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 2.0 2.5 3.0 3.5 4.0 565860626465666870727476 InsuredPartially insured Stage I: Pre-MedicareStage II: Post-Medicare 1.0 SHR

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 Coding Used to Account for Individual-Varying Time of Observation. Wave 1Wave 2Wave 3Wave 4Wave 5Wave 6 Age55-5657-5859-6062-6263-6465-66 Pre-Medicare012345 Post-Medicare000000 Age57-5859-6061-6263-6465-6667-68 Pre-Medicare012344 Post-Medicare000001 Age59-6061-6263-6465-6667-6869-70 Pre-Medicare012333 Post-Medicare000012 Age61-6263-6465-6667-6869-7071-72 Pre-Medicare012222 Post-Medicare000123 Age63-6465-6667-6869-7071-7273-75 Pre-Medicare011111 Post-Medicare001234

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. Multi-group difference test 565860626465666870727476 Insureduninsured Pre-MedicarePost-Medicare Constrain Intercepts SHR

13. Multi-group difference test 565860626465666870727476 Insureduninsured Pre-MedicarePost-Medicare Constrain pre Medicare slopes

14. Multi-group difference test 565860626465666870727476 Insureduninsured Pre-MedicarePost-Medicare Constrain post Medicare slopes

15. Multi-group difference test 565860626465666870727476 Insureduninsured Pre-MedicarePost-Medicare Constrain insured group slopes

16. Multi-group difference test 565860626465666870727476 Insureduninsured Pre-MedicarePost-Medicare Constrain partially insured group slopes

17. Multi-group Summary of the Constraints Used in the Different Models Constraints to be equalModel II Model III Model IV Model V Model VI InterceptX Slope 1, pre65X Slope 2, post65X Slope 1 and 2, insured group X Slope 1 and 2, Uninsured group X Model I is the baseline

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

19. Results InsuredPartially insured Insured Near-Elderly Intercept mean, α 3.46*3.38* Slope 1, β pre65 -.05*-.07* Slope 2, β post65 -.07*-.04 Intercept variance,  ψ.66*.79* Slope 1 variance,  ψ pre65.01*.02* Slope 2 variance,  ψ pre65.02*.04* Note. Model adjusted for gender, marital status, race, education, smoking status, alcohol use, BMI, and physical activity. *p<.001

20. Results Summary of the Constraints Used in the Different Models Constraints to be equalBaselineModel II Model III Model IV Model V Model VI Intercept* Slope 1, pre65* Slope 2, post65ns Slope 1 and 2, insured group * Slope 1 and 2, Uninsured group *