Abstract
This paper is about fitting multivariate normal mixture distributions subject to structural equation modeling. The general model comprises common factor and structural regression models. The introduction of covariance and mean structure models reduces the number of parameters to be estimated in fitting the mixture and enables one to investigate a variety of substantive hypotheses concerning the differences between the components in the mixture. Within the general model, individual parameters can be subjected to equality, nonlinear and simple bounds constraints. Confidence intervals are based on the inverse of the Hessian and on the likelihood profile. Several illustrations are given and results of a simulation study concerning the confidence intervals are reported.
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We thank Harrie Vorst for his generous support. We thank Yiu-Fai Yung for kindly making available his thesis (Yung, 1994), and a copy of his, at the time of revising the present paper, unpublished Psychometrika article (Yung, 1997). We thank Petra Stein for making available her paper with Gerhard Arminger (Arminger & Stein, 1997). A total of five reviews provided by anonymous referees, and additional comments by the editors resulted in a good number of improvements. Finally, we thank Peter Molenaar for his critical comments.
This paper was first submitted to Psychometrika in May of 1996, after a period of about 6 months in which we developed and tested our FORTRAN routines. In two rounds of highly constructive reviews, two dissertations (Stein, 1997; Yung, 1994), and severl articles were brought to our attention, that were either submitted (Arminger & Stein), or in press (Yung, Jedidi et al.). In the mean time, a number of these papers have appeared (Jedidi et al. 1997a, 1997b), and more are sure to follow (Yund, 1997; Arminger & Stein, 1997). It is clear that the subject of structural equation modeling within normal mixtures has taken off over the past few years (though Blåfield's pioneering thesis appeared in 1980). Although we were unaware of the work that was on-going, or indeed completed, when we embarked on this project, it is with pleasure that we acknowledge the precedence of those, whose work, in press, submitted, or otherwise, has come to our attention sice first submitting this paper to Psychometrika.
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Dolan, C.V., van der Maas, H.L.J. Fitting multivariage normal finite mixtures subject to structural equation modeling. Psychometrika 63, 227–253 (1998). https://doi.org/10.1007/BF02294853
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DOI: https://doi.org/10.1007/BF02294853