L9handout - PUBH 7430 Lecture 9 J. Wolfson Division of...

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Unformatted text preview: PUBH 7430 Lecture 9 J. Wolfson Division of Biostatistics University of Minnesota School of Public Health October 4, 2011 The Generalized Linear Model The Generalized Linear Model generalizes the standard linear model by: 1 Letting a function of the mean be a linear combination of the covariates: g ( ) = X 2 Letting the variance be a function of the mean: Var ( Y | X ) = V ( ) GLMs: Coefficient interpretation Coefficient interpretation must take into account the link function g : A one-unit increase in X is associated with a -unit increase/decrease in g ( ) Can work backwards to get familiar cases: Poisson regression: A one-unit increase in X is associated with an exp( ) percent increase/decrease in the mean of Y Logistic regression: A one-unit increase in X is associated with an exp( ) 1+exp( ) percent increase/decrease in the odds of Y Aside: Log transformation When data are positive and display evidence of non-normality, log transformation is often recommended before proceeding with inference. If using a linear model, we are assuming: E [log( Y i ) | x i ] = x i Var [log( Y i ) | x i ] = 2 An alternative is to fit a GLM with a log link and our choice of variance function: log( E [ Y i | x i ]) = x i Var [ Y i | x i ] = V ( i ) Aside: Log transformation...
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L9handout - PUBH 7430 Lecture 9 J. Wolfson Division of...

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