Score Tests for Semiparametric Zero-inflated Poisson Models

Abstract

Count data sets often produce many zeros. It is sometimes potentially questionable to use a linear predictor to model the effect of a continuous covariate of interest in zero-inflated count data. To relax the restriction, Li (2011) proposed a semiparametric zero-inflated Poisson (ZIP) regression model by using fixed-knot cubic basis splines or B-splines to model the covariate effect, and used the likelihood ratio test to assess the validity of the linear relationship between the natural logarithm of the Poisson mean and the covariate. A score test is conducted to assess whether the extra proportion of zeros in the semiparametric ZIP regression model is equal to zero.

Type I multivariate zero-inflated Poisson distribution with applications

“…In the regression setting, van den Broek (1995) proposed a simple score test, which transformed φ and λ in a ZIP model into θ = φ/(1 − φ) and log(λ) = β 0 + β 1 X 1 + · · · + β p X p . Later, Paul (2000, 2005) and Li (2012) have further studied the score tests for ZIP models. At the same time, Jansakul and Hinde (2002) and Min and Czado (2010) have compared the score test with the Wald test and the likelihood ratio test for the hypothesis of no inflation of zeros.…”

A new multivariate zero‐adjusted Poisson model with applications to biomedicine

“…In literature, a class of univariate zero‐truncated discrete models such as zero‐truncated Poisson (ZTP) distribution (David and Johnson, ; Moore, ; Rider, ; Cohen, , ; Finney and Varley, ; Rao and Chakravarti, ; Irwin, ; Dahiya and Gross, ; Gurmu, ; Meng, ; Best et al ., 2007), zero‐truncated binomial distribution (Finney, ; Rider, ), zero‐truncated negative‐binomial distribution (Rider, ; Sampford, ; Hartley, ; Grogger and Carson, ), zero‐truncated generalized negative‐binomial distribution (Gupta, ), zero‐truncated generalized Poisson (Medhi, ; Consul, 1989), and intervened Poisson distribution (Shanmugam, ) were developed to model count data without zero value. On the other hand, the zero‐inflated Poisson (ZIP) model (Cohen, ; Singh, ; Martin and Katti, ; Johnson and Kotz, 1969; Goraski, ; Kemp, ; Mullahy, ; Lambert, ; Böhning et al., ; Cheung, ; Deng and Paul, , ; Winkelmann, 2004; Min and Agresti, ; Min and Czado, ; Neelon et al ., 2010; Li, ), zero‐inflated generalized Poisson model (Angers and Biswas, ; Famoye and Singh, ; Cui and Yang, ; Xie et al ., 2009), zero‐inflated negative binomial model (Ridout et al ., 2001; Yau et al ., 2003; Bago d'Uva, ; Neelon et al ., 2010) were proposed to fit count data with extra zeros.…”

Effect of Missing Data on Estimation of the Impact of Heat Waves: Methodological Concerns for Public Health Practice

“…One process produces Poisson counts, some of which may be zero, and the other produces zeroes based on a binary process, which may or may not be defined using parameters from the Poisson distribution [22,23]. Let Y t c denote the number of heat-related morbidities on day t in county c and let X t c be the exposures within county c, c = 1, .…”