Statistical Modelling 19 (4) (2019), 341–361
A new and intuitive test for zero modification
Paul Wilson
School of Mathematics and Computer Science,
University of Wolverhampton,
United Kingdom.
e-mail: pauljwilson@wlv.ac.uk
Jochen Einbeck
Department of Mathematical Sciences,
Durham University,
Durham,
United Kingdom.
Abstract:
While there do exist several statistical tests for detecting zero modification in count data regression models, these rely on asymptotical results and do not transparently distinguish between zero inflation and zero deflation. In this manuscript, a novel non-asymptotic test is introduced which makes direct use of the fact that the distribution of the number of zeros under the null hypothesis of no zero modification can be described by a Poisson-binomial distribution. The computation of critical values from this distribution requires estimation of the mean parameter under the null hypothesis, for which a hybrid estimator involving a zero-truncated mean estimator is proposed. Power and nominal level attainment rates of the new test are studied, which turn out to be very competitive to those of the likelihood ratio test. Illustrative data examples are provided.
Keywords:
zero inflation; Count data; Poisson-binomial distribution; zero-truncated Poisson distribution; mid-p-values.
Downloads:
R Code and Data can be found here.
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