Deviance for Binary Data Notes

# Deviance for Binary Data Notes - Settings for a...

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Settings for a Binary-Binomial response model Sample of target population. Each individual is independent and classified by success, failure . Response Predictors for each individual Y1=0 x11,x12, ,x1p Y2=0 x21,x22, ,x2p Y3=1 x31,x32, ,x3p Individuals with same values for X 1 , X 2 , . . . , X p are grouped. Group Response n1 Y1 n2 Y2 n3 Y3 n i number of individuals, Y i no. of successes for group i . UNM

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Each group has an equal set of predictor variables. (dose-response experiment) For example, all individuals in group i have the same ”age”. Few replicates of X 1 , X 2 , . . . , X p . Data reported as 0 - 1 Case 1: Binary non-replicated data. Case 2: Grouped data model or stratified Binomial model. Observations grouped at covariate levels Group sizes n i much larger than 1. The MLEs of β 0 , β 1 , . . . , β p do not depend on individuals begin grouped with covariates or not. UNM
Distributional results on Binary/Binomial models If sample size large ( n = n 1 + n 2 + . . . + n N ), then ˆ β i N ( β i , Var ( ˆ β i )) Typically Var ( ˆ β i ) are obtained by software package.

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