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Dynamic analyses of the interrelationship between mothers and daughters on a measure of depressive symptoms

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Dynamic analyses of the interrelationship between mothers and daughters on a measure of depressive symptoms

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DYNAMIC ANALYSES OF THE INTERRELATIONSHIP BETWEEN MOTHERS
AND DAUGHTERS ON A MEASURE OF DEPRESSIVE SYMPTOMS

by

Ricardo Reyes

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

May 2010

Copyright 2010 Ricardo Reyes

ii

Dedication
To my parents

iii

Acknowledgments
I would like to thank my advisor, Jack McArdle, for all the help and for
continually reminding me to appreciate the intricacy of every analysis we run.
Additionally, I thank Merril Silverstein for all of the helpful suggestions along the way.

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 7

Chapter 3: Analysis 1 – Cross Lagged Regression 11

Chapter 4: Analysis 2 – Measurement Selection 16

Chapter 5: Analysis 3 – Measurement Models 19

Chapter 6: Analysis 4 – Extended Measurement Models 23
Chapter 7: Discussion 29

Bibliography 34

Appendices 38
Appendix A: Dyad Selection 38
Appendix B: Correlations for All Variables 39

Appendix C: Promax-rotated Exploratory Factor Loadings 40

Appendix D: Individual Trajectories 42

Appendix E: Mplus Script for Analyses 43

v

List of Tables
Table 1: Mother and Daughter Descriptive Statistics at Time 2 10
Table 2: Cross and Lagged Regression Model Fits 15
Table 3: Measurement Model Cross-Lagged SEM Fits 22
Table 4: Six-Wave Measurement Model Cross-Lagged SEM Fits 27
Table 5: Six-Wave Measurement Model SEM with Incomplete Data 28

vi

List of Figures
Figure 1: Depressed Feelings Reported by Mothers and Daughters at Time 2 10
Figure 2: Cross and Lagged Regression Models 13
Figure 3: One Factor Model of Depressive Affect with Four Items from the CESD 18
Figure 4: Metrically Invariant Common Factor SEMs at Two Times 20
Figure 5: Metrically Invariant Common Factor SEM at Six Times 25

vii

Abstract
Much prior research has attempted to analyze a reciprocal dynamic relationship
between older parents and their adult children. Mothers are generally more invested in
their children’s lives and the relationship between mother and adult daughter has been
shown to have more emotional ties than that between a mother and her adult son. The
goals of this study are to explore the dynamic interrelationship between mother and
daughter on depressive symptomatology using longitudinal data. The focal data are
based on mothers (mean age = 56) and their biological daughters (mean age = 32) from
the University of Southern California’s Longitudinal Study of Generations (LSOG). Four
kinds of structural equation model (SEM) analyses are presented in order of complexity
and each are designed to develop and test specific dynamic structural equation model
hypotheses. The model fits of varying dynamic cross-lagged SEMs are compared for
goodness-of-fit to various forms of the LSOG data. An initial two-time point regression
based model suggests an adult daughter’s depressive affect to be a leading indicator of
her older mother’s depressive symptoms. However, more complex models using more of
the available data and advances in measurement models suggest the directionality of such
developmental processes are not so simple or uniform. Substantive results are discussed
as they pertain to all the models in the paper.

1
Chapter 1: Introduction
Family Research
Family influence and generational transmission remains a highly popular topic for
continued research. Early modern sociologists suggested that the nature of social order
was related to interactions of kin and the accompanying sharing of values and bonds
(Durkheim, 1984). The American family expectedly plays an important role on the
socialization and psychological formation of its successive generations. Among many
others, Vern Bengston, in his work highlighting relevant topics in both the nuclear and
extended family, reminds us that all family research can serve two purposes. It can
answer broad questions asked by social theorists about societal continuity and change as
well as add more (Bengtson, Biblarz, & Roberts, 2002; Bengtson, Furlong, & Laufer,
1974).
Other researchers examine a myriad of familial relationship related issues and
have helped fuel an increase in understanding of the family as a unit of analysis. We
know, for example, that research can consider potential mother/father differences in the
influence their values and attitudes have on their offspring and also how it might differ
between offspring gender (Roest, Dubas & Gerris, 2009). Moreover, a warm parent was
found to motivate children to actively become more similar to their parent (Grusec,
Goodnow, & Kuczynski, 2000). Important work on the heterogeneous nature of
intergenerational family types adds that statements about a ‘modal’ type may be
misleading; family types are diverse (Silverstein & Bengston, 1997). Every seminal
contribution to family literature adds a new layer of intricacy to the familial issues that
2
could guide many aspects of our personal, social and professional lives directly and
indirectly.
A reciprocal relationship
Richard Bell (1968) emphasized the importance of considering reciprocally
dynamic family relationships. Noting that early models of parental socialization were too
simplistic, Bell argued for the emphasis on analyses which take into account the effects
of children on parental behavior. Child to parent relationships should not be included as
potential confounds to research, but instead be a focus of the analyses in family studies
(Bell, 1968, pp. 82). In this view, the child is an important part of the parents’ lives as
well.
Unhappy with the lackluster explanatory potential of non-reciprocal methods, the
research community agrees that Bell’s paper provided a solid theoretical framework
which could be applied to statistical cross panel techniques being developed at about the
same time (Cambell & Stanley, 1963, as cited in Kenny 1975).
The Mother and Daughter Relationship
Much like the idea of a typical American household being confounded by distinct
familial characteristics, parent/child relationships do not adhere to one general typology
either (Silverstein & Bengston, 1997). Research methodologies considering the unique
relationship between differing family dyads has led many researchers to conclude that the
mother-daughter dyad is not equal to the mother-son, father-daughter or father-son dyad,
for example. And although the idea that the four possible dyads are entirely distinct is
still under much scientific discussion, family studies continually point out influential
differences between them.
3
Nonetheless, another body of research has focused specifically on the relationship
between mothers and daughters. Bassoff, in a paper dedicated entirely to the mother and
daughter relationship, describes that the similarities between a mother and her daughter
create a special bond that is unlike any other parent-child connection (Bassoff, 1987, as
cited in Russell & Saebel 1997). Debold, Wilson and Malave (1993) describe the mother
and daughter connection as key to a daughter’s developmental adjustment (as cited in
Russell & Saebel 1997). Silverstein and Bengston (1997) found adult children, and
especially daughters, are important in the life of their mother.
Another recent finding focuses not only on the uniqueness of the relationship but
also on the idea that mothers might actually favor their emotional ties with their
daughter(s) more. Suitor and Pillemer (2006) use measurement tools which avoid the
masking of favorites by forcing choices and not allowing participant women to rate all
their children equally. The authors conclude that older mothers tend to prefer talking
about problems with their adult daughter, would choose their adult daughter over son for
help, and would turn to their adult daughter first in crisis. Additionally, mothers reported
feeling emotionally closest to their daughters. Differences between mother-daughter and
mother-son relationships were partially attributed to similarities present in the all-female
relationship (Pillemer & Suitor 2000; Pillemer & Suitor 2006).
Depressive Symptoms
Consequences
Individuals exhibiting depressive symptoms will suffer degradation in their
quality of life. Our concepts and understanding of depressed feelings are inseparably
attached to the obvious negative ramifications of extended periods of the undesirable
4
mood state. A clinical diagnosis of major depressive disorder in the Diagnostic and
Statistical Manual of Mental Disorders-IV-TR can be given based on feelings of
worthlessness, frequently occurring depressed mood, lack of interest and other symptoms
(American Psychiatric Association, 2000).
An increasing amount of research on the effects of depressed affect on older
adults adds new elements of worry. In elderly populations, depression has been
statistically linked to onset of dementia (Reding, Haycock, & Blass, 1985). Additionally,
depressive symptoms combined with poor physical health have been shown to increase
mortality in women aged 65 and older (Fredman et. al., 1999). Blazer, in a 2003 review
of gerontological research, reports similar findings across the literature. Another study
replicated these findings in a Taiwanese sample of elder adults (Collins, Glei, &
Goldman, 2009).
Family application
Depressive symptom research in the familial context has been limited to the
examination of parental transfer to adolescent children (Shrier, Tompsett, & Shrier,
2004). Adolescent children of depressed mothers tend to show more negative
interpersonal behavior and cognitions (Hammen & Brennan, 2001). Weissman et. al.
found higher prevalence of depression in children whose parents were depressed
(Weissman et. al., 1987).
Current Research Plan
Older parents and their adult children are both at important parts of the human
lifespan. Since older adults have a natural concern for their health the aforementioned
studies linking depressive affect to mortality emphasize that understanding the influence
5
family members may have on one another is of scientific importance. Moreover, a focus
of some care-giving literature is on the adult daughter tending to her older mother.
Adolescent research examining parental influences on depression illustrates the societal
relevance and need to model similar studies with data from older populations.
The current study uses Structural Equation Models (SEMs) to fit dynamic models
of the interrelationship between adult daughters and their older mothers on a measure of
depressive symptoms. We hypothesize that both mother and adult daughter will influence
one another dynamically. Also we expect mother influence will be greater than daughter
influence.
These analyses start with a simple cross-lagged regression SEM model utilizing
depressive symptom composite scores and tests dynamic hypotheses about the mother
and daughter relationship (following Kenny, 1979). We examine how mother or adult
daughter depressive affect item responses at one time might predict the other’s response
at the next time of collection.
The second set of analyses adds a factor analytic structure to the data to establish
a simple one-factor measurement model that might be appropriate for use in
intergenerational family models. After a one common factor model as indicated by
specific items is selected, we implicitly model it into the cross-lagged analyses and retest
dynamic hypotheses about the mother and daughter relationship in both a simple 2 time
point model (Analysis 3) and one utilizing all available time points (Analysis 4). Of
course, these are contemporary applications of latent variable path models (see McArdle
& Prescott, 1992). These structurally more complex models attempt to remove the effects
of measurement bias by restricting all measurement to be equal at every time for both
6
mothers and daughters. A final model is presented where incomplete data are considered
(after McArdle, 1994). Mplus software is used for computation of all models and scripts
are included in the Appendix.

7
Chapter 2: Study Methods and Procedures
Participants
Initial sample selection and procedure
The current study uses participant data from the University of Southern
California’s Longitudinal Study of Generations (LSOG; Bengston, Silverstein &
Giarusso, 1995). The research project began data collection in 1971 and focuses on the
intergenerational family. Three hundred three-generation Californian families were
randomly selected for inclusion from a list of 840,000 health maintenance organization
members in Los Angeles. Families were included into the study if the family had a
grandfather (G1) who was over the age of 60 and had a three-generation family; his
children would be considered G2’s and their children G3’s. Since the study’s beginning,
some members have moved to different parts of the country and another small percentage
has gone overseas (2%).
The project began with N=2044 participants in 1971, collected its second wave of
data in 1985, and has decreased with time to about n=1766 participants in its most recent
data collection year, 2005. As expected in any longitudinal study, response rate has
fluctuated a little but has remained in between about 65 and 74 percent each collection
year. Since wave 2 of collection in 1985, data has been collected in survey form every 3
years until 2000 and then again in 2004 (Bengston et. al., 1995).
All participants were mailed a survey. In the multi-page survey, data for many
scales was collected. Mental health scales are included as are a variety of other measures
including self-reported health, family relationships, feelings of filial responsibility, and

8
demographic information as examples. Some of the measures included are empirically
tested and others were included with little structural analysis done beforehand.
Depressive affect data
The earliest data collection period containing the Center for Epidemiological
Studies Depression (CES-D) inventory (Radloff, 1977) is time two in 1985. It was also
administered at each successive collection period up to the most recent in 2004. Data
from time 8 (2004) is still being processed and is not included for analyses. This study
includes CES-D data collected at six different time points with three-year intervals of
time between them (waves 2 – 7). In each survey, the 20 CES-D items are scored on a 1
to 4 Likert scale ranging from rarely or none of the time to most or all of the time. Each
item asks the respondent to rate how frequently in the past week they experienced a
particular feeling or thought (like sadness or loneliness).
In a first model we use eight items that are sometimes created as a composite
score and sum them up for each mother and daughter (CESD-8; see Van de Velde et. al.).
Selection criteria for analysis 1-4
The inclusion criteria for these analyses were as follow. First, all daughters (G3)
measured at least once during the six time points were selected. Next, each daughter was
paired with her G2 mother’s data. A mother was paired to her daughter if she was also
measured at least once during the 1985 to 2000 collection waves. Because sibling
daughters in the study could have the same mother, steps were taken to avoid dependence
of observations. A SAS script was written so that amongst sibling sisters only one would
be randomly chosen for inclusion (included in Appendix). A total of 250 pairs were
formulated with this criteria; it allows inclusion of incomplete measurements in the dyads
9
and this produces 146 different patterns of incompleteness. Different incompleteness
pattern information including pattern frequencies can be seen in the Appendix. The use of
this incomplete data set is reasonable since fitting incomplete data using likelihood
estimation techniques can estimate SEMs as if everyone had participated (McArdle,
1994).
If only complete dyads are considered, those with 6 complete waves of data for
both mother and daughter, only 78 pairs will be examined. The decrease in sample size
could pose a problem with more complex SEMs but will be considered in analyses. For
all models, complete dyad data is used unless specifically mentioned otherwise.
Mothers included for analyses were on average 56 years old at wave 2 collection
and their daughters 32. At each succeeding time point, a three year increase in age is to
be expected; data was collected approximately every three years. Additionally, table 1
shows marital status percentages, number of children and self-rated health at time 2.
Figures 1a-1b show distribution of scores for mothers and daughters on one key CES-D
item and include means and standard deviations; the nth question asks individuals to
indicate how often they felt depressed in the week prior to reporting. The distributions
show a positive skew with a tendency for both dyad members to indicate they rarely felt
depressed.

10
Table 1: Mother and Daughter Descriptive Statistics at Time 2
% Married #Children Age S-R Health
Gen2(Mothers) 81.5 3.9 (1.8) 56 (4.6) 1.8 (.75)
Gen3(Daughters) 67.7 1.7 (1.4) 33 (2.8) 1.8 (.73)
(Standard Deviation); S-R Health (Self-Rated)

Figure 1: Depressed Feelings Reported by Mothers and Daughters at Time 2

(a)
(b)
11
Chapter 3: Analysis 1 – Cross Lagged Regression
Two Time Points
To examine the dynamic relationship between mothers and adult daughters on
depressive affect (symptomatology), we start by fitting a series of simple cross and
lagged regression models to the complete cases participant CESD-8 data from only time
waves 6 and 7. The average ages in dyads at time six are 68 and 45 (mothers and
daughters, respectively). Aside from the simplicity of estimating parameters for this
model, it allows the testing of several key hypotheses about dynamic coupling
relationships. The SEM will test (1) whether or not there is a dynamic predictive
relationship between mothers’ and daughters’ depression scores, (2) whether the
influences from one to the other are equal and (3) whether either mother or daughter
leads the other’s score from time 6 to time 7. The resulting model comparisons go beyond
the traditional unidirectional mother to offspring model; they include the possibility that
the daughter is influencing the mother.
Figures 2a-2d shows four hypotheses that can be tested with this cross and lagged
approach. With the cross coefficients (γ’s) both constrained to zero as is shown in Figure
2a, we can estimate the statistical fit of a relationship model where neither a mother nor a
daughter time 6 data affects her daughter or mother’s score, respectively, at time 7 (a
baseline test of no dynamic relationship). This is followed by a model where the γ’s from
both dyad members at time 6 to time 7 are forced to be equal. This model, γ
m
= γ
d
, tests
that there is a dynamic relationship between mothers and daughters but each affects the
other equally with neither mother nor daughter leading the influential relationship by
herself (2b). The equal gamma model is seldom testable in dynamic modeling; in using
12
the same items from the CESD-8 we gain the ability to use this extra test because we
assume we are measuring the same thing (McArdle & Hamagami, 2007).
Two more models can be tested and are each a key test saying only one dyad
member influences the other. To test whether one dyad member leads the other in
influence, models where one gamma is constrained to zero can be run; a mother might
lead her daughter’s depressive score but not vice versa (see Figure 2c), for example.
Conversely we could also determine that only a daughter leads her mother’s symptom
scores by accepting the structural hypothesis shown in Figure 2d.
Since each of the cross and lagged models are nested within one another,
goodness of fit statistics are compared to determine which model best fits our data.
Utilizing Chi-Square difference tests with a predetermined probability value of .05, we
conclude which model best fits our data by examining χ
2
changes as a function of change
in degrees of freedom (Browne & Cudeck, 1993).

13
Figure 2: Cross and Lagged Regression Models

(a) No dynamic relationship model; (b) Both mother and daughter at t6 influence one
another’s t7 score; (c) Only mothers have an influential effect; (d) Only daughters have
an influential effect
Note: Time is shown as t1 and t2 instead of 6 and 7.

(c)
(a) (b)
(d)
14
Results of the Two Time Point Cross and Lagged Regression
Table 2 allows comparison between the statistical fit of each of the SEMs shown
in Figure 2 and discussed in the previous section. All fit statistics are estimated using the
aforementioned models with cesd-8 composite scores for both mothers and daughters.
Model 2a tests that there is no dynamic relationship on cesd-8 scores between
mothers and adult daughters. Both γ cross coefficients are forced to zero. This produces a
fit of χ
2
=5.8 on df = 2 and RMSEA ε
a
= .11. The RMSEA suggests that this model is not
a close fit to our data. Model 2b tests the hypothesis of equal influence. This model fits
the data reasonably well, χ
2
=.5 on df = 1 and RMSEA ε
a
= 0.
Model 2c and 2d examine whether one member in our mother daughter dyad
leads the dynamic relationship. Testing whether the mother depressive symptoms leads
the predictive relationship (2c, no D->M influence) results in an unexpected statistical fit
decrease [compared to 2a]. For a one df change, chi-square statistic remains the same but
probability of close fit as measured by RMSEA is worse (χ
2
=5.5, df =1, ε
a
= .17). In
model 2c mother to daughter cross coefficient is set to zero and daughter to mother effect
is freely estimated. In this model, the goodness of fit improves to a satisfactory level
(χ
2
=.03 on df = 1 and RMSEA ε
a
= .00).
Model 2d which suggests that daughter depressive symptom scores at time 6
predict mother scores at time 7 with no cross from mother to daughter best fit our data.
This model had a larger estimated probability of perfect fit and a better confidence
boundary for RMSEA (see Table 2). Picking this as the best fitting model suggests that
mother depressive symptoms do not lead daughter depressive symptoms; daughter cesd-8
scores do lead mother scores (γ
d
=

.12,
γ
m
=

0). In other words, an adult daughter’s
15
depressive symptoms score is a positive putative leading indicator of her mother’s
depressive symptoms at a later time.

Table 2: Cross and Lagged Regression Model Fits
Statistic

No
Restrictions

No
Coupling

(a)

γ
m
= γ
d

(b)

No
D-‐>M

(c)

No
M-‐>D

(d)

X
2

0
5.8
.50
5.5
.03

df
0
2
1
1
1

P(perfect)
-‐
.06
.49
.02
.61

RMSEA
-‐
.11
.00
.17
.00

-‐90%(rmsea)
-‐
.00
.00
.06
.00

+90%(rmsea)
-‐
.22
.19
.32
.17

P(close)
-‐
.12
.57
.05
.67

γ
m

.05
0
.10*
.05
0

γ
d

.12*
0
.10*
0
.12*

* = statistically significant at .05 level

16
Chapter 4: Analysis 2 – Measurement Selection
Factor Analysis and Item Selection
The next analysis attempts to better the use of depressive symptom items from the
CES-D scale for specific application to our study’s sample. Although, the CESD-8 has
been tested for general use with older populations (see Van de Velde et. al.), participants
in LSOG assumedly undergo many changes from years 1985 to 2000. Considering adult
daughters in the study started at a mean age of 32, interpretation and endorsement of
particular items could differ between mother and daughter. This idea has led many
researchers who use this scale to seek item arrangements which may be better suited for
use in specific populations (Knight et. al, 1997).
One benefit of using an empirically tested factor structure with the CES-D scale is
potential comparison to other related work with those items. For an adult-daughter and
mother sample, we decide to seek the most parsimonious and concise set of items that
will both fit our data and potentially facilitate more complex modeling of this dyadic
longitudinal relationship.
We begin with an exploratory factor analysis utilizing all 20 original CES-D items
for all 2
nd
and 3
rd
generation females in the LSOG study at time 2. Modern work in SEM
estimation techniques allows the use of estimation procedures which take into account the
categorical nature of 4-level CES-D items (Muthen & Kaplan, 1985). We also specify an
oblique Promax rotation algorithm with the assumption that the different factors of
depression measured in the scale are correlated and non-orthogonal.
The next step was to determine how many measurement factors are in the CES-D.
In a first exploration, we estimated eigenvalues, and selected those which are over or very
17
close to 1 (following Kaiser, 1968; Horn, 1973). Similar to existing research, we estimate
there to be at least three but probably four factors measured with the scale. Three
eigenvalues are greater than 1 and the fourth is .91. The Appendix shows estimated
exploratory rotated factor structures for three and four factor models of the depression
scale.
Keeping in mind our goal to choose a small set of items that could be considered
as measuring depressive symptomatology, we look only for items that load on the same
factor as the ‘felt depressed’ item in the four factor estimation. Other criteria for item
selection into our desired factor are that it’s loading is greater than .50 and that it does not
cross load with another factor greater than .30. Several items meet these criteria but only
four are chosen: blues, depressed, lonely and sad.
Although other items load on what looks to be depressive affect factor, we decide
to limit the number of items to four; those that make most intuitive sense are included. To
verify that the selected items will prove adequate for use with adult-daughter/mother
dyads, a restricted analysis for this depressive affect factor is run. For model
identification purposes, the loading of the first item is set to one (λ
1
=1) and the remaining
3 loadings are scaled to that item (λ
2
, λ
3
, λ
4
). Model fit is good and the four items load
strongly on the one factor, χ
2
=3.2 on df = 2, RMSEA ε
a
= .03 (λ
1
=1, λ
2
=1.08, λ
3
=0.87,
λ
4
=0.94). The relatively good fit of this factor model suggests that the four items chosen
can be used for modeling with two different generations of women. Additionally, each of
the four items has loaded on depressed affect factor in several other reputable studies’
factor analyses (Gatz & Hurwicz, 1990; McArdle et. al., 2001). As a result we choose the
items about feeling blue, depressed, lonely, and sad (see Figure 3).
18

Figure 3: One Factor Model of Depressive Affect with Four Items from the CESD

Four categorical items loading on depressive affect.

19
Chapter 5: Analysis 3 – Measurement Models
Adding Measurement Invariance
Utilizing the four items selected as most parsimoniously fitting the mother and
daughter data, measurement invariance is added to the two-time point model already
described. The same series of models is fit and each of the coupling hypotheses is tested
in the same order. Figures 4a- 4d depict the same key coupling tests but demonstrates
how the models are fit utilizing metric invariance.
Because the model introduces the use of the CES-D items as categorical variables,
means-adjusted weighted least squares estimation is used for model estimation (WLSM;
Muthen, 1983). The inclusion of measurement invariance into this model constrains all
item loadings for each item to be equal across time and across mothers and daughters (see
McArdle, 2007). By utilizing an invariant measurement model for the dyads at all time
points, we assert that ‘depressive affect’ as measured by the four CES-D items is the
same latent factor at each occasion. We fit the measurement model SEM to eliminate the
effects of measurement bias and to allow only the effects of our latent construct,
depressive affect, to affect model results (Meredith & Horn, 2001).

20
Figure 3: Metrically Invariant Common Factor SEMs at Two Times

(a) (b)
(c) (d)
21
(a) No dynamic relationship model; (b) Both mother and daughter at t6 influence one
another’s t7 score; (c) Only mothers have an influential effect; (d) Only daughters have
an influential effect
Note: Time is shown as t1 and t2 instead of 6 and 7. Items are treated categorical but are
not specifically illustrated that way in this image.

Results of the Two Time Point Measurement SEM
Goodness-of-fit indices for each of the SEMs are listed in Table 3.
A baseline model (4a) where γ
m
and γ
d
are constrained to zero produces a χ
2
=230 on df =
138 and RMSEA ε
a
= .09; this tests that there is no influential dynamic relationship in
latent factor scores between mothers and adult daughters. The increase in degrees in
freedom, as compared to the composite score models, is expected and related to the
increased number of parameters estimated when 3 thresholds for each 4 category item are
fit to the model.
From this point forward we will not to consider changes in chi-square fit statistics
for changes in degrees of freedom as nested models for direct comparison. The strict use
of the WLSM estimator does not allow the interpretation (Satorra & Bentler, 1994).
Model 4b1 relaxes the zero constraint on both cross coefficients (γ’s). The test however,
makes no restrictions about gamma equality. This produces a fit, χ
2
=244 on df = 136 and
RMSEA ε
a
= .10.
The test of mother depressive symptoms leading the predictive relationship (4c),
results in another unsatisfactory fit (χ
2
=241, df =137, ε
a
= .10). In model 4d, mother to
daughter cross coefficient is set to zero and daughter to mother effect is freely estimated.
In this run, goodness of fit is χ
2
=232 on df = 137 and RMSEA ε
a
= .10.
22
Neither of the models fits particularly well when considering the RMSEA value is
in every case greater than the traditional .05 cutoff point. Even the baseline model where
coupling parameters are forced to zero appears to fit as well (and unsatisfactorily) as any
other model in this series. Moreover, gamma parameters did not meet statistical
significance.

Table 3: Measurement Model Cross-Lagged SEM Fits
Statistic

No CROSS-LAGS
(a)
γ
m
≠ γ
d

(b1)
γ
m
= γ
d

(b2)
No
D-‐>M

(c)

No
M-‐>D

(d)

X
2

230
244
235
241
232

df
138
136
137
137
137

P(perfect)
.00
.00
.00
.00
.00

RMSEA
.09
.10
.10
.10
.10

CFI
.98
.98
.98
.99
.99

TFI
.98
.98
.98
.99
.99

Scaling
Correction

Factor

.71
.66
.69
.67
.70

γ
m

0
.02
.03
.02
0

γ
d

0
.03
.03
0
.01

* = statistically significant at .05 level

23
Chapter 6: Analysis 4 – Extended Measurement Models
A Six Time-point Extension
As an extension of the models already discussed, this analysis includes our
measurement model SEM but applied to all available time points (2-7). Note again that
the model forces invariance of all loadings and thresholds across both mothers and
daughters and time. Program syntax used to accomplish this can be seen in Appendix.
Metric factorial invariance in our dynamic models is of primary concern for this study.
As was the case in the previous measurement models, we separate out differences based
on the way in which depressive symptoms were measured and estimate fit statistics
considering only the effects of the psychological construct of interest.
The same ordered series of testable hypotheses is conducted using the more
structurally complex model shown in Figure 5 for all complete cases. By constraining
both cross coefficients to zero, this model similarly begins with a baseline measuring the
goodness of fit for a SEM where there are no influential pathways predicting depression
from either dyadic member to the other (γ
m
= γ
d
= 0). Following this test of no dynamic
relationship, a model equating the coupling parameters is fit. In this model both γ
m
and γ
d

are constrained to be equal but allowed to be estimated as greater than zero (allowable
due to metric invariance). The next model is essentially the opposite. Now, the gamma
coupling coefficients are freely estimated but specifically constrained not to be identical
to one another; this is a test of a dual influential dynamic system between mother and
daughter symptom factors with each dyad member having a unique predictive strength.
Much like every model series, the final two models focus specifically on testing
whether one dyad member is leading the influential relationship. For this model this is
24
accomplished in the same way as in the previous coupling SEMs. In two individual tests,
each coupling parameter is forced to zero while the other is allowed to be freely
estimated. Finally, the same series of measurement invariant SEM models are run using
the dyads which do contain incompleteness to examine if the increase in sample size will
provide any change in substantive interpretations.

Figure 4: Metrically Invariant Common Factor SEM at Six Times

Although the multiple models tested are not each individually pictured, the same parameters constraint changes are applied to
this model at every step. Items are treated categorical but are not specifically illustrated that way in this image.
25
26
Results of the Six Time Point Measurement SEM
Complete cases
Table 4 contains the statistical fit of each of the SEMs for both complete and
incomplete case samples. In the complete case only models, the baseline model (a) test of
no influential dynamic relationship produces a χ
2
=2502 on df = 1217 and RMSEA ε
a
=
.12. When cross-lagged constraints are relaxed but not constrained to be equal the fit of
the model (b1) does not change at all for 2 degrees of freedom (χ
2
=2502 on df = 1215 and
ε
a
= .12). The model seemingly fits worse when γ
m
= γ
d
constraint is tested (b2; χ
2
=2518,
df =1216, ε
a
= .12).
The test of mother depressive symptoms leading the predictive relationship (i.e.
no cross coefficient from daughter to mother) (c), results in an apparent fit decrease
where χ
2
=2530, df =1216, ε
a
= .12. In model (d) mother to daughter cross coefficient is
set to zero and daughter to mother effect is freely estimated. In this run, goodness of fit is
slightly judging solely by the smallest chi-squared misfit of all models, χ
2
=2464 on df =
1216 and RMSEA ε
a
= .12.
Neither of the models fit particularly well when considering the RMSEA. For this
6 time wave model series, however, model (d) (daughter as a putative indicator) appears
to fit best. This substantive interpretation is similar to our findings in the initial SEM that
utilized composite CESD-8 scores in the sense that daughter leads the relationship; it is
different in an important way, however. In this case, an adult daughter’s depressive
symptoms score might be a negative putative leading indicator of her mother’s depressive
symptoms at a later time (γ
d

=
-‐.08,
γ
m

=
0).

27
Table 4: Six-Wave Measurement Model Cross-Lagged SEM Fits
Statistic

No
Coupling

(a)

γ
m
≠ γ
d

(b1)

γ
m
= γ
d

(b2)

No
D-‐>M

(c)

No
M-‐>D

(d)

X
2

2502
2502
2518
2530
2464

df
1217
1215
1216
1216
1216

P(perfect)
.00
.00
.00
.00
.00

RMSEA
.12
.12
.12
.12
.12

CFI
.95
.95
.95
.95
.95

TFI
.95
.95
.95
.95
.95

Scaling
Correction

Factor

.83
.81
.82
.82
.82

γ
m

0
0
-‐.03
.03
0

γ
d

0
-‐.08*
-‐.03
0
-‐.08*

* = statistically significant at .05 level

Incomplete cases
The same series of models are run using incomplete cases, not only in an attempt
to try and increase statistical accuracy but to try and model the dynamic relationship as if
everyone had participated (McArdle, 1994). As can be seen in Table 5, the addition of
incompleteness does better the model fit as indicated by the more satisfactory RMSEA of
each model, but the resulting χ
2
statistics tell us little about whether any model fits better
than the γ
m
= γ
d
= 0 baseline model. Implications are discussed in the next section.

28
Table 5: Six-Wave Measurement Model SEM with Incomplete Data
Statistic

No
Coupling

(a)

γ
m
≠ γ
d

(b1)

γ
m
= γ
d

(b2)

No
D-‐>M

(c)

No
M-‐>D

(d)

X
2

2469
2477
2484
2464
2468

df
1233
1231
1232
1232
1232

P(perfect)
.00
.00
.00
.00
.00

RMSEA
.06
.06
.06
.06
.06

CFI
.96
.96
.96
.96
.96

TFI
.96
.96
.96
.96
.96

Scaling
Correction

Factor

.84
.83
.84
.83
.84

γ
m

0
.04
0
.05
0

γ
d

0
-‐.01
0
0
-‐.03

* = statistically significant at .05 level

29
Chapter 7: Discussion
Overview
The analyses presented in this research examine a series of longitudinal dynamic
structural equation models investigating depressive affect transfer between mothers and
their adult-daughters. Even more specifically, we examine how mother or adult daughter
depressive affect item responses at one time might predict the other’s response at the next
time of collected; we assume the items are a good measure of depressive affect.
Previous work taking the multidirectional dynamic relationship between a parent
and child, as suggested by Bell, has focused on adolescent children (Shrier et. al., 2004).
This makes sense because a child generally spends a lot, if not the majority, of his/her
formative years at home with parents. As a result of the appropriate theoretical attention
to the adolescent child’s effect on her parents, we are not aware of any study that fits the
same framework to the adult-child older-parent relationship and depressive
symptomatology. Moreover, an increase in the amount of daughters stepping up to help
their elder mothers means that the dynamic relationship is very important to the mental
and physical health of both (Brody, 1985).
This paper began by looking at a simple cross-lagged regression testing several
coupling parameter hypotheses (Table 2). The best fitting model suggests that daughter
symptomatology at time 6 (1997) was a positive putative leading indicator of mother
symptoms at time 7 (2000); an increase in daughter score predicts an increase in her
mother’s score. The model, however, does not address two important issues. First, SEM
parameters for categorical items treated as continuous data may be estimated properly
when there is not significant skew but this is not the case with depressive symptom items
30
as seen in Figure 1 (Muthen, 1983; Muthen & Kaplan, 1985). Much like its skewed
distribution in the general population, women participants from the longitudinal study of
generations generally report few or no depressive symptoms. Second, this model assumes
we are measuring the same latent psychological construct across dyad member and time
but does not implicitly model this critical assumption in the SEM. As a result, the model
does not distinguish between the effects attributed to depressive affect and those that
might be caused by some sort of measurement bias.
The second set of analyses is implemented into this paper to justify the use of a
common one-factor model for depressive affect with four indicators. The goal was to
reduce the amount of indicators to at least four which load strongly and predominantly on
only the latent factor of interest. This was done to simplify the addition of measurement
invariance to additional models for consideration in this paper and in future use with
intergenerational relationships.
The remaining models in Figures 4 and 5 add the measurement invariance model
generated from the factor analyses first to the simpler two time point model and then to
data available for six waves of survey collection from 1985 to 2000. Substantive
interpretation is convoluted by the failure to reach the same interpretation when
measurement bias is adjusted for in the Figure 4 models. Additionally, the move to the
more structurally complex measurement models increases RMSEA but demonstrates that
taking all time points into account, a daughter score may actually be a negative indicator
of her mother’s at a later time point. This is important because when considering a
longitudinal 15 year dynamic system, an increase in daughter depressive affect is
accompanied by a decrease in her mother’s depressive affect at a later time. One
31
explanation: daughters experiencing increases in symptoms may lead to their mother
focusing attention away from their own depressive thoughts in an effort to comfort their
offspring (leading to a decrease in mother symptoms).
An identical series of models was then fit to the dataset with incomplete dyads
and resulted in no apparent differences between any of the models in the series (see Table
5). The loss of statistically accurate gamma coefficients and substantive interpretation
may be attributed to non-random ‘missingness.’ MLE estimation for incomplete cases
assumes data is missing at random and has been shown to converge accurately (McArdle,
1994). This should be investigated further by examining attrition in the LSOG women
and considering the results in continued model refinement. Additionally, simulated data
with similar patterns of incompleteness could be used to investigate under which
conditions using all incomplete data is statistically sound in categorical measurement
SEMs with means-adjusted weighted least squares estimation.
Final thoughts
A priori hypotheses are rejected and results from two series of models testing
different configurations of a reciprocal mother and daughter relationship suggest that
daughter to mother influence may be a leading indicator in transfer of depressive affect
within the older-mother adult-daughter relationship. A measurement model using all
available time waves suggests daughter to mother influence might be a negative
indicator. But not all model series made the same distinction; others suggested that there
was no dynamic relationship.
Implications for continued work on this theoretical relationship are numerous.
First, it is proposed that a more rigorous series of longitudinal metric invariance models
32
be tested to determine what level of invariance is best suited for intergenerational use at
all time points. Factor analyses may have been too lenient in their application to only one
time point of data. Additionally, sample size imposed limitations on the use of
theoretically relevant covariates. For example, at time 2 and time 7 less than 10 female
daughters reported living with her mother and group difference test models could not be
fit. Future work should take relevant familial solidarity into consideration.
Moreover, LSOG data was collected from a predominantly non-Hispanic white
population (92% and 85% of G2 and G3 participants, respectively). In a study of adult
daughters and their closeness with mom, non-Hispanic white daughters self-rated their
closeness lower than both Asian and Hispanic American daughters (Rastogi & Wampler,
1999). In their review of this study, the authors cite a 1994 study that found non-Hispanic
white mothers most valued the independence of their daughters (Julian, McKenry, &
McKelvey, 1994, as cited in Rastogi & Wampler 1999). This suggests that the models
presented in this paper may produce different substantive results in more collectivist
cultures.
On a similar note, Silverstein and Bengston pointed out the presence of various
family typologies (Silverstein & Bengston, 1997). Keeping this in mind, the study should
be extended to differentiate substantive results depending on family type. The
heterogeneity of each familial pairing could be masking results. Utilizing more of the
available data may allow us to separate families into latent classes that could be used as
‘groups’ for comparison.
On a technical note, it seems no published study has discussed in detail the
behavior of different fit statistics in their use with the specific categorical measurement
33
SEMs presented here. We chose to discuss RMSEAs but include two more indices of it in
each table (CFI and TFI). Still, differences in calculated chi-squares for each model were
not drastic enough to suggest that misinterpretation of a fit index confounded the results
of this study, however, it deserves consideration.
The modeling approach used in this paper is useful for considering time specific
relationships between two constructs over time. Change models not included in this
study, in contrast, look at systematic individual differences in their developmental
trajectories. Seminal work by McArdle and Hamagami (2004) suggest that this approach
could theoretically be combined with measurement models for a unique individual level
analysis that does take into account the accumulation of influences over time (McArdle,
2008). Unique patterns in individual score trajectories for both mothers and daughters
indicate change models should be considered (see Appendix).
The results presented here suggest that models where adult daughter influence is a
leading indicator of her older mother’s depressive affect are worth fitting to longitudinal
family data. This substantive conclusion should elevate interest in the theory by
caregiving researchers who might be interested in older daughters stepping up to help
their older mothers. Additional family dyads could also be considered for comparison.

34
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38
Appendices
Appendix A: Dyad Selection
After Creating a family variable, it was used to randomly select only one dyad from each
created family pairing:

data lsog.allg3g2womenf;
set lsog.allg3g2women;
family=.;
if famr7 ~=. AND family=. then family=famr7;
if famr6 ~=. AND family=. then family=famr6;
if famr5 ~=. AND family=. then family=famr5;
if famr4 ~=. AND family=. then family=famr4;
if famr3 ~=. AND family=. then family=famr3;
if famr2 ~=. AND family=. then family=famr2;

if mfamr7 ~=. AND family=. then family=mfamr7;
if mfamr6 ~=. AND family=. then family=mfamr6;
if mfamr5 ~=. AND family=. then family=mfamr5;
if mfamr4 ~=. AND family=. then family=mfamr4;
if mfamr3 ~=. AND family=. then family=mfamr3;
if mfamr2 ~=. AND family=. then family=mfamr2;
run;

data justrandomE;
set lsog.allg3g2womenf;
randomn=ranuni(090324);
run;
proc sort; by randomn; run;

/* this command will randomly delete one of the dyads--this will create
a new output file z */
proc sort nodupkey data=justrandomE out=lsog.z;
by family;
run;

39
Appendix B: Correlations for All Variables

40
Appendix C: Promax-rotated Exploratory Factor Loadings

These loadings were obtained in analyses 2. The corresponding questions are listed below
for reference.

1 2 3 4
______ ______ ______ ______
C1 0.431 0.039 0.038 0.225
C2 0.619 -0.235 0.006 0.160
C3 0.583 -0.028 0.243 0.168
C4 0.144 -0.090 -0.650 0.025
C5 0.240 0.088 -0.152 0.429
C6 0.581 0.072 0.218 0.172
C7 0.051 0.077 0.075 0.696
C8 -0.125 -0.046 -0.629 0.015
C9 0.338 0.286 0.206 0.095
C10 0.363 0.175 0.019 0.292
C11 0.197 -0.059 0.110 0.350
C12 -0.217 0.056 -0.730 -0.058
C13 0.621 -0.098 -0.044 0.150
C14 0.491 0.114 0.151 0.128
C15 -0.035 0.496 -0.090 0.324
C16 -0.201 0.076 -0.695 -0.182
C17 0.843 0.277 0.004 -0.229
C18 0.813 0.299 0.040 -0.157
C19 0.093 0.801 -0.002 0.089
C20 -0.069 0.117 0.076 0.750

Original 20-item CES-D Inventory Questions as asked in the LSOG:
1. I was bothered by things that usually don’t bother me.
2. I did not feel like eating; my appetite was poor.
3. I felt that I could not shake off the blues even with help from my family or friends.
4. I felt I was just as good as other people.
5. I had trouble keeping my mind on what I was doing.
6. I felt depressed.
7. I felt that everything I did was an effort.
8. I felt hopeful about the future.
9. I thought my life had been a failure.
10. I felt fearful.
11. My sleep was restless.
12. I was happy.
13. I talked less than usual.
14. I felt lonely.
15. People were unfriendly.
16. I enjoyed life.
17. I had crying spells.
18. I felt sad.
19. I felt that people dislike me.
20. I could not get “going.”

41
Rarely or none of the time (1)
A little of the time (2)
A moderate amount of time (3)
Most or all of the time (4)

42
Appendix D: Individual Trajectories
Individual CESD-8 Scores Trajectories for Mothers and Daughters:

(a) All mothers CESD-8 individual trajectories; (b) All daughters CESD-8 individual
trajectories; (c) Random n=50 mother trajectories; (d) Random n=50 daughter
trajectories.

(a) (b)
(c) (d)
43
Appendix E: Mplus Script for Analyses

Note that only one variation of each script is shown for each set of analyses.

TITLE: Categorical EFA of G2 and G3 cesd20 at T2;

DATA: FILE = g3g2_cesd20t2.dat;

VARIABLE: NAMES = id gen fam
c1 c2 c3 c4 c5 c6 c7 c8 c9 c10
c11 c12 c13 c14 c15 c16 c17 c18 c19 c20;

USEVAR = c1-c20;

CATEGORICAL = c1-c20;

MISSING= ALL (-99);

ANALYSIS: TYPE=MEANSTRUCTURE MISSING EFA 1 5;
ITERATIONS = 10000;
CONVERGENCE = 0.00005;
COVERAGE = 0.10;
Rotation = Promax;

OUTPUT: PATTERNS SAMPSTAT STANDARDIZED RESIDUAL TECH1;

TITLE: SimpleCross Lagged Regression of Mother and Daughters
Time6/Time7 Model 1

DATA: FILE =simplHRS.dat;

VARIABLE: NAMES= G2T7d G2T6d G3T7d G3T6d;

USEVAR= G2T6d G3T6d G2T7d G3T7d;

MISSING = ALL(-99);

ANALYSIS: TYPE = MEANSTRUCTURE MISSING;

MODEL:
!FS Model w/ labels
G2T7d ON G2T6d (Bm); ! ->T7
G2T7d ON G3T6d (Ym);

44
G3T7d ON G3T6d (Bd);
G3T7d ON G2T6d (Ym);

G2T6d WITH G3T6d (CovT6);
G2T7d WITH G3T7d (CovT7);

!means var and residuals labeled
[G2T6d];
[G3T6d];
[G2T7d] (mG2T7);
[G3T7d] (mG3T7);

G2T6d (vG2T6);
G3T6d (vG3T6);
G2T7d (vG2T7);
G3T7d (vG3T7);

OUTPUT: SAMPSTAT STANDARDIZED RESIDUAL;

title: 2 Time Point Cross/Lag with Factor Items (CompleteC)
Data: file = ccasesdata.dat;
variable:
NAMES = Mblu7 Mdep7 Mlon7 Msad7 Mblu6 Mdep6 Mlon6 Msad6
Mblu5 Mdep5 Mlon5 Msad5 Mblu4 Mdep4 Mlon4 Msad4
Mblu3 Mdep3 Mlon3 Msad3 Mblu2 Mdep2 Mlon2 Msad2
Dblu7 Ddep7 Dlon7 Dsad7 Dblu6 Ddep6 Dlon6 Dsad6
Dblu5 Ddep5 Dlon5 Dsad5 Dblu4 Ddep4 Dlon4 Dsad4
Dblu3 Ddep3 Dlon3 Dsad3 Dblu2 Ddep2 Dlon2 Dsad2;

USEVAR = Mblu7 Mdep7 Mlon7 Msad7 Mblu6 Mdep6 Mlon6 Msad6
Dblu7 Ddep7 Dlon7 Dsad7 Dblu6 Ddep6 Dlon6 Dsad6;

CATEGORICAL = Mblu7 Mdep7 Mlon7 Msad7 Mblu6 Mdep6 Mlon6 Msad6
Dblu7 Ddep7 Dlon7 Dsad7 Dblu6 Ddep6 Dlon6 Dsad6;

MISSING = ALL (-99);

Analysis: Type = Meanstructure missing;
ITERATIONS = 10000;
ESTIMATOR = WLSM;
PARAMETERIZATION=THETA;

Model:
Mt6 by Mblu6-Msad6 (L1-L4);
Mt7 by Mblu7-Msad7 (L1-L4);
45

Dt6 by Dblu6-Dsad6 (L1-L4);
Dt7 by Dblu7-Dsad7 (L1-L4);

!latent Variable Means as 0
[Mt6@0]; [Mt7*];
[Dt6@0]; [Dt7*];

!(mS) Mom Stabilities and (mG) Gammas from Daughters
Mt7 on Mt6 (mS);
Mt7 on Dt6@0 (mG);

!(dS) Daughter Stabilities and (dG) Gammas from Mother

Dt7 on Dt6 (dS);
Dt7 on Mt6@0 (dG);

!Time Covariance
Dt6 with Mt6 (Cov);
Dt7 with Mt7 (Cov2);

!Time Errors
Dt6;
Dt7;
Mt6;
Mt7;

!Thresholds equal for each item and across time;

[Mblu6$1](a); [Mdep6$1](d); [Mlon6$1](g); [Msad6$1](j);
[Mblu7$1](a); [Mdep7$1](d); [Mlon7$1](g); [Msad7$1](j);

[Mblu6$2](b); [Mdep6$2](e); [Mlon6$2](h); [Msad6$2](k);
[Mblu7$2](b); [Mdep7$2](e); [Mlon7$2](h); [Msad7$2](k);

![Mblu6$3](c); [Mdep6$3](f);
[Mlon6$3](i); ![Msad6$3](l);
![Mblu7$3](c);
[Mdep7$3](f); [Mlon7$3](i); ![Msad7$3](l);

!Daughters

[Dblu6$1](a); [Ddep6$1](d); [Dlon6$1](g); [Dsad6$1](j);
[Dblu7$1](a); [Ddep7$1](d); [Dlon7$1](g); [Dsad7$1](j);
46

[Dblu6$2](b); [Ddep6$2](e); [Dlon6$2](h); [Dsad6$2](k);
[Dblu7$2](b); [Ddep7$2](e); [Dlon7$2](h); [Dsad7$2](k);

[Dblu6$3](c); [Ddep6$3](f); [Dlon6$3](i); [Dsad6$3](l);
[Dblu7$3](c); [Ddep7$3](f); [Dlon7$3](i); [Dsad7$3](l);

Output: sampstat residual standardized;

title: 6 Time Point Cross/Lag with Factor Items (Incomplete)
Data: file = incompleteCESD4.dat;
variable:
NAMES = Mblu7 Mdep7 Mlon7 Msad7 Mblu6 Mdep6 Mlon6 Msad6
Mblu5 Mdep5 Mlon5 Msad5 Mblu4 Mdep4 Mlon4 Msad4
Mblu3 Mdep3 Mlon3 Msad3 Mblu2 Mdep2 Mlon2 Msad2
Dblu7 Ddep7 Dlon7 Dsad7 Dblu6 Ddep6 Dlon6 Dsad6
Dblu5 Ddep5 Dlon5 Dsad5 Dblu4 Ddep4 Dlon4 Dsad4
Dblu3 Ddep3 Dlon3 Dsad3 Dblu2 Ddep2 Dlon2 Dsad2;

USEVAR = Mblu7 Mdep7 Mlon7 Msad7 Mblu6 Mdep6 Mlon6 Msad6
Mblu5 Mdep5 Mlon5 Msad5 Mblu4 Mdep4 Mlon4 Msad4
Mblu3 Mdep3 Mlon3 Msad3 Mblu2 Mdep2 Mlon2 Msad2
Dblu7 Ddep7 Dlon7 Dsad7 Dblu6 Ddep6 Dlon6 Dsad6
Dblu5 Ddep5 Dlon5 Dsad5 Dblu4 Ddep4 Dlon4 Dsad4
Dblu3 Ddep3 Dlon3 Dsad3 Dblu2 Ddep2 Dlon2 Dsad2;

CATEGORICAL = Mblu7 Mdep7 Mlon7 Msad7 Mblu6 Mdep6 Mlon6 Msad6
Mblu5 Mdep5 Mlon5 Msad5 Mblu4 Mdep4 Mlon4 Msad4
Mblu3 Mdep3 Mlon3 Msad3 Mblu2 Mdep2 Mlon2 Msad2
Dblu7 Ddep7 Dlon7 Dsad7 Dblu6 Ddep6 Dlon6 Dsad6
Dblu5 Ddep5 Dlon5 Dsad5 Dblu4 Ddep4 Dlon4 Dsad4
Dblu3 Ddep3 Dlon3 Dsad3 Dblu2 Ddep2 Dlon2 Dsad2;

MISSING = ALL (-99);

Analysis: Type = Meanstructure missing;
ITERATIONS = 10000;
ESTIMATOR = WLSM;
PARAMETERIZATION=THETA;

Model:

!Invariant Factors for each time (Mothers)
Mt2 by Mblu2-Msad2 (L1-L4);
47
Mt3 by Mblu3-Msad3 (L1-L4);
Mt4 by Mblu4-Msad4 (L1-L4);
Mt5 by Mblu5-Msad5 (L1-L4);
Mt6 by Mblu6-Msad6 (L1-L4);
Mt7 by Mblu7-Msad7 (L1-L4);
!Invariant Factors for each time (Daughters)
Dt2 by Dblu2-Dsad2 (L1-L4);
Dt3 by Dblu3-Dsad3 (L1-L4);
Dt4 by Dblu4-Dsad4 (L1-L4);
Dt5 by Dblu5-Dsad5 (L1-L4);
Dt6 by Dblu6-Dsad6 (L1-L4);
Dt7 by Dblu7-Dsad7 (L1-L4);

!latent Variable Means as 0
[Mt2@0]; [Mt3-Mt7*];
[Dt2@0]; [Dt3-Dt7*];

!(mS) Mom Stabilities and (mG) Gammas from Daughters
Mt3 on Mt2 (mS);
Mt3 on Dt2 @0(mG);

Mt4 on Mt3 (mS);
Mt4 on Dt3 @0(mG);

Mt5 on Mt4 (mS);
Mt5 on Dt4 @0(mG);

Mt6 on Mt5 (mS);
Mt6 on Dt5 @0(mG);

Mt7 on Mt6 (mS);
Mt7 on Dt6 @0(mG);

!(dS) Daughter Stabilities and (dG) Gammas from Mom
Dt3 on Dt2 (dS);
Dt3 on Mt2 @0(dG);

Dt4 on Dt3 (dS);
Dt4 on Mt3 @0(dG);

Dt5 on Dt4 (dS);
Dt5 on Mt4 @0(dG);

Dt6 on Dt5 (dS);
Dt6 on Mt5 @0(dG);
48

Dt7 on Dt6 (dS);
Dt7 on Mt6 @0(dG);

!Time Covariance
Dt2 with Mt2 (Cov);
Dt3 with Mt3 (Cov);
Dt4 with Mt4 (Cov);
Dt5 with Mt5 (Cov);
Dt6 with Mt6 (Cov);
Dt7 with Mt7 (Cov);

!Time Errors
Dt2@1;
Dt7;
Mt2@1;
Mt7;

!Thresholds equal for each item and across time;
[Mblu2$1](a); [Mdep2$1](d); [Mlon2$1](g); [Msad2$1](j);
[Mblu3$1](a); [Mdep3$1](d); [Mlon3$1](g); [Msad3$1](j);
[Mblu4$1](a); [Mdep4$1](d); [Mlon4$1](g); [Msad4$1](j);
[Mblu5$1](a); [Mdep5$1](d); [Mlon5$1](g); [Msad5$1](j);
[Mblu6$1](a); [Mdep6$1](d); [Mlon6$1](g); [Msad6$1](j);
[Mblu7$1](a); [Mdep7$1](d); [Mlon7$1](g); [Msad7$1](j);

[Mblu2$2](b); [Mdep2$2](e); [Mlon2$2](h); [Msad2$2](k);
[Mblu3$2](b); [Mdep3$2](e); [Mlon3$2](h); [Msad3$2](k);
[Mblu4$2](b); [Mdep4$2](e); [Mlon4$2](h); [Msad4$2](k);
[Mblu5$2](b); [Mdep5$2](e); [Mlon5$2](h); [Msad5$2](k);
[Mblu6$2](b); [Mdep6$2](e); [Mlon6$2](h); [Msad6$2](k);
[Mblu7$2](b); [Mdep7$2](e); [Mlon7$2](h); [Msad7$2](k);

[Mblu2$3](c); [Mdep2$3](f); [Mlon2$3](i); [Msad2$3](l);
[Mblu3$3](c); [Mdep3$3](f); [Mlon3$3](i); [Msad3$3](l);
[Mblu4$3](c); [Mdep4$3](f); [Mlon4$3](i); [Msad4$3](l);
[Mblu5$3](c); [Mdep5$3](f); [Mlon5$3](i); [Msad5$3](l);
[Mblu6$3](c); [Mdep6$3](f); [Mlon6$3](i); [Msad6$3](l);
[Mblu7$3](c); [Mdep7$3](f); [Mlon7$3](i); [Msad7$3](l);

!Daughters
[Dblu2$1](a); [Ddep2$1](d); [Dlon2$1](g); [Dsad2$1](j);
[Dblu3$1](a); [Ddep3$1](d); [Dlon3$1](g); [Dsad3$1](j);
[Dblu4$1](a); [Ddep4$1](d); [Dlon4$1](g); [Dsad4$1](j);
49
[Dblu5$1](a); [Ddep5$1](d); [Dlon5$1](g); [Dsad5$1](j);
[Dblu6$1](a); [Ddep6$1](d); [Dlon6$1](g); [Dsad6$1](j);
[Dblu7$1](a); [Ddep7$1](d); [Dlon7$1](g); [Dsad7$1](j);

[Dblu2$2](b); [Ddep2$2](e); [Dlon2$2](h); [Dsad2$2](k);
[Dblu3$2](b); [Ddep3$2](e); [Dlon3$2](h); [Dsad3$2](k);
[Dblu4$2](b); [Ddep4$2](e); [Dlon4$2](h); [Dsad4$2](k);
[Dblu5$2](b); [Ddep5$2](e); [Dlon5$2](h); [Dsad5$2](k);
[Dblu6$2](b); [Ddep6$2](e); [Dlon6$2](h); [Dsad6$2](k);
[Dblu7$2](b); [Ddep7$2](e); [Dlon7$2](h); [Dsad7$2](k);

[Dblu2$3](c); [Ddep2$3](f); [Dlon2$3](i); [Dsad2$3](l);
[Dblu3$3](c); [Ddep3$3](f); [Dlon3$3](i); [Dsad3$3](l);
[Dblu4$3](c); [Ddep4$3](f); [Dlon4$3](i); [Dsad4$3](l);
[Dblu5$3](c); [Ddep5$3](f); [Dlon5$3](i); [Dsad5$3](l);
[Dblu6$3](c); [Ddep6$3](f); [Dlon6$3](i); [Dsad6$3](l);
[Dblu7$3](c); [Ddep7$3](f); [Dlon7$3](i); [Dsad7$3](l);

Output: sampstat residual standardized;

Abstract (if available)

Abstract Much prior research has attempted to analyze a reciprocal dynamic relationship between older parents and their adult children. Mothers are generally more invested in their children’s lives and the relationship between mother and adult daughter has been shown to have more emotional ties than that between a mother and her adult son. The goals of this study are to explore the dynamic interrelationship between mother and daughter on depressive symptomatology using longitudinal data. The focal data are based on mothers (mean age = 56) and their biological daughters (mean age = 32) from the University of Southern California’s Longitudinal Study of Generations (LSOG). Four kinds of structural equation model (SEM) analyses are presented in order of complexity and each are designed to develop and test specific dynamic structural equation model hypotheses. The model fits of varying dynamic cross-lagged SEMs are compared for goodness-of-fit to various forms of the LSOG data. An initial two-time point regression based model suggests an adult daughter’s depressive affect to be a leading indicator of her older mother’s depressive symptoms. However, more complex models using more of the available data and advances in measurement models suggest the directionality of such developmental processes are not so simple or uniform. Substantive results are discussed as they pertain to all the models in the paper.

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Asset Metadata

Creator Reyes, Ricardo (author)

Core Title Dynamic analyses of the interrelationship between mothers and daughters on a measure of depressive symptoms

School College of Letters, Arts and Sciences

Degree Master of Arts

Degree Program Psychology

Publication Date 02/08/2010

Defense Date 01/27/2010

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

Tag adult children,daughter,Depression,Family,Generations,longitudinal,measurement,mother,OAI-PMH Harvest

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor McArdle, John J. (committee chair), Read, Stephen J. (committee member), Silverstein, Merril (committee member)

Creator Email reyesr@usc.edu,ricardo.reyes@me.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m2842

Unique identifier UC1151035

Identifier etd-Reyes-3493 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-301302 (legacy record id),usctheses-m2842 (legacy record id)

Legacy Identifier etd-Reyes-3493.pdf

Dmrecord 301302

Document Type Thesis

Rights Reyes, Ricardo

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