Finite mixtures of covariance structure models with regressors - Loglikelihood function, minimum distance estimation, fit indices, and a complex example

Models of finite mixtures of normal densities conditional on regressor variables are specified and estimated. The authors consider mixtures of multivariate normals where the expected value for each component depends on nonnormal regressor variables. The expected values and covariance matrices of the mixture components are parameterized using conditional mean-and covariance-structures. The authors discuss the construction of the likelihood function and outline the estimation of parameters. in addition, they define fit indices and discuss aspects of model specification and modification that are specific to mixtures of mean- and covariance-structures. Finally they give an empirical example in which they analyze the importance of automobiles to individuals depending on the latent constructs individualism and ecology-mindedness. It is shown that the sample under consideration comes from three heterogeneous subpopulations. It is demonstrated that each subpopulation may he characterized by a different mean-and covariance-structure.