Goodness-of-Fit Tests for Multinomial Log-Link Regression Models

• Activity Number: 43
• Type: Contributed
• Date/Time: Sunday, August 1, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Leigh Blizzard*+ and Steve John Quinn and David W. Hosmer and Jana D. Canary
• Companies: Menzies Research Institute and Menzies Research Institute and University of Massachusetts, Amherst and University of Tasmania
• Keywords: Regression ; multinomial likelihood ; logarithmic link ; risk ratio ; goodness of fit

Abstract

For nominal outcomes with J>2 attributes, relative risk estimates can be obtained from the log multinomial model. We examine the properties of several tests of goodness-of-fit for this model. One test is based on an extension of the Hosmer-Lemeshow test for binary logistic regression. The n observations are sorted by the sum of the fitted probabilities, classified into g groups, and cross-tabulated in a J × g contingency table. The test statistic is the Pearson ?2 statistic for the table, with expected frequencies calculated as the sum of the fitted multinomial logistic regression probabilities. We show that the null distribution for the log multinomial model is well-approximated by the chi-squared distribution with (g-2)×(J-1) degrees of freedom. Power simulations for models with a uniform covariate show adequate power to detect moderate deviations for sample sizes of n = 500 or larger