They encompass a multi dimensional and extensible model class for approximating overall distribution function in a semi-parametric dimension and this makes the modeling technique a popular technique accounting for a relevant diversity. Tere has been an increase in applications as model estimation has become feasible with the nowadays easily computing power in the previous ten years. Te simplest finite model mixtures are those finite mixtures for distribution, ued for model-based clustering. Terefore, te model takes the form of a combination of finite numbers with different distribution where each distribution to as component.
Te insertion of different types of models has led to the development of more complex mixtures. A obvious extension is to estimate generalized linear model for each component. Fnite mixtures of GLMs allow settling the assumption that the regression coefficients and dispersion parameters are similar observations. Cntrary to mixed effects models, were it is assumed that the distributions of the parameters of the observations is known, fnite mixture models do not require to specify this distribution a-prior but allow to approximate in the data given I the standard linear model, te dependant variable takes assumption of following a Gaussian distribution where the mean value is determined through a linear relationship.
Te assumption that the dependant variables follow a Gaussian distribution is relaxed in the generalized linear model framework. Te distribution of the dependant variable assumed to be from the exponential family distributions. Tis enables collection of certain data characteristics into certain accounts such as that the dependant variable is for example the counting variable with values, gnerally assumed to follow a poisoned distribution. Fr Gaussian distribution the identity function is the conical link, fr the poison the log function and for the gamma distribution the reciprocal function.
Te GLM framework is embedded in the finite mixture framework by placing GLMs in the components. Sveral special cases and extension of this model class exist. Te component specific densities are from the same paramedic family for each component. Fr notational simplicity and the link, fnction is also the same for all the components. I cluster wise regression settings, tis will be an obvious model choice no a priori knowledge...
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