MCL: Stata module to estimate multinomial conditional logit models

MCL stands for Multinomial Conditional Logit, a term coined by Breen (1994). An MCL model uses a conditional logit program to estimate a multinomial logistic model. This produces the same log likelihood, estimates and standard errors, but allows greater flexibility in imposing constraints. The MCL approach makes it possible to impose different restrictions on the response variable for different independent variables. For example, linear logits could be imposed for certain independent variables and an unordered response for others. One specific application is to include models for the analysis of square tables, e.g. quasi-independence, uniform association, symmetric association, into a multinomial logistic model (Logan 1983, Breen 1994). Mclest can also estimate two types of models with both linear and multiplicative terms. The Stereotyped Ordered Regression model (SOR) estimates a metric for the dependent variable and a single parameter for each independent variable (Anderson 1984, DiPrete 1990). It is more flexible than ologit because it does not assume ordered categories, although it does assume that the response categories can be scaled on a single dimension. This makes it useful for "semi-ordered" variables such as occupation, where the rank of categories such as farmers is not altogether clear. A second special model that can be estimated by mclest is the Row and Columns model 2 (Goodman 1979). This model, originally developed for loglinear analysis, estimates a metric for a categorical independent variable as well as the response variable. The effect of the independent variable can therefore be expressed through a single parameter. The SOR and RC2 models are estimated by iteratively running MCL models, taking first one element of the multiplicative terms as given, then the other.