above there is a clear mean difference on both
outcome variables between the groups. We do not see any differential effect of transfer
of training because the transfer coefficient ( δ
nf
) is not different between groups. In
other words, the training does not alter the effect of the Near score on the Far score.

25
Table 2: Two Group SEM with Nested ANOVA Models

26
Chapter 4: Analysis 2 – Pre-Post Treatment Effects
Pre-Post Treatment Analysis
The next set of analyses uses the scores gathered prior to training to monitor
individual changes over time. While the participants may have been randomly assigned
to a group there may be differences in initial ability levels between groups. The benefit
for the current analyses of pre-post data is the ability to model individual changes in
performance (McArdle & Prindle, 2008). Figure 3 provides a single group
representation of the model to be fit, two groups are to be assumed as in Figure 2.
In this aspect of the analysis there are three main components to be examined:
the pre-test score, the post-test score, and the latent change experienced between the
two scores. We start with the first pre-test score of which all participants have both
scores. There are no group differences in the means of the pre-test scores and these
outcome scores are allowed to covary. Both groups should be equal at the pre-test time
point given by the common mean and there is individual measurement error for the
variable scores (n[0] and f[0]).
The next step is to examine the post-test score which is made up of the score at
the pre-test plus some unobserved change. This is done by saying that the coefficients
of the pre-test and change are 1 and the post-test score is simply the addition of these
two elements for each participant as denoted by the i subscript. The equation for this is
given in Eq. (3) of the technical appendix.
With the latent changes now put into the model, the full model can be identified
by Eq. (4) as presented in the technical appendix. These equations indicate that the

27
change comes from several different elements, a portion coming from the previous
score on the same variable and some effect from the other score that crosses over. The
direct effect of a score on itself at a later time is determined by the β coefficient and
effect of the crossed score on the change score is determined by the γ coefficient.
In implementing this model we assume that the pre-test means, variances, and
covariances are equal between groups. We are assuming that the randomization of
group assignment has worked. That is, the groups should be level at the pre-test and
one does not have an advantage over the other. While this is a strong assumption, we
could remedy any bias that may exist between groups by relaxing invariance for the pre-
test scores. Examination of the pre-test demographics and outcome variables indicates
that the groups are not vastly different in their initial scores (see Table 1). From this
point on the pre-test scores are allowed to impact the change within the variables
themselves as well as across to the other outcome score. Here we can see the direct
impact of the initial levels on the changes, the lagged and crossed elements. From
Figure 2 we carry over the regression element of Near Æ Far on the post-test scores and
apply it to the change scores. This provides a way to examine the indirect effects of the
training on the change in the Far transfer variable, as we present in our hypotheses. If
there is difference in transfer that does not appear in the crossed coefficients, it may
show in the regression between the change scores. We can allow the parameters that
are associated with the change scores to vary across groups and use the idea of nested
models to find the best fitting model.

28
Figure 3: A Bivariate Latent Change Score SEM for a Pre-Post Analysis

Results of the Memory Training on Pre-Post Treatment Scores
The results for this series analyses are given in Table 3 as applied to the same
data from Table 1. The parameter estimates are given with their t-values in parentheses.
The follow up post-test scores are added to the model to identify individual change
scores on the Near and Far varible scores. The same Rivermead and EPT measures are
used in this sequence of analyses.
The first model (3a) is the invariant model where all parameters are held equal
across groups. The expected mean scores can be calculated in the same way as done in
the previous section. By assuming these constraints the model fit is given as χ
2
=75.2 on

29
df = 14 and RMSEA ε
a
= .079, which is not satisfactory fit. In the next pair of models
(3b and 3c) the mean of the transfer scores are relaxed one at a time. This yields a fit
index of χ
2
=30.2 on df = 13 and RMSEA ε
a
= .043 when the Near transfer score is freed
and χ
2
=74.3 on df = 13 and RMSEA ε
a
= .082 when the Far transfer score is freed.
Model 3b has a good index of fit, but model 3c fits worse than the initial model. Model
3d provides a fit idex of dχ
2
=45.9 on ddf = 2 and RMSEA ε
a
= .045, when both the
transfer scores are freed at the same time. The next model (3e) then allows the beta
weights to vary between groups, which is an improvement in fit of dχ
2
=2.6 on ddf = 2,
which is not a substantial gain in fit for the degrees of freedom lost. The same is true of
model 3f, dχ
2
=.7 on ddf = 2 when compared to model 3e. The next gain is seen by
allowing the regression of the ΔNear Æ ΔFar. By allowing this parameter to vary we
improve the fit of model 3g by dχ
2
=5.9 on ddf = 1 ( δ
fn
(C)
=.064, δ
fn
(T)
=.191). The last
model (3h) frees the variances of the change scores over groups and the misfit of this
model is χ
2
=6.01 on df = 9 and RMSEA ε
a
= .017. This is an improvement over the
previous model by dχ
2
=14.1 on ddf = 2, indicating that the variances of the change
scores are different between groups. The Trained individuals had more variability in
their change scores than those with no contact.
This sequence goes beyond the previous analyses by taking into account
individual change scores, looking at where the participants started and where they are
ending. Previously we looked at mean differences in a post-test score without concern
for whether change was achieved. The only mean difference in the change scores
between groups is in the Near transfer change score. There is no observed difference in

30
the Far transfer change score. We also find that the mechanism of transfer is stronger in
the Trained group than in the Control group. And the final difference in the groups
comes in the variance of the change scores. There is more spread associated with the
Trained group, meaning the training caused more variation in change scores
experienced on the outcome measures

31
Table 3: Two Group SEM with Pre-Post Scores

32
Chapter 5: Analysis 3 – Measurement Invariance Effects
Factor Invariance Analysis
The data has multiple variables that are thought to indicate the same construct.
By including them in the analysis, we are reducing the measurement error associated
with each individual measure to more accurately track progress. In this case we have
three measures for the Near transfer and the Far transfer abilities. The set of equations
that describe the factor structure are presented in the technical appendix Eq. (5) & (6).
The common factor is identified as Near[t], with the factor loadings indicating
the strength of association to the common factor ( λ
1
, λ
2
, λ
3
). The variance term is split
into two parts, the common variance ( φ
n
2
) and the other is the variance of the unique
measures that make up the factor ( ψ
j
2
). The model is not identified without scale
specification, so we fix the first loading of each factor ( λ
1
=1), which scales the results to
match the scaling of the first variable. The same process is done with the Far transfer
factor
The difference in the Far transfer factor is that OTDL was not measured at post-
test and these parameters are forced to be the same as the pre-test score. This drop in
unique indicators means that the statistical power is not as strong as it could be if all
measures were gathered at each time point (McArdle, 1994). In testing for Factor
invariance, we start with a restrictive model in which the factors are invariant over time
and over groups (metric invariance). We then fit a model where the constraints are
dropped over the groups and compare the fit indices. We can also drop the time
constraints to see if the factor structure changes within groups as time passes.

33
Figure 4: An Invariant Common Factor SEM with a Latent Change Score

Results of Factor Invariance Tests
The results for factorial invariance are provided in Table 4 one factor at a time,
starting with the Near factor. Once again, unstandardized parameter estimates are given
with t-values in parentheses. Model 4a is invariant over time and across groups in the
Near transfer factor. The factor loadings are somewhat strong ( λ
1
=1, λ
2
=1.15, λ
3
=0.71),
there is a small change mean ( θ
Δ
= -1.37), the regression of the change on the pre-test
factor is significant ( β
Δ0
= .111), and the latent change residual ( φ
Δ
2
= 29.6). This
model yields a bad fit ( χ
2
=768 on df = 39 and RMSEA ε
a
= .163). The next model (4b)
allows for differences in the latent change scores of the Near factor. The change mean
is significantly different between groups ( θ
Δ
(c)
= -2.55, θ
Δ
(t)
= -0.13). The fit of this

34
improvement is χ
2
=733 on df = 36 and RMSEA ε
a
= .166, which is dχ
2
=35 on ddf = 3.
The next model (4c) relaxes invariance across groups but not over time. This misfit of
this model is given as χ
2
=721 on df = 34 and RMSEA ε
a
= .170, with dχ
2
= 12 on ddf = 2
from model 4b. The last model for this factor has a fit of χ
2
= 683 on df = 30 and
RMSEA ε
a
= .176, which is dχ
2
=85 on ddf = 9. There is a substantial gain in fit by
allowing the factor loadings to vary over time.
The steps outlined above are then applied to the Far transfer factor. The first
model of this series is (4d) and it provides factor loadings ( λ
4
=1, λ
5
=0.71, λ
6
=0.51), the
latent change intercept ( θ
Δ
= 1.45), regression ( β
Δ0
= -0.04), and latent change residual
variance ( φ
Δ
2
= 3.41). The fit of this model is given as χ
2
= 30.1 on df = 26 and RMSEA
ε
a
= .015. Moving onto model 4e the fit is χ
2
= 22.4 on df = 23 and RMSEA ε
a
< .001.
The model is a marginal gain in fit, as is model (4f) (dχ
2
= 1.1 on ddf = 2 from model 4e)
where invariance over groups is dropped. No gain is made by allowing loadings to vary
over time (dχ
2
= 0 on ddf = 4).
The above analysis shows us that the Far factor is invariant between groups and
over time. The same is not true of the Near factor. This sequence has indicated that
there are not only differences in the factor loadings between groups, but also over time
within the groups. This misfit is primarily evident in the Near Factor structure for the
Trained group. This provides evidence for the In addition the training procedure
seemed to help the Trained group to maintain performance over the Control group,
although not to a large degree. The last part showed no significant differences in the

35
Far transfer factor, providing evidence that the training had no effect on this aspect of
cognition, and only affected the Near transfer factor measures.

36
Table 4: Factorial Invariance Testing

37
Chapter 6: Analysis 4 – Bivariate Latent Change Scores
Bivariate Latent Change Analysis
The next set of analyses looks to combine the SEMs in Figure 3 with the factor
structure of Figure 4. The overall effect of this combination is shown in Figure 5 (see
McArdle & Prindle, 2008). The models in this section assume factorial invariance
across groups and time. This is so that the factor change scores mean that the change
we see is the difference in performance from one time point to the next. Without metric
factorial invariance the change score is not interpretable (Meredith & Horn, 2001;
McArdle, 2007).
The bivariate change model is used in the same way with the pre and post-test
scores replaced with factors. These factors are indicated by the three variables from the
previous analysis. We constrain the means of the variables to be the same over time so
that the difference scores of the latent factors indicate how much gain was made within
the factor score between the two time points. Also the metric factorial invariance is
handled by constraining the loadings of the variables on the factors to be the same
across groups and over time, hence there is no grouping superscript. The mathematical
reference to this structure is given in the technical appendix Eq. (7). We use the same
process as in Table 3 to explain model misfits but add on the factor structures with
multiple indicators for each time point. The outcome from the previous section about
the lack of invariance will be explored further in the discussion section.

38
Figure 5: A Bivariate Latent Change Score SEM with Invariant Common Factors

Results of Bivariate Latent Change Analysis
Once again, we start with the simplified model (5a), where invariance is
assumed for all of the parameters in the figure. The misfit index is χ
2
= 1780 on df = 122
and RMSEA ε
a
= .139, which is not a good fit for the data. The second and third
models free up the latent factor means on the Near and Far change scores respectively.
There is a substantial gain by freeing the Near latent change score (dχ
2
= 34 on ddf = 1)
and almost no gain by freeing the Far latent change score (dχ
2
= 1 on ddf = 1). The two
relaxations are then combined in model (5d) to provide a misfit of χ
2
= 1745 on df = 120

39
and RMSEA ε
a
= .139. Figure 5 provides the output of model (5d) with raw scores and
standardized estimates in parentheses. The Control scores are listed before the Trained
scores.
There are significant differences in the ΔNear[1] change scores ( α
n
(c)
= -2.5, α
n
(t)

= -.14). This is a 2.5 point difference is passed onto the ΔFar[1] change score, but to a
small effect ( δ
fn
= -1.52). In the ΔFar[1] change scores ( α
f
(c)
= -2.4, α
f
(t)
= 1.2) the
differences are not significant. In model 5e the lagged pre-test scores are allowed to
vary over groups and this does little to improve the model fit ( χ
2
= 1741 on df = 118 and
RMSEA ε
a
= .140). The same is true of model 5f when the crossed elements are freed
( χ
2
= 1740 on df = 118 and RMSEA ε
a
= .141). The final model (5g) allows the
regression of ΔNear[1] Æ ΔFar[1] to vary across groups and this provides a modest
improvement in fit, dχ
2
= 6 on ddf = 1 from the previous model (5f). The differences in
the regression coefficient are dissimilar but not strong effects (( δ
fn
(C)
= -1.05, δ
fn
(T)
=-
2.02).
The series of analyses outlined above provide a similar depiction of interactions
between Near and Far transfer variables as seen in Table 3. The biggest gain in fit was
freeing the Near latent change score between groups. The impact on the Far latent
change score is small because the change regression does not have a strong effect and
only presents as small difference between the Control and Trained groups. There exists
significant transfer from Near to Far, but it is not a unique feature of the Trained group
only.

40
Table 5: Bivariate Latent Change Factor Score Model

41
Chapter 7: Analysis 5 – Adding Covariates to the Models
Covariate Models
In this section we look at the effects of covariates on the previous model, as well
as the possibility that there are unobserved groups within the training program. The
covariates taken into account include, age, gender, education, and MMSE score. We
want to note if there are different effects of these variables depending on grouping. By
testing possible group differences on age, gender, education and MMSE scores, we are
introducing possible interaction terms into the equation. If evidence can be provided
that there is no difference for these variables between groups then the covariates do not
have to be included in the final model.
The second portion of this extended analysis looks at the Trained group to test
for group homogeneity. This testing process uses latent class logic (implemented in the
M-plus program) to divide the participants within the Trained group based on certain
parameters that we think they may differ on. This will yield groups of individuals with
different patterns of change. This latent mixture modeling provides a clue as to whether
we should treat the Trained group as one pure group, or if there are two or more groups
within the overall group.
Results of Covariate Analysis
The two group models with covariates are presented in Table 6. The first model
is the same baseline model as in Table 5, with covariates added to the pre-test scores
and to the latent change scores. The only effect that shows as significant is that of the
mean of the Near transfer change ( α
n Δ
= -1.61). Age (centered at 75 in decade units) is

42
negatively associated with the pre-test score (Age Æ Near [0] = -6.20 and Age Æ Far
[0] = -6.88) and positively associated with the Far change score (Age Æ ΔFar [1] =
1.41). Education (centered at 12 by year units) only impacts the pre-test scores
(Education Æ Near [0] = .85 and Education Æ Far [0] = 2.14). Gender was half effect
coded towards females and has a positive effect on the pre-test scores (Gender Æ Near
[0] = 7.42 and Gender Æ Far [0] = 3.04). There is a negative impact of Gender on post-
test change score for the Far transfer factor (Gender Æ ΔNear [1] = -1.18). The MMSE
score (centered at 27) was positively associated with the pre-test scores (Gender Æ
Near [0] = 2.52 and Gender Æ Far [0] = 4.57) and negatively associated with the Near
post-test change score (Gender Æ ΔNear [1] = -.847).
In the next model (6b) the mean change scores of the factors were freed between
groups. The mean of ΔNear is significantly higher for the Trained group compared to
the Control group. The effects of the Covariates have not changed but the model does
have a significant gain in fit over the previous one at α=0.01 (dχ
2
= 33 on ddf = 2). In
the final model we have the effects of the covariates allowed to vary over the changes.
The increase in fit is not enough to make this step significant (dχ
2
= 7 on ddf = 8). We
can note that the effect of gender on the Near transfer change score is significant at
α=0.01 in the Trained group (Gender Æ ΔNear
(t)
[1] = -1.82). The Training group sees
a decrease in Near changes for females compared to males, which is not seen in the
Control group.
The covariates are added to the model in order to see if the training programs
may have been affected by other variables we could not account for. These effects are

43
those that are not a direct result of the experiment design, but may have interacted with
it. In our case age and education had minor effects in latent change scores that helped
people that were younger and had more education, but these trends were not significant.
MMSE score and gender were significant and favored females and lower MMSE score
for more change in the factor scores.

44
Table 6: Bivariate Latent Change Score Models with Covariates

45
Chapter 8: Discussion
The analyses of this research offer a contemporary alternatives to the mean
differences performed in the previous RCT analyses (Ball et al., 2002; Willis et al.,
2006). Group randomization built into the design of the study is beneficial to making a
causal inference about the effects of the training programs (Fisher, 1928). The
traditional viewpoint on RTC looks to compare mean differences between groups to test
treatment effects (see Ball et al., 2002; Willis et al., 2006), and do not examine the
dynamics associated with change due to treatments(as in Cnaan, Laird, & Slasor, 1997).
Even with this procedure the mean differences between groups may not be enough to
provide evidence of training effects based on group association because this may not be
apparent in the mean scores.
The analyses of this paper are novel because they focused on the Memory
Trained group and the No-Contact control group. The first model (Table 2) shows an
effect of training on the Near variable for the Trained group over the Controls and a
significant transfer of training (Near Æ Far) with α=0.01, with no difference between
the groups in amount of transfer. The next model (Table 3) adds latent changes to the
SEM and indicates that training only has an effect on the Near variable and the transfer
of training is smaller than in the previous model. The following SEM (Table 4)
examines the factor structure of the Near and Far factors and the latent change score of
both. The Near factor shows less decline in the latent change score, but it also indicates
that the factor structure varies over time and across groups. The Far factor shows no
training effects in the latent change score and is invariant over time and across groups.

46
The next model (Table 5) assumes factorial invariance and the Near training effect is
still apparent. The transfer of training effect is not significant in the bivariate factor
model. When the covariates are added into the model (Table 6) MMSE score has an
effect on the Near latent change score, but gender is only significant in the trained
group. The Latent Mixture Model (Table 7) provided evidence for participants with
higher MMSE scores and Education years to have a higher Far change score and a
lower Near change score. Age and Sex had no significant effect on the LMM
classifications. The lack of invariance in the Near factor structure across and within is
one of the key findings in these results.
The last two analyses (Table 6 and Table 7) are more exploratory in their
implementation. For Model (6) we add covariates to test for interactions that may occur
with the training program. While this list is not exhaustive, these are common
demographic variables that provide the most potential for influence. The LMM in itself
is a highly exploratory process in itself and has received criticism in its inability to
accurately classify participants (Bauer & Curran, 2003). These results, while not
definitive, provide some insight for future research.
The invariance issue is of concern for the bivariate factor model (Table 5) and
what those results mean. In the bivariate model, factorial invariance is assumed and
from the previous analysis (Table 4) the invariance assumption does not hold for the
Near factor. Given this result we cannot say that the same factor is measured over time
for the two groups. The factor structure is modified by the training specifically, the
loading for the Rivermead task is most notably different over time. When this variable

47
is allowed to vary across time gains in fit are significant by our specified alpha level.
One possibility is the process which the Trained participants do the Rivermead task
changes as they use one strategy before training and a new strategy after the training is
complete. In this way the variable is not measuring the same ability over time. This is
of critical concern if we want to measure any kind of change in performance within a
given domain. We cannot be sure that change is being experienced if the scale of
measurement changes with each testing.
Given this conclusion the outcome variables used must be reexamined to
determine they are actually capturing the construct of memory. These results indicate
that HVLT and AVLT are consistent over time and Rivermead is the one that changes
with training. The different mediums of the tasks may provide the difference in
performance over time. The HVLT and AVLT are both text based and not as applicable
to everyday activities. The Rivermead task on the other hand is more visualization and
seems to be affected by the training, as evidence by the change in the loading through
time within the factor structure. A memory construct would do well to incorporate all
of the four components (meaningfulness, organization, visualization, and association) as
individual indicators for the Memory factor. The training focuses on these elements and
the factor should work to see how well these specific aims were met.
Final Thoughts
The lack of invariance in the Near factor is only one issue to be explored further
within this dataset. In addition to the Memory Trained group there are also Speed of
Processing and Reasoning training groups that participants were randomly assigned to.

48
Future analyses can include these groups, and can be extended to examine performance
on all factors within each group. From this perspective we can examine the possibility
of leakage of training from one realm to another. For example, Memory training may
also enhance Speed of Processing performance through repeated practice. Further
issues that exist are put forth by the Latent Mixture Model analysis presented earlier.
Not only are there subgroups that were affected differentially within the training, but
were there differences between those that completed the training, or the trial on a
broader scope. These ideas along with the availability of one year, two year and soon to
be five year follow-up data points provide extensions of the models presented.
The need to go further is not exactly clear given the initial ACTIVE report in
which the two year data was analyzed (Ball et al., 2002). Here there was no transfer of
training gains to the Far outcome measures. Then in Willis et al. (2006) there is a
significant transfer effect where the Reasoning training provides a significant effect on
IADL. This sleeper effect has not been shown to exist in psychology since it was first
coined in Hovland, Lumsdaine, and Sheffield (1949) and it is not explained why this
one effect would pop out five years after training. In this instance the training has more
persuasive power over the Far abilities as time goes on, but there is no hypothesis as to
why this should be the case. An extension of the SEMs to include more time points as
they become available should help identify if this “sleeper effect” is visible at the factor
level.

49
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53
Technical Appendix
The Equations listed below correspond to the figures and analyses carried out in
the attached paper. The Near and Far scores for Rivermead and EPT respectively are
given as the following system of equations:
(1)
) ( ) (
1
) (
] 1 [ ] 1 [
g
i
g
n
g
i
n Near + = μ and

) ( ) ( ) (
1
) (
] 1 [ ] 1 [ ] 1 [
g
i
g
i fn
g
f
g
i
f Near Far + + = δ μ .
They indicate that each score is synthesized from a group mean score ( μ) plus some
individual error denoted by n and f. The Far item has the additional effect of Near on
its score derivation because of our hypothesized directional effect of Near onto Far.
This set of equations is represented visually in Figure (2a). We test this model by
holding all parameters equal over groups and then progressively relax these constraints
until satisfactory fit is reached.
The next series of models are combinations of one another to show how the
latent change score can be derived. Equation (2) is presented as:
(2)
i n i
n Near ] 0 [ ] 0 [ + = μ and

i f i
f Far ] 0 [ ] 0 [ + = μ .
These simultaneous equations define the parameters of the pre-test Near and Far scores.
Once again there is a group mean ( μ) that indicates the average score for each variable
plus some individual error score that each individual has. We then model the post-test
score as a function of this pre-test score:
(3)
) ( ) (
] 1 [ ] 0 [ ] 1 [
g
i i
g
i
Near Near Near Δ + = and

54

) ( ) (
] 1 [ ] 0 [ ] 1 [
g
i i
g
i
Far Far Far Δ + = .
Here we see that the post-test score is a function of the pre-test score plus whatever
change has been experienced between the two time points. These scores are based on
individual performance and the error in measurement is associated with the pre-test
score and we can rearrange the equations so that the latent change is on the left hand
side. The system of equations for the latent change scores are now given as:
(4)
) ( ) ( ) ( ) ( ) (
1
) (
] 1 [ ] 0 [ ] 0 [ ] 1 [
g
i
g
i
g
fn i
g
n
g
n
g
i
n Far Near Near + + + = Δ γ β α and
) ( ) ( ) ( ) ( ) ( ) ( ) (
1
) (
] 1 [ ] 1 [ ] 0 [ ] 0 [ ] 1 [
g
i
g
i
g
fn
g
i
g
fn i
g
f
g
f
g
i
f Near Near Far Far + + + + = Δ δ γ β α
Now the latent change scores are given as a mean score ( α) plus some effect from the
pre-test score on the lagged element ( β) and the cross-lagged element ( γ). Additionally
the regressive component of Near onto Far is added to the model as was done in
Equation (1) to represented the hypothesized effect of Near transfer to Far from training.
The next set of equations uses three outcome variables from each construct to
form a factor score for the Far and Near factors. The three that produce the Near factor
are AVLT, HVLT and Rivermead and represented by the following series of equations:
(5)
i i i
t n t Near t AV ] [ ] [ ] [
1 1
+ = λ ,

i i i
t n t Near t HV ] [ ] [ ] [
2 2
+ = λ , and

i i i
t n t Near t RM ] [ ] [ ] [
3 3
+ = λ .
These equations indicate that the Near factor is common to all of the variables to an
extent weighted by the loadings lambda ( λ). The residuals given by n are the unique
variances of the variables uncorrelated with the other variables in the model. The

55
model tests that the same factor structure exists over time and between groups (see
Figure 4 for a topographical representation). When we can assume that the factor
structure is invariant then the latent change score can be read as a true change in
performance on the factor in question.
The next set of equations is those for the Far factor. The same SEM as outlined
above is implemented here on the three Far indicators, EPT, OTDL, and TIADL. Then
same set of assumptions are used for SEM specification and for testing invariance of the
factor over time and between groups.
(6)
i i i
t n t Far t EPT ] [ ] [ ] [
4 4
+ = λ ,

i i i
t n t Far t OTDL ] [ ] [ ] [
5 5
+ = λ , and

i i i
t n t Far t TIADL ] [ ] [ ] [
6 6
+ = λ .
The following system of equations is a combination of the previous two models,
model (3) and model (4). Here the Far and Near latent change scores are given a
function of the Far and Near factors at pre-test and post-test. The lambda ( Λ) in this
case is a vector of the three loadings for each of the indicators. The same format for the
derivation of the latent change score is the same with a mean score followed by the
lagged and then cross-lagged element. The regression of Far on Near is added tot eh
Far equation to implement the transfer of training from Near to Far.
(7)
) ( ) ( ) ( ) ( ) (
1
) (
] 1 [ ] 0 [ ] 0 [ ] 1 [
g
i
g
i f
g
fn i n
g
n
g
n
g
i
n Far Near Near + Λ + Λ + = Δ γ β α and
) ( ) ( ) ( ) ( ) ( ) ( ) (
1
) (
] 1 [ ] 1 [ ] 0 [ ] 0 [ ] 1 [
g
i
g
i n
g
fn
g
i n
g
fn i f
g
f
g
f
g
i
f Near Near Far Far + Λ + Λ + Λ + = Δ δ γ β α

Abstract (if available)

Abstract Latent Change Score models are used to examine training effects in a randomized clinical trial on memory training (see McArdle & Prindle, 2008). Data are taken from the Memory and Control groups of ACTIVE (Jobe, Smith, Ball, et al., 2001). First, we examined mean differences in SEMs and find training effects within the trained domain (memory) and transfer to everyday problem solving present for both groups. Second, pre-post test latent change score models find mean training effects for the memory variable with less transfer of training. Third, we use two common factor models to test measurement. Standard likelihood ratio testing suggests invariant loadings do not fit the Near factor but fit the Far factor. Fourth, a latent change score model with common factors did not offer any new information over previous models. Implications and ideas for future analyses are presented in the discussion section.

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Asset Metadata

Creator Prindle, John Janson (author)

Core Title Latent change score analysis of the impacts of memory training in the elderly from a randomized clinical trial

School College of Letters, Arts and Sciences

Degree Master of Arts

Degree Program Psychology

Publication Date 12/01/2008

Defense Date 10/15/2008

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag active,cognitive training,latent change score,memory,OAI-PMH Harvest,SEM

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor McArdle, John J. (committee chair), Walsh, David A. (committee member), Wilcox, Rand R. (committee member)

Creator Email janson.prindle@gmail.com,jprindle@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m1841

Unique identifier UC1229188

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Legacy Identifier etd-Prindle-2486.pdf

Dmrecord 128218

Document Type Thesis

Rights Prindle, John Janson

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu