Improved random-starting method for the EM algorithm for finite mixtures of regressions

Two methods for generating random starting values for the expectation maximization (EM) algorithm are compared in terms of yielding maximum likelihood parameter estimates in finite mixtures of regressions. One of these methods is ubiquitous in applications of finite mixture regression, whereas the other method is an alternative that appears not to have been used so far. The two methods are compared in two simulation studies and on an illustrative data set. The results show that the alternative method yields solutions with likelihood values at least as high as, and often higher than, those returned by the standard method. Moreover, analyses of the illustrative data set show that the results obtained by the two methods may differ considerably with regard to some of the substantive conclusions. The results reported in this article indicate that in applications of finite mixture regression, consideration should be given to the type of mechanism chosen to generate random starting values for the EM algorithm. In order to facilitate the use of the proposed alternative method, an R function implementing the approach is provided in the Appendix of the article.