A study of the score test in discrimination poisson and zero-inflated poisson models

Vanessa Siqueira Peres Da Silva,Marcelo Angelo Cirillo,Juliana Garcia Cespedes

doi:10.4025/actascitechnol.v35i2.15071

Vanessa Siqueira Peres Da Silva, Marcelo Angelo Cirillo + Show 1 more

Open Access

https://doi.org/10.4025/actascitechnol.v35i2.15071

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Abstract

In many experimental situations the sample may present excess zero observations and generally are used probabilistic models for zero inflated to represent them. However no one knows precisely the amount of zero observations that these models support. Depending on the sample size and null observations number the Poisson model can be used. Based on this question, the objective of this paper is to evaluate the properties of Type I error and power of the score test (proposed by Van Den Broek (1995) to discriminate the Poisson and Zero-inflated Poisson models) and ascertain the most appropriate model to represent a sample with excess zeros without compromising the statistical inference. Through Monte Carlo simulation we concluded that when considering a sample of size at least n = 40 with 30% of the null observations, the score test had a high discriminatory power between the ZIP and Poisson model indicating that in fact is relevant the use of the ZIP model.

Highlights

Before defining which probabilistic model is used in data modeling, the researcher may be faced with samples that have a significant amount of zero observations
For θ = 10 the results were conservative for almost all sample sizes
This fact is somewhat consistent with the construction of the score test proposed by Van Den Broek (1995), as besides the test is asymptotic, the distribution of score statistic is approximately distributed by chi-square, and necessarily it requires assumption of normality

Summary

Introduction

Before defining which probabilistic model is used in data modeling, the researcher may be faced with samples that have a significant amount of zero observations In this situation, the usual method of parameters estimation, the maximum likelihood method, should be modified so that estimates can contemplate the effect of the presence of these observations. Technology is sensitive to the presence of outliers and suggests a correction in the estimates because different models used for response have varied sensitivity in detecting outliers To work around this problem, zero-inflated models can be used in the analysis of these data (CZADO et al, 2007; FAMOYE; SINGH, 2006; LAMBERT, 1992; MIN; CZADO, 2010; MULLAHAY, 1997; SLYMEN et al, 2006; SILVA; CIRILLO, 2010)

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