This paper presented four parametric count distributions: Poisson (P), Negative Binomial (NB), Poisson Hurdle (PH) and Negative Binomial Hurdle (NBH) regression models. Data used was extracted from the 2018 National Demographic and Health Survey. The LRT, Vuong test, rootograms, Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC) were used as goodness-of-fit and model selection measures. The objectives of this study were to examine the models for analyzing ideal number of children data exhibiting overdispersion, evaluate their performance and interpret the result of the best model selected that significantly assess some factors contributing to fertility preferences in Nigeria. It was revealed that Poisson-type (P and PH) models were more appropriate in handling of the overdispersion in the ideal number of children data than the NB-type (NB and NBH) models. The result further showed that there was no difference between the PH and NBH models (Z = 0.2435, p = 0.4038). According to both AIC and BIC of the four competing models, it shows that PH model provided a good fit to the ideal number of children data best than the other models (P, NB and NBH). The finding from this study was that mother’s current age, age at first birth, age at first intercourse, place of residence, region of residence except South-West; middle wealth quintile category and Muslim women were found to be significant factors for mothers choosing no child and at least a child as the ideal number of children to have for their whole life in Nigeria.

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