The Role of the Scale Parameter in the Estimation and Comparison of Multinomial Logit Models

Multinomial logit (MNL) models are widely used in marketing research to analyze choice data, but it is not generally recognized that the unit of the utility scale in a MNL model is inversely related to the error variance. This means that, for instance, parameters of two identical utility specifications estimated from different data sources with unequal variances will necessarily differ in magnitude, even if the true model parameters that generated the utilities are identical in both sets. Despite a growing number of papers that compare MNL coefficients, no examples of appropriate tests of the joint and separate hypotheses of scale and parameter equality in MNL models exist in the marketing literature. The purpose of this paper is to address the proper procedure for MNL parameter comparisons between different data sets and to propose a simple relative scaling test that can be implemented with standard MNL estimation software. Several examples are given to illustrate the approach.