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

Abstract:

: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 Cg, is obtained by calculating the Pearson chi2 statistic where the estimated expected frequencies are the sum of the model-based estimated logistic probabilities. Simulations compare the properties of Cg with those of the ungrouped Pearson chi2 test (X2) and its normalized test (z). The null distribution of Cg is well approximated by the chi2 distribution with (g-2) x (c-1) degrees of freedom. The sampling distribution of X2 is compared with a chi2 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 Cg 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.

journal_name

Stat Med

journal_title

Statistics in medicine

authors

Fagerland MW,Hosmer DW,Bofin AM

doi

10.1002/sim.3202

subject

Has Abstract

pub_date

2008-09-20 00:00:00

pages

4238-53

issue

21

eissn

0277-6715

issn

1097-0258

journal_volume

27

pub_type

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