Simultaneous Inference in Finite Mixtures of Regression Models

A general framework for simultaneous inference in finite mixtures of generalized linear regression models is presented. Assuming asymptotic normality of the maximum likelihood estimate of all interesting model parameters, confidence regions and p-values using a maximum norm for the multivariate t-statistic are derived. This allows to simultaneously test all regression coefficients whether they are zero. Another application is to test for constant effects across mixture components. Size and power of the new methods are evaluated using artificial data. A real world data set on the productivity of PhD students is used to demonstrate the application of the procedures.