practicalities of piecewise growth curve models
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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 - PowerPoint PPT PresentationTRANSCRIPT
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 76
Insured uninsured
Pre-Medicare Post-Medicare
Constrain Intercepts
SHR
Multi-group difference test
56 58 60 62 64 65 66 68 70 72 74 76
Insured uninsured
Pre-Medicare Post-Medicare
Constrain pre Medicare slopes
Multi-group difference test
56 58 60 62 64 65 66 68 70 72 74 76
Insured uninsured
Pre-Medicare Post-Medicare
Constrain post Medicare slopes
Multi-group difference test
56 58 60 62 64 65 66 68 70 72 74 76
Insured uninsured
Pre-Medicare Post-Medicare
Constrain insured group slopes
Multi-group difference test
56 58 60 62 64 65 66 68 70 72 74 76
Insured 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)
Results
Insured Partially insured
Insured 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
*
