Confidence Intervals for Finite Mixture Regression Based on Resampling Techniques

Finite Mixture Regression is a popular approach for regression settings with present but unobserved sub-populations. Over the past decades an extensive toolbox has been developed covering various kinds of distributions and effect types. As for any other thorough statistical analysis, reporting of e.g.\ confidence intervals for the parameters of the latent models is of high practical relevance. However, standard theory neglects the additional variability arising from also estimating class assignments, which consequently leads to the corresponding uncertainty estimates usually being too optimistic. In this work we propose a resampling technique for finite mixture regression models to construct confidence intervals for the regression coefficients in order to hold the type-I error threshold. The mechanism relies on bootstrapping which already proved useful for different problems arising for mixture models in the past and is evaluated via various simulation studies and two real world applications. Overall, the routine successfully holds the type-I error threshold and is less computationally expensive than alternative approaches.