08GLMM - PubH8452 Longitudinal Data Analysis - Fall 2011...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PubH8452 Longitudinal Data Analysis - Fall 2011 Generalized Linear Mixed Models Generalized Linear Mixed Models Outline Subject-specific Models Conditional Inference Hierarchical Generalized Linear Model Beta-Binomial Model Poisson-Gamma Model Generalized Linear Mixed Model 1 PubH8452 Longitudinal Data Analysis - Fall 2011 Generalized Linear Mixed Models Subject-Specific Models Assumptions Given the subject-specific effects b i (a q-vector), the responses Y ij ( i = 1 , . . . , m, j = 1 , . . . , n i ) are independent and follow a distribution from the exponential family Y ij | b i f ( y ij | b i , ) . Let E( Y ij | b i ) = ij then g ( ij ) = ij = X T ij + Z T ij b i , where ij is the linear predictor and g is the link function. X ij and Z ij are p- and q-vector of covariates, with Z often being a subset of X . 2 PubH8452 Longitudinal Data Analysis - Fall 2011 Generalized Linear Mixed Models Three Ways to Handle Subject-specific Parameters Treated as fixed unknown parameters. Neyman and Scott (1948) showed that the ML estimates may be inconsistent due to the fact that the number of unknown parameters increases with the sample size. Conditional likelihood approach appropriate when only interested in regression coefficients that do not vary across subjects; subject-specific effects b 1 , b 2 , . . . , b m are treated as nuisance parameters ; estimate using the conditional likelihood given the sufficient statistics for b i . Full likelihood-based approach appropriate when subject-specific coefficients are of interest or conditioning discards too much information. treat b i as unobserved random variables and integrate them out to get the marginal likelihood of 3 PubH8452 Longitudinal Data Analysis - Fall 2011 Generalized Linear Mixed Models the parameters . The random effects b i are independent and identically distributed with mean and variance D ( ). Its distribution G is completely specified with parameters . That is, G does not depend on any covariates. Estimation of inference for is obtained from ML estimation, based on the marginal density for Y i . Examples include linear mixed model, hierarchical generalized linear model (beta-binomial model, poisson-gamma model) and generalized linear mixed model. 4 PubH8452 Longitudinal Data Analysis - Fall 2011 Generalized Linear Mixed Models Conditional Inference Sufficiency Suppose a random vector Y has density indexed by parameter , and s = s ( y ) is a statistic. s is said to be sufficient for if f ( y ; ) g ( s ; ) h ( y | s ) . The inference for can be based on the marginal density of s and no information is lost. The conditional density h ( y | s ) is useful for model checking but not in inference for ....
View Full Document

This note was uploaded on 11/21/2011 for the course PUBH 8452 taught by Professor Xianghualuo during the Fall '11 term at Minnesota.

Page1 / 109

08GLMM - PubH8452 Longitudinal Data Analysis - Fall 2011...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online