On hypothesis testing in latent class and finite mixture stochastic frontier models, with application to a contaminated normal-half normal model

Latent class and finite mixture stochastic frontier models have been proposed as a means of allowing either for technological heterogeneity or more flexible distributions of noise and inefficiency. As in the wider literature on latent class and finite mixture models, we are interested in class enumeration, particularly testing against homogeneity. We apply a modified likelihood ratio test for homogeneity in a stochastic frontier setting, based on established results for non-Gaussian latent class and finite mixture models, and provide evidence from Monte Carlo experiments which suggest the applicability of results regarding a modified likelihood ratio test to the stochastic frontier setting. We demonstrate an application to testing a model with a contaminated normal noise term against a model with a normally distributed noise term, finding that the former is preferred, with significant implications for efficiency prediction.