Deviance for Binary Data Notes

P value for d p d dobs obtained from 2dof unm other

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Unformatted text preview: of covariate combinations − no. of estimated regression coefficients. In general, large values of D imply model lack of fit. D not testing for Binomial assumption of the data. D testing if one or more predictors have been omitted from the model. p-value for D : P [D > Dobs ] obtained from χ2dof ) . ( UNM Other ’diagnostics’ (summaries) pseudo R 2 statistic, pseudo R 2 = ˆ logLs − logL(β ) logLs where LS is the max. likelihood for the saturated model ˆ and L(β ) is the max likelihood for a model with covariates. ”proportional improvement in log-likelihood”. Another pseudo R 2 statistic (Mc Fadden’s) ˆ ˆ logL(β0 ) − logL(β ) pseudo R 2 = ˆ logL(β0 ) Efron’s R2 = 1 − N i =1 (yi N i =1 (yi − πi )2 ˆ ¯ − Y )2 UNM Residuals Yi number of successes. ni number of trials. πi estimated probability of success based on a glm ˆ Pearson chi-square residuals ri = Yi − ni πi ˆ ni πi (1 − πi ) ˆ ˆ ; i = 1, 2, . . . , N Chi-square statistic, N X2 = ri2 i =1 has the same dofs as D , N − (p + 1). How does deviance work for a Poisson regression? UNM...
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This note was uploaded on 01/27/2014 for the course STAT 574 taught by Professor Gabrielhuerta during the Fall '13 term at New Mexico.

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