Mixture modeling with applications in schizophrenia research

Abstract

Finite mixture modeling, together with the EM algorithm, have been widely used in clustering analysis. Under such methods, the unknown group membership is usually treated as missing data. When the “complete data” (log-)likelihood function does not have an explicit solution, the simplicity of the EM algorithm breaks down. Authors, including Rai and Matthews [Rai, S.N., Matthews, D.E., 1993. Improving the em algorithm. Biometrics 49, 587–591], Lange [Lange, K., 1995a. A gradient algorithm locally equivalent to the em algorithm. Journal of the Royal Statistical Society B 57(2) 425–437], and Titterington [Titterington, D.M., 1984. Recursive parameter estimation using incomplete data. Journal of the Royal Statistical Society B. 46, 257–267] developed modified algorithms therefore. As motivated by research in a large neurobiological project, we propose in this paper a new variant of such modifications and show that it is self-consistent. Moreover, simulations are conducted to demonstrate that the new variant converges faster than its predecessors.