  Count data play a critical role in medical research, such as heart disease.
The Poisson regression model is a common technique for evaluating the impact of
a set of covariates on the count responses. The mixture of Poisson regression
models with experts is a practical tool to exploit the covariates, not only to
handle the heterogeneity in the Poisson regressions but also to learn the
mixing structure of the population. Multicollinearity is one of the most common
challenges with regression models, leading to ill-conditioned design matrices
of Poisson regression components and expert classes. The maximum likelihood
method produces unreliable and misleading estimates for the effects of the
covariates in multicollinearity. In this research, we develop Ridge and
Liu-type methods as two shrinkage approaches to cope with the ill-conditioned
design matrices of the mixture of Poisson regression models with experts.
Through various numerical studies, we demonstrate that the shrinkage methods
offer more reliable estimates for the coefficients of the mixture model in
multicollinearity while maintaining the classification performance of the ML
method. The shrinkage methods are finally applied to a heart study to analyze
the heart disease rate stages.
