기부횟수 분석을 통한 기부성향의 분석

The Analysis of the Number of Charitable Donations Using a Mixture of Poisson Regression on a Survey Data in S.Korea

The aim of this study is to analyze survey data on the number of charitable donations using a mixture of Poisson regression model to detect explanatory variables affecting the number of donations. The survey was conducted in S. Korea in 2008 by Volunteer 21, a non-profit organization in S. Korea. The number of donations per year which is the response variable takes a non-negative integer and thus Poisson regression might be the appropriate tool. The distribution of the number of donations indicates that the whole population be divided into three groups, namely, a fixed zero group, a small and a large groups, where the border line between the small and the large groups is eight per year. Noting the larger number of zero donations we fit zero inflated Poisson (ZIP). In addition to the ZIP, a mixture of two Poisson regression model is used for the two distinct groups. The zip+mixture of two Poisson model may be considered as a special case of a mixture of three Poissons in which one component is concentrated on zero mass. We employed an EM algorithm for estimating the regression parameters and detected several significant explanatory variables affecting the number of donations. These are the frequency of volunteer, income (10 levels), religion (binary) and white color job (binary). The proportions of fixed zero, small and large groups turn out to be 0.28, 0.57 and 0.15, respectively.