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Abstract:
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The past decade has seen significant advances in developments of mixtures-of-regressions models. Many of these developments have focused on the setting with continuous responses. When the response is count data, and the distribution of that response conditioned on a set of known predictors follows a mixture distribution, then a pragmatic choice is to use a mixture of Poisson regressions model. However, traditional methods assume that the predictors are mea- sured without error, which leads to bias in the estimation. We discuss estimation of a mixture of Poisson regressions model when there is measurement error in the predictors. Three estimators of the parameters are derived and compared with respect to their relative efficiencies. We then apply our model to a dataset involving counts of clandestine methamphetamine laboratories.
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