Application of the Power Series Probability Distributions for the Analysis of Zero-Inflated Insect Count Data

Abstract

Excess number of zeros (zero inflation, ZI) in count data is a common phenomenon which must be addressed in any analysis. The extra zeros may be a result of over-dispersion in the data. Ignoring zero-inflation can result in biased parameter estimates and standard errors. Over-dispersion is also associated with a zero-inflated data. Depending on the selected model, different results and conclusions may be reached. In this paper two commonly encountered models in count data are considered, namely, the Zero-Inflated Poisson (ZIP) and Zero-Inflated Negative Binomial (ZINB) probability distributions. Emphasis is placed on the Maximum Likelihood (ML) estimation of the model parameters. Specifically of interest was to es-timate the zero-inflation parameter and hence, the corrected frequencies. It was found that for the Poisson model, the zero-inflation parameter estimate was considerably higher than that from the Negative Binomial model. From the results however, it is suspected that the effectiveness of adjusting for the high number of zeros in both models might have been greatly affected by the inherent high variability between sites. It is then proposed that in future research, the problem of heterogeneity in count data be addressed before any further analysis.