Regression-based imputation of explanatory discrete missing data

Imputation of missing values is a strategy for handling non-responses in surveys or data loss in measurement processes, which may be more effective than ignoring the losses and omitting them. The characteristics of variables presenting missing values must be considered when choosing the imputation method to be used; in particular when the variable is a count the literature dealing with this issue is scarce. If the variable has an excess of zeros it is necessary to consider models including parameters for handling zero-inflation. Likewise, if problems of over- or under-dispersion are observed, generalizations of the Poisson, such as the Hermite or Conway–Maxwell Poisson distributions are recommended for carrying out imputation. The aim of this study was to assess the performance of various regression models in the imputation of a discrete variable based on Poisson generalizations, in comparison with classical counting models, through a comprehensive simulation study considering a variety of scenarios and a real data example. To do so we compared the results of estimations using only complete data, and using imputations based on the most common count models. The COMPoisson distribution provides in general better results in any dispersion scenario, especially when the amount of missing information is large.