Recursive Computation of the Conditional Probability Function of the Quadratic Exponential Model for Binary Panel Data

We propose a general recursive algorithm for the computation of the conditional probability function of the quadratic exponential model for binary panel data given the total of the responses, which is a sufficient statistic for the individual intercept parameter. This recursion permits to implement conditional and pseudo-conditional maximum likelihood estimators of the parameters of this model, and related models such as the dynamic logit model, even when one or more statistical units are observed at many occasions. In this way we solve a typical problem in dealing with distributions with a complex normalizing constant. The advantage in terms of computational load with respect to standard techniques is assessed by simulation and illustrated by an application based on a popular dataset about brand loyalty.