Scale parameter of discrete choice model based on extreme value distribution

In order to understand the role of scale parameter in the process of modeling, analysis and application, multinomial logit model and nested logit model were discussed based on extreme value distribution. Starting with the distribution of error terms, the properties of scale parameter in two models were studied in aspects of model expressions and error term properties, and a comparison analysis was made. Analysis result shows that scale parameter not only restricts the scale of utility function, but also reflects the variance of error terms. However, it reveals different properties at two different models in terms of scale restriction, variance and independence degree of error terms, and numerical areas. For multinomial logit model, the scale parameter reflects the variance of entire error terms, while for nested logit model, it only reflects the variance of a part concerning the observed term for a specific alternative.