Deviance Test Logistic Regression. It measures the disagreement between the maxima of the observed and the fitted log likelihood functions. This test procedure is analagous to the general linear F test procedure for multiple linear regression.
The larger the deviance the poorer the fit. This increase in deviance is evidence of a significant lack of fit. This suggests the following residual called the deviance residual.
The smaller the deviance the closer the fitted value is to the saturated model.
This is possible because the deviance is given by the chi-squared value at a certain degrees of freedom. Many software packages provide this test either in the output when fitting a Poisson regression model or can perform it after fitting such a model eg. Deviance residuals The other approach is based on the contribution of each point to the likelihood For logistic regression X i fy ilog ˇ i 1 y ilog1 ˇ ig By analogy with linear regression the terms should correspond to 1 2 r 2 i. Suppose we want to run the above logistic regression model in R we use the following command.
