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Modeling health survey data with excessive zero and K responses
Author(s) -
Lin Ting Hsiang,
Tsai MinHsiao
Publication year - 2012
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.5650
Subject(s) - poisson distribution , count data , poisson regression , zero (linguistics) , statistics , multinomial distribution , zero inflated model , multinomial logistic regression , mathematics , logistic regression , overdispersion , negative binomial distribution , econometrics , population , demography , linguistics , philosophy , sociology
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. Copyright © 2012 John Wiley & Sons, Ltd.