Asymptotic properties of maximum likelihood estimator for two-step logit models

Two-step logit models are extensions of the ordinary logistic regression model, which are designed for complex ordinal outcomes commonly seen in practice. In this paper, we establish some asymptotic properties of the maximum likelihood estimator (MLE) of the regression parameter vector under some mild conditions, which include existence of the MLE, convergence rate and asymptotic normality of the MLE. We relax the boundedness condition of the regressors required in most existing theoretical results, and all conditions are easy to verify.