practicalities of piecewise growth curve models nathalie huguet portland state university

Practicalities of piecewise growth curve models

Nathalie HuguetPortland 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 1992.• 10-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

2.0

2.5

3.0

3.5

4.0

56 58 60 62 64 65 66 68 70 72 74 76

Insured Partially insured

Stage I: Pre-Medicare Stage 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 NightmareCoding Used to Account for Individual-Varying Time of Observation.

Wave 1 Wave 2 Wave 3 Wave 4 Wave 5 Wave 6

Age 55-56 57-58 59-60 62-62 63-64 65-66

Pre-Medicare 0 1 2 3 4 5

Post-Medicare 0 0 0 0 0 0

Age 57-58 59-60 61-62 63-64 65-66 67-68

Pre-Medicare 0 1 2 3 4 4

Post-Medicare 0 0 0 0 0 1

Age 59-60 61-62 63-64 65-66 67-68 69-70

Pre-Medicare 0 1 2 3 3 3

Post-Medicare 0 0 0 0 1 2

Age 61-62 63-64 65-66 67-68 69-70 71-72

Pre-Medicare 0 1 2 2 2 2

Post-Medicare 0 0 0 1 2 3

Age 63-64 65-66 67-68 69-70 71-72 73-75

Pre-Medicare 0 1 1 1 1 1

Post-Medicare 0 0 1 2 3 4

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

56 58 60 62 64 65 66 68 70 72 74 76Insured uninsured

Pre-Medicare Post-Medicare

Constrain Intercepts

SHR

Multi-group difference test

56 58 60 62 64 65 66 68 70 72 74 76Insured uninsured

Pre-Medicare Post-Medicare

Constrain pre Medicare slopes

Multi-group difference test

56 58 60 62 64 65 66 68 70 72 74 76Insured uninsured

Pre-Medicare Post-Medicare

Constrain post Medicare slopes

Multi-group difference test

56 58 60 62 64 65 66 68 70 72 74 76Insured uninsured

Pre-Medicare Post-Medicare

Constrain insured group slopes

Multi-group difference test

56 58 60 62 64 65 66 68 70 72 74 76Insured uninsured

Pre-Medicare Post-Medicare

Constrain partially insured group slopes

Multi-groupSummary of the Constraints Used in the Different Models

Constraints to be equal

Model II

Model III

Model IV

Model V

Model VI

Intercept X

Slope 1, pre65 X

Slope 2, post65 X

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)

ResultsInsured Partially

insuredInsured Near-Elderly Intercept mean, α 3.46* 3.38* Slope 1, βpre65 -.05* -.07* Slope 2, βpost65 -.07* -.04 Intercept variance, ψ .66* .79* Slope 1 variance, ψpre65 .01* .02* Slope 2 variance, ψpre65 .02* .04*Note. Model adjusted for gender, marital status, race, education,

smoking status, alcohol use, BMI, and physical activity. *p<.001

ResultsSummary of the Constraints Used in the Different Models

Constraints to be equal

Baseline

Model II

Model III

Model IV

Model V

Model VI

Intercept *

Slope 1, pre65 *

Slope 2, post65 ns

Slope 1 and 2, insured group

*

Slope 1 and 2, Uninsured group

*