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The Log Multinomial Regression Model for Nominal Outcomes with More than Two Attributes


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Blizzard, CL and Hosmer, DW 2007 , 'The Log Multinomial Regression Model for Nominal Outcomes with More than Two Attributes' , Biometrical Journal: journal of mathematical methods in biosciences, vol. 49, no. 6 , pp. 889-902 , doi: 10.1002/bimj.200610377.

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An estimate of the risk or prevalence ratio, adjusted for confounders, can be obtained from a log
binomial model (binomial errors, log link) fitted to binary outcome data. We propose a modification of
the log binomial model to obtain relative risk estimates for nominal outcomes with more than two
attributes (the “log multinomial model”). Extensive data simulations were undertaken to compare the
performance of the log multinomial model with that of an expanded data multinomial logistic regression
method based on the approach proposed by Schouten et al. (1993) for binary data, and with that of
separate fits of a Poisson regression model based on the approach proposed by Zou (2004) and Carter,
Lipsitz and Tilley (2005) for binary data. Log multinomial regression resulted in “inadmissable” solutions
(out-of-bounds probabilities) exceeding 50% in some data settings. Coefficient estimates by the
alternative methods produced out-of-bounds probabilities for the log multinomial model in up to 27%
of samples to which a log multinomial model had been successfully fitted. The log multinomial coefficient
estimates generally had lesser relative bias and mean squared error than the alternative methods.
The practical utility of the log multinomial regression model was demonstrated with a real data example.
The log multinomial model offers a practical solution to the problem of obtaining adjusted estimates
of the risk ratio in the multinomial setting, but must be used with some care and attention to

Item Type: Article
Authors/Creators:Blizzard, CL and Hosmer, DW
Keywords: Log binomial regression; Log link; Multinomial likelihood; Risk ratio.
Journal or Publication Title: Biometrical Journal: journal of mathematical methods in biosciences
ISSN: 0323-3847
DOI / ID Number: 10.1002/bimj.200610377
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