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Abstract:
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In principle, the log binomial model can be modified to obtain relative risk estimates for nominal outcomes with more than two attributes. We examine some technical issues that arise when one attempts to fit to multinomial data a model with log link (the "log multinomial model"). In extensive simulations, its performance is compared with that of an alternative method based on the approach proposed by Schouten et al. (1993) for binary data, and with separate fits of a Poisson regression model. Log multinomial regression resulted in "failure" rates (non-convergence, out-of-bounds probabilities) exceeding 50% in some data settings. The other methods produced out-of-bounds probabilities for data successfully fitted by a log multinomial model. Log multinomial coefficient estimates had least relative bias and mean squared error, but with greater-than-nominal confidence interval coverage.
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