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Stat Med. 2013 Apr 30;32(9):1572-83. doi: 10.1002/sim.5650. Epub 2012 Oct 11.

Modeling health survey data with excessive zero and K responses.

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Department of Statistics, National Taipei University, 151 University Rd., San Shia District New Taipei City, 23741,Taiwan.


Zero-inflated Poisson regression is a popular tool used to analyze data with excessive zeros. Although much work has already been performed to fit zero-inflated data, most models heavily depend on special features of the individual data. To be specific, this means that there is a sizable group of respondents who endorse the same answers making the data have peaks. In this paper, we propose a new model with the flexibility to model excessive counts other than zero, and the model is a mixture of multinomial logistic and Poisson regression, in which the multinomial logistic component models the occurrence of excessive counts, including zeros, K (where K is a positive integer) and all other values. The Poisson regression component models the counts that are assumed to follow a Poisson distribution. Two examples are provided to illustrate our models when the data have counts containing many ones and sixes. As a result, the zero-inflated and K-inflated models exhibit a better fit than the zero-inflated Poisson and standard Poisson regressions.

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