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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
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
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)
logL(β0 ) − logL(β )
pseudo R 2 =
R2 = 1 − N
i =1 (yi
i =1 (yi − πi )2
− Y )2
UNM Residuals Yi number of successes. ni number of trials.
πi estimated probability of success based on a glm
Pearson chi-square residuals
ri = Yi − ni πi
ni πi (1 − πi )
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?
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- Fall '13