Practicalities of piecewise growth curve models Nathalie Huguet Portland State University

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?

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?

Data Source Health and Retirement Survey Longitudinal study launch in years of follow-up Data collected every 2 years

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

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

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

Hypothetical model InsuredPartially insured Stage I: Pre-MedicareStage II: Post-Medicare 1.0 SHR

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

CODING Nightmare Coding Used to Account for Individual-Varying Time of Observation. Wave 1Wave 2Wave 3Wave 4Wave 5Wave 6 Age Pre-Medicare Post-Medicare Age Pre-Medicare Post-Medicare Age Pre-Medicare Post-Medicare Age Pre-Medicare Post-Medicare Age Pre-Medicare Post-Medicare001234

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

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

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

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

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

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

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

Other issues Weighting Complex sampling design (Stratified sampling)

Results InsuredPartially insured Insured Near-Elderly Intercept mean, α 3.46*3.38* Slope 1, β pre *-.07* Slope 2, β post *-.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

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 *