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Chapter 58: Mixture Models
Mixture models involving a discrete mixture of specified (kernel) distributions allow the flexible fitting of observations for a response variable measured across a number of units. These measurements could be more dispersed than expected for a generalized linear model, or their marginal distribution may have a complex shape with multiple modes, suggesting a missing categorical explanatory variable, or considerable skewness reflecting a small number of extreme units. Essentially, the manner in which the kernel distribution is mixed is estimated in the form of parameters of an unknown discrete mixing distribution, along with estimates of the parameters of the kernel distributions, such as their means.
As an illustration of mixture models with a wide range of applicability, models for count data will be considered. ...