Assessment and Selection of Competing Models for Count Data: An Application to Early Childhood Caries

Abstract

Count data has been witnessed in a wide range of disciplines in real life. Poisson, negative binomial (NB), zero inflated Poisson (ZIP) and zero inflated negative binomial (ZINB) are some of the regression models proposed to model data with count response. All the count models are potential candidates that can model count data, but there is no means to choose the one that would perform better than the others. This study aimed to assess the count models mentioned earlier at various degrees of zero inflation. Datasets were simulated with ZIP distribution with different conditions of zero inflation (0%, 2%, 5%, 10%, 15%, 20%, 30% and 40%). Poisson and NB were observed to predict regression coefficients well when the proportion of zero is below 15%. The two ZIM performed well at higher degrees of zero inflation; beyond 15% for ZIP and 20% for ZINB. Exploratory examination of the caries data revealed a zero inflation below 15%, that is, 3.23%. Analysis of early childhood caries (ECC) data among 3-6 year old children who visited Lady Northey Dental Clinic was then performed with Poisson and NB. Akaike information criterion (AIC) test was used to compare all the competing models both under simulation and with real data. Poisson yielded lower AIC values at lower zero inflation rates as compared to other three models. ZIP had the lowest AIC value at 10%, 15%, 20%, 30% and 40% levels of zero inflation. NB model had the lowest AIC value when real data was analyzed. Education level of the father-primary school completed, chewing gum several times a week, Feeding habit jam several times a day, Feeding habit juice every day, Feeding habit soda every day and Feeding habit sweets several times a week were found to be significant factors causing ECC.

Statistical modeling for zero-inflated data using GAMs

“…Zero inflated Poisson models (ZIP) (Lambert, 1992) and Zero inflated negative binomial models (ZINB) (Greene, 1994) are used to deal with these characteristics. Although used in many areas such as psychology (Atkins and Gallop, 2007), computer science (Souza et al, 2016) and several other applied fields (Farhadi Hassankiadeh et al, 2018;Njambi Wanjau, 2019), if the non-zero part of data is over-dispersed, the parameter estimates of a ZIP can be biased just as standard errors may be underestimated. Zero-inflated models are also used in the analisys of longitudinal data (Neelon et al, 2010;Rose et al, 2006).…”