The Use of Two-Component Mixture Models with One Completely or Partly Known Component

If Generalized Linear Models do not fit the data at hand, then Finite Mixed Generalized Linear Models may be useful alternatives. Very often, mixture models having only two components improve the goodness of fit sufficiently in such cases. In this paper, situations are considered, where one of the two mixture components is completely or partly known. Procedures are given, which provide maximum likelihood estimators of the unknown parameters of such models as well as their standard errors. Generalized deviances based on a generalized Likelihood-Ratio test are proposed. A simulated data set is used to show the merits of using prior knowledge of one mixture component to improve effect estimates and the respective inference