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Activity Number: 137
Type: Contributed
Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistics in Epidemiology
Abstract - #309354
Title: Case-Wise Diagnostics for the Multinomial Log-Link Regression Model
Author(s): Leigh Blizzard*+ and David W. Hosmer and Stephen J. Quinn and Jana D. Canary
Companies: University of Tasmania and University of Massachusetts Amherst and Flinders Clinical Effectiveness and Menzies Research Institute Tasmania
Keywords: Regression ; Multinomial likelihood ; Logarithmic link ; Goodness of fit ; Regression diagnostics

For nominal outcomes with more than two attributes, relative risk estimates are obtained by fitting a multinomial logistic regression model with a log link. This is the log multinomial regression model. Several summary measures of goodness-of-fit provide a global test of the adequacy of a fitted log multinomial model, and a range of diagnostic quantities can be used to identify observations that influence the estimated coefficients of the fitted model and/or its predicted probabilities. These case-wise diagnostics are a natural adaption of those proposed by Pregibon (1981) for the binary logistic model, and extended to the multinomial logistic model by Lesaffre & Albert (1989). We provide estimation formulae for log multinomial diagnostics, investigate the implications of the different mathematical structures of the logit and log links, and demonstrate their calculation using example data sets. The usefulness of graphical plots are explored, troublesome cases in which different diagnostics provide conflicting results are highlighted, and guidance in their interpretation of their values is offered with tentative guidelines for identifying outlying and influential observations.

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