A product-multinomial framework for categorical data analysis with missing responses

We extend the multinomial modeling scenario for the analysis of categorical data with missing responses described by Paulino (1991, Brazilian Journal of Probability and Statistics, 5, 1-42) to the product-multinomial setup so that the inclusion of explanatory variables is allowed. Assuming an ignorable missing data mechanism, linear and log-linear models may be fitted via maximum likelihood. Weighted least squares methodology may as well be used to fit more general functional linear models, if a missing completely at random mechanism is assumed. We also consider a hybrid approach, where any missingness process is fitted by maximum likelihood in a first step, and the estimated marginal probabilities of categorization and their covariance matrix are used in a second stage to fit the model via weighted least squares, in the spirit of functional asymptotic regression methodology. Goodness-of-fit tests are present, and the methodology is illustrated via two data sets. All the methods were computationally implemented via subroutines written in R.