Adding a Variable in Generalized Linear Models

The likelihood ratio statistic can be used to determine the significance of an explanatory variable in a generalized linear model. In order to obtain such a statistic, however, we need two sets of iterations for two maximum likelihoods. Moreover, the statistic is not directed to detect influential or outlying observations that affect the importance of the variable considered. Therefore we develop relatively simple procedures to help the analyst select an appropriate model and detect the effects of such observations on adding a variable into any model. Two examples are given for illustration.