Time-varying and time-invariant covariates in a
latent growth model of negative interactions
and depression in widowhood
Jason T. Newsom & David L. Morgan
Institute on Aging
Portland State University
Introduction
• Increase in depressive symptoms following a loss
common
• Steady recovery over 1-2 years common
• Depression commonly approaches normal levels at end
of this period
• These patterns are common but not universal (Wortman
& Silverman, 1989)
• Increased attention to individual differences in process of
recovery and variables that may affect them
• Growth curve analysis ideal for examining individual
differences in initial depression levels and rate of recovery
Methods
Sample
376 widows recruited using death certificates
Ages 59 through 85
Followed over 18 months
Initial interview 3-6 months after loss
Face-to-face interviews every 6 months
311 with complete data
Attrition
No Significant Differences
Income
Education
Depression
Perceived health
Negative social interactions
Significant Differences
Age: nonrespondents 1.46 yrs older
Measures
Dependent Measure
• Depression
Time-invariant Covariates
Age
Education
Time-varying Covariates
Negative Social Interactions
Perceived Health
Depression
Center for Epidemiologic Studies—Depression scale (CES-D;
Radloff, 1977)
20 items (e.g., bothered by things that do not usually
bother you, felt depressed, enjoyed life)
Frequency of symptom in last week
0 = None of the time (< 1 day)
1 = A little of the time (1-2 days)
2 = A moderate amount of the time (3-4 days)
3= Most of the time (5-7 days)
Possible range: 0-60
Time-invariant Covariates
Age at baseline
Education
Number of years
Time-varying Covariates
Negative Social Interactions
• Number of network members who were source of
negative interactions
• Three domains: emotional, instrumental, informational
• Average of number network members in the three
domains
Perceived Health
“Compared to others your age, how do you rate your
overall health—would you say it is excellent, very good,
good, fair, or poor?”
Possible range: 1-5
Latent Growth Curve Analyses
Mplus 2.0 (Muthen & Muthen, 2001)
Maximum Likelihood
Three Models
Model 1: Basic growth model
Depression at three time points
Model 2: Adds time-invariant covariates
Age, education
• Model 3: Adds time-varying covariates
• Perceived health, negative interactions
Model 1
Basic Latent Growth Curve Model
Mean Structure Provides Information About:
• Average rate of decline in depression (mean slope)
• Average initial depression (mean intercept)
Latent Variances Provide Information About:
• Variability of initial depression levels
• Variability of rate of decline in depression
• Correlation of initial level and decline
Figure 1
Growth curve model of depression at three time points
Slope
(Rate of change of
Depression)
Intercept
(Initial Depression)
1
1
Dep
t0
0
1
1
Dep
t1
2
Dep
t2
Model 2
Adding Time-Invariant Covariates
Age and education added as predictors of intercepts and slopes
Structural means become intercept values
Initial level and rate of decline adjusted for covariates
Age and education are “centered” to facilitate
interpretation
Variability of initial levels and decline become residual
variances, representing unaccounted for variance
Figure 2
Time-invariant covariates in depression growth curve model
Age
Educ
Intercept
(Initial Depression)
1
Dep
t0
1
Slope
(Rate of change of
Depression)
0
1
1
Dep
t1
2
Dep
t2
Model 3
Adding Time-varying Covariates
Perceived Health and Negative Interactions Added
Both variables measured at 3 time points
Included as predictors of depression at each time point
Initial level and decline in depression adjusted for
health and negative interactions at each time point
Figure 3
Time-varying and time-invariant covariates
in depression growth curve model
Age
Educ
Intercept
(Initial Depression)
Slope
(Rate of change of
Depression)
0
1
1
Dep
t0
Health
t0
1
1
Negs
t0
Dep
t1
Health
t1
2
Dep
t2
Negs
t1
Health
t2
Negs
t2
Table 1
Sample characteristics of widows.
Variable
Age
Education
Income (thousands)
Depression, T0
Depression, T1
Depression, T2
Perceived Health, T0
Perceived Health, T1
Perceived Health, T2
Negative Interactions, T0
Negative Interactions, T1
Negative Interactions, T2
Mean
71.0
13.0
23.7
12.4
11.5
8.5
3.7
3.6
3.7
.74
.73
.58
Std. Dev.
6.2
2.0
16.3
9.4
9.5
8.2
1.0
1.0
1.0
.98
.85
.84
Table 2
Basic model growth curve results
Parameter
Unstan Coeff
Stan Coeff
Sig
Ave intercept
12.622
1.633
<.001
Ave slope
-1.982
-.737
<.001
Intercept variance
59.715
1.000
<.001
7.228
1.000
<.05
-9.839
-.474
<.05
Slope variance
Intercept/slope covariance
Model fit statistics:
N=311, c2 (1) = 7.168, p = .0074, IFI = .979, SRMR = .033.
Table 3
Model including time-invariant covariates.
Parameter
Unstan Coeff
Stan Coeff
Sig
Growth Parameters
Ave intercept
12.663
1.645
<.01
Ave slope
-2.018
-.758
<.001
Intercept variance
59.007
.996
<.001
7.042
.993
<.05
-9.501
-.463
<.05
Age at t0 -> Intercept
-.076
-.061
ns
Educ (yrs) -> Intercept
-.080
-.021
ns
Age at t0 -> slope
.034
.078
ns
Educ (yrs) -> slope
-.045
-.034
ns
Slope variance
Intercept/slope covariance
Time-invariant Covariates
Model fit statistics:
N= 311, c2 (3) = 10.538, p = .0144, IFI = .975 , SRMR = .026.
Table 4
Model including time-invariant covariates and time-varying covariates.
Parameter
Unstan Coeff
Stan Coeff
Sig
Growth Parameters
Ave intercept
19.393
2.87
-.608
-.281
45.312
.993
<.001
4.649
.991
ns
-7.247
-.495
<.10
Age at t0 -> Intercept
-.092
-.084
ns
Educ (yrs) -> Intercept
-.027
-.008
ns
Age at t0 -> slope
.032
.092
ns
Educ (yrs) -> slope
-.015
-.014
ns
1.665
.179
<.001
-2.206
-.237
<.001
1.409
.134
-2.289
-.258
1.010
.105
-2.779
-.352
Ave slope
Intercept variance
Slope variance
Intercept/slope covariance
<.001
ns
Time-invariant covariates
Time-varying covariates
Negatives t0 -> Dep t0
Health t0 -> Dep t0
Negatives t1 -> Dep t1
Health t1 -> Dep t1
Negatives t2 -> Dep t2
Health t2 -> Dep t2
<.01
<.001
<.01
<.001
Model fit statistics:
N=311, c2 (15) =35.519 , p = .0021, IFI = .950, SRMR = .050
Summary of Results
• High levels of depression following loss
• Steady recovery over 18-month period
• Significant differences in initial levels of depression and in
recovery rates
• Age and education do not predict initial levels or recovery
rate
• Age and education do not account for variability in initial
levels or recovery rate
• Change in depression over time becomes nonsignificant once
variation due to changes in perceived health and negative
interactions is removed
• Variability in recovery rates becomes nonsignificant once
variation due to changes in perceived health and negative
interactions is removed
Conclusions and Limitations
• Unique approach to examining individual differences in initial
depression and rate of recovery among widows
• Change in negative interactions or health appear to explain
recovery rates of older widows
• More explicit causal models can be tested (e.g., using
growth factors for health or negative interactions as
predictors)
• Despite longitudinal data, causal directionality unclear (e.g.,
do negative interactions predict depression or does depression
predict negative interactions)
• Health may play a role as a moderator (e.g., those in poor
health may have slower recovery rates)