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.
Highlights
It is common to see count data with large numbers of zeros in many disciplines, e.g., biomedical studies, criminology, environmental economics, traffic accidents, et al To handle count data with excess zeros, a so-called zero-inflated Poisson (ZIP) distribution is employed (Singh, 1963; Johnson, Kotz, & Kemp, 1992)
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
Summary
It is common to see count data with large numbers of zeros in many disciplines, e.g., biomedical studies, criminology, environmental economics, traffic accidents, et al To handle count data with excess zeros, a so-called zero-inflated Poisson (ZIP) distribution is employed (Singh, 1963; Johnson, Kotz, & Kemp, 1992). The seminal work on ZIP regression by Lambert (1992) was used to model the extra proportion of zeros π and the mean of the Poisson distribution λ simultaneously with linear predictors using the appropriate link functions, and the parametric ZIP regression model was applied to the manufacturing data Many authors adopted this basic modeling structure, and a number of important extensions have been made (e.g., Welsh, Cunningham, Donnelly, & Lindenmayer, 1996; Shankar, Milton, & Mannering, 1997; Bohning, Dietz, Schlattmann, Mendonca, & Kirchner, 1999; Yau & Lee, 2001; Cheung, 2002; Hall & Zhang, 2004; Lu, Lin, & Shih, 2004; Min & Agresti, 2005; Hall & Wang, 2005; Hu, Li, & Lee, 2011).
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