This project is funded by AG 14130 from the National Institute on Aging. Email: newsomj@pdx

1. The Importance of Accounting For Covariates and Prior Measurements in Longitudinal Gerontology Studies Jason T. Newsom Institute on Aging, Portland State University Portland, OR Karen S. Rook University of California, Irvine Kathleen J. Bonn Institute on Aging, Portland State University Portland, OR This project is funded by AG14130 from the National Institute on Aging. Email: newsomj@pdx.edu

2. Cross-lagged Panel Models • Interest and availability of longitudinal designs in gerontology is increasing • Cross-lagged panel models are useful for questions about causal directionality and change over a discrete interval with passive observational designs • Cross-lagged panel models examine the predictive association between two variables over time, each controlling for effects at earlier time points Xt0 Xt1 Yt0 Yt1

3. Causality • Kenny (1979) summarized three criteria for concluding causality: • Correlation • Time precedence • Nonspuriousness • Cross-lagged panel models address correlation and time precedence criteria • These models, however, rarely address nonspuriousness by controlling for third variables which may covary with either variable • Omission of covariates can lead to biases in the stability of a variable over time or the longitudinal association of two variables over time • Time invariant or time-specific covariates can be included

4. Background • Negative social exchanges involve criticisms, intrusiveness, demands, or rejection from family or friends • Large body of work suggests a strong relationship between negative social exchanges and psychological distress among older adults (Rook, 1992) • Most research has been cross-sectional, but longitudinal studies support causal hypothesis that negative exchanges affect distress (e.g., Finch & Zautra, 1992; Newsom, Nishishiba, Morgan & Rook, 2003) • Question often raised about whether psychological distress or mood may affect reports of negative exchanges

5. Study Design and Methods • Participants are from the Later Life Study of Social Exchanges (LLSSE), a national sample of adults 65-90 years old. • 3 in-person interviews at 12-mo intervals (T1, T3, T5) • N =916 completed interviews at Time 1, N = 667 completed interviews at Time 5 • At baseline, average age = 74.16; 62% female; 63% HS degree or less education; 83% Caucasian, 11% African American, 5% Latino, 1% other groups.

6. Negative Social Exchanges Measure • 12-item measure, 4 domains, 3 items each. • Frequency of occurrence in the past month • Subscale scores for 4 factors were indicators of negative social exchanges latent variable • Unsympathetic/insensitivebehavior (e.g., “… act unsympathetic or critical about your personal concerns?”) • Failure to provide needed aid (e.g., “…let you down when you needed help?”) • Unwanted advice (e.g., “… give you unwanted advice?”) • Neglect/rejection (e.g., “…forget or ignore you?”)

7. Depression Measure • Center for Epidemiologic Studies Depression scale (CES-D; Radloff, 1977) • Brief 9-item version developed by Santor and Coyne (1997) • Subscale scores for 3 factors (following McCallum, MacKinnon, Simons, & Simons, 1995) were indicators of depression latent variable: • Positive affect (e.g., “You were happy”) • Negative Affect (e.g., “You felt sad”) • Somatic Symptoms (e.g., “Your sleep was restless”)

8. Health Health was measured by three indicators at Time 1: • Self-rated health: How would you describe your health at the present time? Would you say it is …”(0 = poor, 4=excellent) • The number of chronic conditions out of 12 (e.g., heart disease, cancer, chronic lung disease) • 15 Activities of daily living (e.g., climb stairs, use the telephone, bathe or dress)

9. Analyses • Structural equation models using Mplus, version 3.11 (Muthen & Muthen, 2004). • Sample size based on Time 5 complete interviews (N=667) • FIML missing data estimation used for missing responses not due to attrition • Because of concerns about multivariate non-normality, Yuan-Bentler (2000) estimation for non-normal missing data were used.

10. Model Specification Precautions • Using latent variables can reduce bias in autoregressive paths and cross-lag paths • Correlated measurement errors over time reduce bias in autoregressive paths (Finkel, 1995) • At least partial longitudinal measurement invariance (loadings) should be established through chi-square difference tests • Equality constraints in autoregressive paths, cross-lagged paths, or synchronous correlations

11. Model Specification Precautions • Using latent variables can reduce bias in autoregressive paths and cross-lag paths • Correlated measurement errors over time reduce bias in autoregressive paths (Finkel, 1995) • At least partial longitudinal measurement invariance (loadings) should be established through chi-square difference tests • Equality constraints in autoregressive paths, cross-lagged paths, or synchronous correlations

12. Correlated Measurement Errors Depression T1 Depression T2 SomT1 SomT2 PAT1 NAT1 PAT2 NAT2

13. Model Specification Precautions • Using latent variables can reduce bias in autoregressive paths and cross-lag paths • Correlated measurement errors over time reduce bias in autoregressive paths (Finkel, 1995) • At least partial longitudinal measurement invariance (loadings) should be established through chi-square difference tests • Equality constraints in autoregressive paths, cross-lagged paths, or synchronous correlations

14. Measurement Invariance Equality Constraints Depression T1 Depression T2 SomT1 SomT2 PAT1 NAT1 PAT2 NAT2

15. Model Specification Precautions • Using latent variables can reduce bias in autoregressive paths and cross-lag paths • Correlated measurement errors over time reduce bias in autoregressive paths (Finkel, 1995) • At least partial longitudinal measurement invariance (loadings) should be established through chi-square difference tests • Equality constraints in autoregressive paths, cross-lagged paths, or synchronous correlations

16. Autoregressive Equality Constraints Depression T1 Depression T3 Depression T5 NSE T1 NSE T3 NSE T5

17. Cross-lag Equality Constraints Depression T1 Depression T3 Depression T5 NSE T1 NSE T3 NSE T5

18. Synchronous Correlation Equality Constraints Depression T1 Depression T3 Depression T5 NSE T1 NSE T3 NSE T5

19. Basic Cross-lagged Panel Model Between Depression and Negative Social Exchanges (NSE’s) .137*** .626*** .680*** .134*** Depression T1 Depression T3 Depression T5 .067 .065 .418*** .105** .097** NSE T1 NSE T3 NSE T5 .669*** .652*** c2 (172, N= 667) = 262.673, IFI = .976 , SRMR = .044

20. Cross-lagged Panel Model Between Depression and Negative Social Exchanges (NSE’s) with Covariate .138*** .132*** .566*** .610*** Depression T1 Depression T3 Depression T5 .099* .105* .434*** .075* .075* NSE T1 NSE T3 NSE T5 .229*** .657*** .659*** .167** -.062 .502*** .077 .075 Health T1 c2 (229, N= 667) = 386.526, p < .001 IFI = .964, SRMR = .043

21. Summary and Conclusions • Results suggested that negative social exchanges did not significantly predict depression when health was omitted from the model • When health was included, findings also support an effect of negative social exchanges on depression • Conclusions about the causal direction of the relationship between two variables can differ if the correct covariates are not included in the model • Results may be revealing about the role of health. One reason for the correlation between NSEs and depression may be that NSEs affect depression among those with worse health by contributing to health-related conflicts and disappointments (Margolin & McIntyre-Kingsolver, 1988 Newsom, 1999;; Skelton & Dominian, 1973)

22. General Comments • Effects of covariates can be complex, because covariate is controlled in autoregressive paths as well as cross-lagged paths • These analyses only included a measure of health, but other important covariates likely • Stable health was assumed, but health or other variables can be included as time-specific covariates • Including time-specific covariates requires additional cross-lagged paths and autoregressive paths, adding substantially to the complexity of the model

23. Recommended Readings • Ferrer, E., & McArdle, J.J. (2003). Alternative structural models for multivariate longitudinal data analysis. Structural Equation Modeling, 10, 493-524. • Finkel, S.E. (1995). Causal analysis with panel data. Thousand Oaks: Sage. QASS #105 • Joreskog, K.G. (1979). Statistical estimation of structural models in longitudinal-developmental investigations. In J.R. Nesselroade & P.B. Baltes (Eds.), Longitudinal research in the study of behavior and development (pp. 303-352). New York: Academic. • Kessler, R.C., & Greenberg, D.F. (1981). Linear panel analysis: Models of quantitative change. New York: Academic. • McArdle, J.J., & Hamagami F. (2001). Latent difference score structural models for linear dynamic analyses with incomplete longitudional data. In L. Collins & A. Sayer (Eds.), New methods for the analysis of change (pp. 139-175). Washington, D.C.: American Psychological Association. • Wheaton, B., Muthen, B., Alwin, D.F., & Summers, G.F. (1977). Assessing reliability and stability in panel models. In D. R. Heise (Ed.), Sociological Methodology 1977 (pp. 84-136). San Francisco: Jossey-Bass.

24. A copy of this talk will be available at the GSA Measurement, Statistics, and Research Design Interest group website: http://www.ioa.pdx.edu/newsom/gsaquant