Analysis Consequences of Dependent Measurement Problems in Research on Older Couples Jason T. Newsom Institute on Aging

1. Analysis Consequences of Dependent Measurement Problems in Research on Older Couples Jason T. Newsom Institute on Aging Portland State University Presented at the 55th annual meeting of the Gerontological Society of America, Boston, MA (November, 2002). newsomj@pdx.edu This research was supported by grant AG5159 from the National Institute on Aging. I thank Nicole Adams, Azra Rahim, Heather Mowry, Joe Rogers, Phillip King, Thea Lander, and Reggie Silbert for assistance with data collection.

2. Background • A common research question involves comparison of the unique effects of a variable measured for each member of the couple on a dependent variable • Example: husbands’ and wives’ perceived stress as predictors of life satisfaction • When identical measures are used for each dyad member, the within-dyad correlation can be overestimated because of correlated measurement errors • The overestimation of the within-dyad correlation will lead to an underestimation of the unique (partial) relationships to a dependent variable

3. Correlated Errors • A correlated measurement error is an association between two items beyond that due to the correlation between their respective latent variables • Example: Husband and wife’s sleep may be a function of snoring rather than depression Wife’s Depression Husband’s Depression sleep sleep • Correlated errors can occur with any two latent variables, but they are especially likely when parallel item sets are used to measure a construct in two members of a dyad • May be due to item content, specific wording, or methodological factors

4. Effect of Measurement Errors • Focus on measurement errors among predictor (exogenous) variables • If correlated errors exist but are not estimated, the correlation between the latent variables will be overestimated b Eta 1 Eta 2 a c X3 X5 X6 X1 X2 X4 f d e

5. Effect of Measurement Errors • The correlation between latent variables is a function of several factors: b Eta 1 Eta 2 a c X3 X5 X6 X1 X2 X4 f d e

6. Effect of Measurement Errors • Prediction of a dependent variable will be underestimated as a result of the overestimation of the correlation between exogenous variables h Eta 1 Eta 3 j Eta 2 • Total variance accounted for in dependent variable (R2) will be underestimated

7. Artificial Data Example Data and Analysis • Structural equation models using Mplus, version 2.02 (Muthen & Muthen, 1998) • Artificial correlation matrix as input, N=200, standardized coefficients • Correlation with dependent variable = .25, varied correlation among items • Single replication for each variation (i.e., effects of sampling variability were not examined) • 2 exogenous latent variables, 4 indicators each • Single measured dependent variable • Comparison of parameters with and without correlated errors

8. Artificial Data Example Structural Model X1 X2 Eta 1 X3 X4 Y X5 X6 Eta 2 X7 X8

9. Low Correlation Between Latent Variables Smaller Measurement Error Correlation

10. Low Correlation Between Latent Variables Smaller Measurement Error Correlation Larger Measurement Error Correlation

11. High Correlation Between Latent Variables Smaller Measurement Error Correlation

12. High Correlation Between Latent Variables Smaller Measurement Error Correlation Larger Measurement Error Correlation

13. Caregiving Example Study Description • 118 married couples (N=108 due to missing data) • Community sample from Portland, OR metropolitan area • Caregivers and care recipients interviewed about helping transactions • Examine relationship between perceptions of marital conflict (as reported by both caregivers and care recipient) and recipient’s reports of negative helping behaviors • Care recipients had difficulty with one or more ADL/IADLs due to wide range of health conditions (e.g., arthritis, claudication, knee problems, heart disease) • Covariates: gender, education, age, ADL/IADL difficulties, self-rated health

14. Caregiving Example Measures • Dependent variable: negative helping behaviors • “When my spouse has to help me, he/she becomes angry” • “When I need help with something, my spouse is critical of me” • “My spouse seems to resent helping me” • “When my spouse helps me do something, he/she is always courteous” (reversed) • 4-point scale of agreement

15. Caregiving Example Measures • Independent variables: • Marital conflict as reported by caregiver and care recipient (Skinner, Steinhauer, Santa-Barbara, 1983; Williamson & Schulz, 1992). • 4 items on 5-point scale of agreement (e.g., “My spouse gets too involved in my affairs”) • Gender (male=0, female=1), education, age • Difficulty rating of 21 ADL/IADLs, 4-point scale • Self-rated health, poor, fair, good, very good, excellent

16. Caregiving Example Structural Model not close too involv- ed CG conflict wrong way Negative Helping Behaviors don’t believe not close too involv- ed acts angry resents helping not courteous critical CR Conflict wrong way don’t believe Gender, Education, Age, ADL/IADLs, self-rated health

17. Relative Effects of Reports of Marital Conflict on Negative Helping Behaviors

18. Summary • Bias in predictive paths: • Increases with larger or more measurement error correlations • Only occurs to the extent that exogenous variables are correlated • Can have biasing effect on other covariates in the model • Not limited to dyadic data, but most likely when item wording is strictly parallel (e.g., friend instrumental support, friend emotional support) • Modification indices or nested tests can be used, but at least with small samples a priori estimation is encouraged • Bias occurs in regression or hierarchical linear models

19. Further Readings Cook, W.L. (1994). A structural equation model of dyadic relationships with the family system. Journal of Consulting and Clinical Psychology, 62, 500-509. Kashy, Deborah A; Kenny, David A. The analysis of data from dyads and groups. In H.T. Reis & C.M. Judd (2000). Handbook of research methods in social and personality psychology. (pp. 451-477). New York, NY, US: Cambridge University Press. Kenny, D. A., & Cook, W. (1999). Partner effects in relationship research: Conceptual issues, analytic difficulties, and illustrations. Personal Relationships, 6, 433-448. Newsom, J.T. (2002). A multilevel structural equation model for dyadic data. Structural Equation Modeling, 9, 431-447. Gerbing, D. W., & Anderson, J.C. (1984). On the meaning of within-factor correlated measurement errors. Journal of Consumer Research, 11, 572-580. Gillespie, M. W., & Fox, J. (1980). Specification errors and negatively correlated disturbances in "parallel" simultaneous-equation models. Sociological Methods and Research, 8, 273-308.