Transcription of Generalized Linear Models - UW Faculty Web Server
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' $. Generalized Linear Models Objectives: Systematic + Random. Exponential family. Maximum likelihood estimation & inference. & %. 45 Heagerty, Bio/Stat 571. ' $. Generalized Linear Models Models for independent observations Yi , i = 1, 2, .. , n. Components of a GLM: . Random component Yi f (Yi , i , ). f exponential family & %. 46 Heagerty, Bio/Stat 571. ' $.. Systematic component i = X i . i : Linear predictor Xi : (1 p) covariate vector : (p 1) regression coefficient . Link function E(Yi | X i ) = i g( i ) = X i . g( ) : link function & %. 47 Heagerty, Bio/Stat 571. ' $. Generalized Linear Models GLMs generalize the standard Linear model : Yi = X i + i.
Generalized Linear Models † GLMs extend usefully to overdispersed and correlated data:. GEE: marginal models / semi-parametric estimation & inference. GLMM: conditional models / likelihood estimation & inference 49 Heagerty, Bio/Stat 571 ’ & $ %
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