Practicalities of piecewise growth curve models

1. Practicalities of piecewise growth curve models Nathalie Huguet Portland State University

2. Background • Over 40 million of uninsured Americans • Increasing number of near-elderly (55+) are uninsured • Almost all elderly (65+) have health care coverage via Medicare • Why not extend Medicare to other age groups?

3. Research questions • Does having health insurance prior to Medicare coverage influence the health of Medicare beneficiaries? • Is there a difference in the change in health status prior to versus after Medicare enrollment? • Does the change in health status over time varies depending on the respondent's insurance status prior to the Medicare eligibility age?

4. Data Source • Health and Retirement Survey • Longitudinal study launch in 1992. • 10-years of follow-up • Data collected every 2 years

5. Outcome and covariates • Outcome: Self-rated health • Covariates measured at baseline: gender, marital status, race, education, smoking status, alcohol use, BMI, and physical activity • Variable of interest: Insured vs. partially insured

6. Growth curve modeling • Measure change overtime: can be positive, negative, linear, nonlinear • Intercept: what is the initial level? Intercept variance: variation in intercepts between individual • Slope: how rapidly does it change? Slope variance: variation in slopes between individual

7. Piecewise Growth curve • Measures rate of change • Separate growth trajectories into multiple stages

8. Hypothetical model Stage I: Pre-Medicare Stage II: Post-Medicare 4.0 3.5 3.0 SHR 2.5 2.0 1.0 56 58 60 62 64 65 66 68 70 72 74 76 Insured Partially insured

9. Individually-varying time of observation • In the HRS, the age of participants at baseline varied between 55 and 83 • Respondents reached the age of 65 at different waves. • To account for the variability at baseline, I used individually-varying times of observation

10. CODING Nightmare

11. Multi-group • Insured vs. partially uninsured • Each parameter is constrained to be equal across groups • Compare the fit between baseline model and the constrain model • Baseline model is the piece wise GLM with covariates and the group variable

12. Insured uninsured Multi-group difference test Constrain Intercepts SHR 56 58 60 62 64 65 66 68 70 72 74 76 Pre-Medicare Post-Medicare

13. Insured uninsured Multi-group difference test Constrain pre Medicare slopes 56 58 60 62 64 65 66 68 70 72 74 76 Pre-Medicare Post-Medicare

14. Insured uninsured Multi-group difference test Constrain post Medicare slopes 56 58 60 62 64 65 66 68 70 72 74 76 Pre-Medicare Post-Medicare

15. Insured uninsured Multi-group difference test Constrain insured group slopes 56 58 60 62 64 65 66 68 70 72 74 76 Pre-Medicare Post-Medicare

16. Insured uninsured Multi-group difference test Constrain partially insured group slopes 56 58 60 62 64 65 66 68 70 72 74 76 Pre-Medicare Post-Medicare

17. Multi-group Model I is the baseline

18. Other issues • Weighting • Complex sampling design (Stratified sampling)

19. Results

20. Results