Multinomial goodness-of-fit tests for logistic regression models.

摘要

We examine the properties of several tests for goodness-of-fit for multinomial logistic regression. One test is based on a strategy of sorting the observations according to the complement of the estimated probability for the reference outcome category and then grouping the subjects into g equal-sized groups. A g x c contingency table, where c is the number of values of the outcome variable, is constructed. The test statistic, denoted as C(g), is obtained by calculating the Pearson chi(2) statistic where the estimated expected frequencies are the sum of the model-based estimated logistic probabilities. Simulations compare the properties of C(g) with those of the ungrouped Pearson chi(2) test (X(2)) and its normalized test (z). The null distribution of C(g) is well approximated by the chi(2) distribution with (g-2) x (c-1) degrees of freedom. The sampling distribution of X(2) is compared with a chi(2) distribution with n x (c-1) degrees of freedom but shows erratic behavior. With a few exceptions, the sampling distribution of z adheres reasonably well to the standard normal distribution. Power simulations show that C(g) has low power for a sample of 100 observations, but satisfactory power for a sample of 400. The tests are illustrated using data from a study of cytological criteria for the diagnosis of breast tumors. Copyright (c) 2008 John Wiley & Sons, Ltd.