{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

L20handout - PUBH 7430 Lecture 20 J Wolfson Division of...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
PUBH 7430 Lecture 20 J. Wolfson Division of Biostatistics University of Minnesota School of Public Health November 17, 2011 1 / 25
Background image of page 1

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

View Full Document Right Arrow Icon
Generalized linear mixed models 2 / 25
Background image of page 2
Linear mixed models So far, we have dealt with the linear mixed model (LMM) Y ij = x 0 ij β + z 0 i b i + ij b i MVN (0 , Σ) , ij N (0 , σ 2 ) Assumptions Given b i , Y ij is Normally distributed... ... with mean μ ij = x 0 ij β + z 0 i b i ... and variance σ 2 (i.e. V ( μ ij ) = 1) 3 / 25
Background image of page 3

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

View Full Document Right Arrow Icon
Linear mixed models Linear mixed model most appropriate for data which are Continuous Approximately normally distributed Have constant variance (no mean-variance 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
Background image of page 4
Extending the linear mixed model In the linear mixed model, we assume that the mean E ( Y | X ) μ has a Normal distribution. Two main approaches to extend the linear mixed effects model to non-normal outcomes: 1 Generalized Linear Mixed Models: Assume that g ( μ ) has a Normal distribution for some link function g 2 ”Mixture” models: Assume that μ arises from some other specified distribution. Beyond scope of this course. 5 / 25
Background image of page 5

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

View Full Document Right Arrow Icon
Generalized linear mixed models First approach: Assume that g ( μ ) has a Normal distribution Assumptions μ ij is linked to the linear predictor via g ( μ ij ) = x 0 ij β + z 0 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
Background image of page 6
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
Background image of page 7

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

View Full Document Right Arrow Icon
GLMM - example
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}