1. Jason T. Newsom & David L. Morgan Portland State University
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

2. Introduction Steady recovery over 1-2 years common
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

3. 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

4. Measures Dependent Measure Depression Time-invariant Covariates Age
Education
Time-varying Covariates
Negative Social Interactions
Perceived Health

5. 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

6. Time-invariant Covariates
Age at baseline
Education
Number of years

7. 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

8. 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

9. 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

10. Growth curve model of depression at three time points
Figure 1
Growth curve model of depression at three time points
Slope
(Rate of change of
Depression)
Intercept
(Initial Depression) 1 1 1 2 1
Dep t0
Dep t1
Dep t2

11. Adding Time-Invariant Covariates
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

12. Time-invariant covariates in depression growth curve model
Figure 2
Time-invariant covariates in depression growth curve model
Age
Educ
Intercept
(Initial Depression)
Slope
(Rate of change of
Depression) 1 1 1 2 1
Dep t0
Dep t1
Dep t2

13. Adding Time-varying Covariates
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

14. Figure 3 Time-varying and time-invariant covariates
in depression growth curve model
Age
Educ
Intercept
(Initial Depression)
Slope
(Rate of change of
Depression) 1 1 1 1 2
Dep t0
Dep t1
Dep t2
Health t0
Negs t0
Health t1
Negs t1
Health t2
Negs t2

15. Table 1
Sample characteristics of widows.
Variable Mean Std. Dev.
Age
Education
Income (thousands)
Depression, T
Depression, T
Depression, T
Perceived Health, T
Perceived Health, T
Perceived Health, T
Negative Interactions, T
Negative Interactions, T
Negative Interactions, T

16. Basic model growth curve results
Table 2
Basic model growth curve results
Model fit statistics:
N=311, c2 (1) = , p = .0074, IFI = .979, SRMR = .033.

17. Table 3
Model including time-invariant covariates.
Model fit statistics:
N= 311, c2 (3) = , p = .0144, IFI = .975 , SRMR = .026.

18. Table 4
Model including time-invariant covariates and time-varying covariates.
Model fit statistics:
N=311, c2 (15) = , p = .0021, IFI = .950, SRMR = .050

19. Summary of Results Steady recovery over 18-month period
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

20. 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)