Testing for two components in a switching regression model

We consider switching regression models with independent or Markov-dependent regime. Based on the modified likelihood ratio test (LRT) statistic by Chen, Chen and Kalbfleisch (2004, JRSSB) we propose a test for two against more states of the underlying regime, and derive its asymptotic distribution in case when there is a single switching parameter. We show that its asymptotic distribution is robust when the regime is no longer independent but rather Markov-dependent. In a simulation study we investigate the finite-sample behavior of the test. Finally, we apply the methodology to data of a dental health trial. Here, the model selection criteria AIC and BIC favor distinct binomial regression models with switching intercept (AIC three states, BIC two states). The modified LRT allows us to reject the hypothesis of two states in favor of three states.