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Unformatted text preview: PubH8452 Longitudinal Data Analysis  Fall 2011 Modeling Strategies Modeling Strategies  Marginal Models, Random Effects Models, and Transition Models Outline Summary of Modeling Strategies Modeling Mean Responses Modeling Covariances Interpretation Continuous Response Binary Response Count Data 1 PubH8452 Longitudinal Data Analysis  Fall 2011 Modeling Strategies Summary of Modeling Strategies Modeling Mean Responses Marginal models: The marginal expectation of the response, E( Y ij ) = ij , depends on the covariates, x ij , through a link function g , E( Y ij ) = ij = g 1 ( x T ij ) . Random effects (conditional) models: Conditional on subject specific, unobserved random variables b i , E( Y ij  b i ) = * ij = g 1 ( x T ij * + z T ij b i ) . 2 PubH8452 Longitudinal Data Analysis  Fall 2011 Modeling Strategies Transition models: Let H ij = ( Y i 1 , . . . , Y ij 1 ) denote the history of Y ij , E( Y ij H ij ) = ** ij = g 1 ( x T ij ** + s X r =1 f r ( H ij , ) ) . 3 PubH8452 Longitudinal Data Analysis  Fall 2011 Modeling Strategies Modeling Covariances Marginal models: The marginal variance of the response depends on the marginal mean, Var( Y ij ) = V ( ij ) , where V is a known function and the scale parameter may also depend on some covariates. The correlation between Y ij and Y ik is a function of the marginal mean: Cor( Y ij , Y ik ) = ( ij , ik , ) , where is a known function and the correlation parameters may depend on covariates. 4 PubH8452 Longitudinal Data Analysis  Fall 2011 Modeling Strategies Random effects (conditional) models: Typically, conditioning on the random effects, b i , the responses Y i 1 , . . . , Y in i are independent with an exponential family distribution. The random effects b i have mean and variance D . Typically the random effects are assumed to be multivariate Gaussian. Correlation among observations from the same person arises from their sharing unobservable variables, i.e., random effects. 5 PubH8452 Longitudinal Data Analysis  Fall 2011 Modeling Strategies Transition models: Typically, Y ij H ij is assumed to have an exponential family distribution with variances Var( Y ij H ij ) = V ( ** ij ) . Correlation among Y i 1 , . . . , Y in i exists because the past response values explicitly influence the present observation. 6 PubH8452 Longitudinal Data Analysis  Fall 2011 Modeling Strategies Interpretation Marginal model: is the mean (expected) difference in the response for the two populations (indi viduals) with the identical covariate values but differ in X by one unit....
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This note was uploaded on 11/21/2011 for the course PUBH 8452 taught by Professor Xianghualuo during the Fall '11 term at Minnesota.
 Fall '11
 XianghuaLuo

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