eCite Digital Repository

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


Blizzard, CL and Hosmer, DW, The Log Multinomial Regression Model for Nominal Outcomes with More than Two Attributes, Biometrical Journal: journal of mathematical methods in biosciences, 49, (6) pp. 889-902. ISSN 0323-3847 (2007) [Refereed Article]

DOI: doi:10.1002/bimj.200610377


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 detail. © 2007 WILEY-VCH Verlag GmbH & Co. KGaA.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Statistics
Research Field:Applied statistics
Objective Division:Health
Objective Group:Other health
Objective Field:Other health not elsewhere classified
UTAS Author:Blizzard, CL (Professor Leigh Blizzard)
ID Code:50515
Year Published:2007
Web of Science® Times Cited:57
Deposited By:Menzies Institute for Medical Research
Deposited On:2007-08-01
Last Modified:2008-06-03

Repository Staff Only: item control page