  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 them. When the variable represents a count, the literature dealing
with this issue is scarce. Likewise, if problems of over- or under-dispersion
are observed, generalisations of the Poisson distribution are recommended for
carrying out imputation. In order to assess the performance of various
regression models in the imputation of a discrete variable compared to
classical counting models, this work presents a comprehensive simulation study
considering a variety of scenarios and real data. To do so we compared the
results of estimations using only complete data, and using imputations based on
the Poisson, negative binomial, Hermite, and COMPoisson distributions, and the
ZIP and ZINB models for excesses of zeros. The results of this work reveal that
the COMPoisson distribution provides in general better results in any
dispersion scenario, especially when the amount of missing information is
large. When the variable presenting missing values is a count, the most widely
used method is to assume that a classical Poisson model is the best alternative
to impute the missing counts; however, in real-life research this assumption is
not always correct, and it is common to find count variables exhibiting
overdispersion or underdispersion, for which the Poisson model is no longer the
best to use in imputation. In several of the scenarios considered the
performance of the methods analysed differs, something which indicates that it
is important to analyse dispersion and the possible presence of excess zeros
before deciding on the imputation method to use. The COMPoisson model performs
well as it is flexible regarding the handling of counts with characteristics of
over- and under-dispersion, as well as with equidispersion.
