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Unformatted text preview: PUBH 7430 Lecture 20 J. Wolfson Division of Biostatistics University of Minnesota School of Public Health November 17, 2011 1 / 25 Generalized linear mixed models 2 / 25 Linear mixed models So far, we have dealt with the linear mixed model (LMM) Y ij = x ij + z i b i + ij b i MVN (0 , ) , ij N (0 , 2 ) Assumptions Given b i , Y ij is Normally distributed... ... with mean ij = x ij + z i b i ... and variance 2 (i.e. V ( ij ) = 1) 3 / 25 Linear mixed models Linear mixed model most appropriate for data which are Continuous Approximately normally distributed Have constant variance (no meanvariance relationship) But, as we saw when introducing GLMs, these assumptions may be violated for a variety of data generating processes (eg. binary data, count data, etc.) 4 / 25 Extending the linear mixed model In the linear mixed model, we assume that the mean E ( Y  X ) has a Normal distribution. Two main approaches to extend the linear mixed effects model to nonnormal outcomes: 1 Generalized Linear Mixed Models: Assume that g ( ) has a Normal distribution for some link function g 2 Mixture models: Assume that arises from some other specified distribution. Beyond scope of this course. 5 / 25 Generalized linear mixed models First approach: Assume that g ( ) has a Normal distribution Assumptions ij is linked to the linear predictor via g ( ij ) = x ij + z ij b i b i arise from a Normal distribution Conditional on b i , Y ij has a distribution from the exponential family, and the Y ij are independent The resulting model is called the Generalized Linear Mixed Model (GLMM) 6 / 25 GLMM  example Gum data Recall that we had oral MS (bacteria) measurements at baseline, 1 week, 4 weeks, and 12 weeks Some measurements were missing We may be interested in predictors of the probability of having a missing measurement Binary data: 1 = missing, 0 = not missing 7 / 25 GLMM  example...
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This note was uploaded on 11/21/2011 for the course PUBH 7430 taught by Professor Prof.eberly during the Fall '04 term at Minnesota.
 Fall '04
 Prof.Eberly

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