Mixtures of conditional mean- and covariance-structure models

Models and parameters of finite mixtures of multivariate normal densities conditional on regressor variables are specified and estimated. We consider mixtures of multivariate normals where the expected value for each component depends on possibly nonnormal regressor variables. The expected values and covariance matrices of the mixture components are parameterized using conditional mean- and covariance-structures. We discuss the construction of the likelihood function, estimation of the mixture model with regressors using three different EM algorithms, estimation of the asymptotic covariance matrix of parameters and testing for the number of mixture components. In addition to simulation studies, data on food preferences are analyzed.

[1]  Gerhard Arminger,et al.  Specification and Estimation of Mean Structures: Regression Models , 1995 .

[2]  Yiu-Fai Yung,et al.  Finite mixtures in confirmatory factor-analysis models , 1997 .

[3]  N. Kiefer.  Discrete Parameter Variation: Efficient Estimation of a Switching Regression Model , 1978 .

[4]  Dennis J. Aigner,et al.  Latent variables in socio-economic models , 1978 .

[5]  Clifford C. Clogg,et al.  Handbook of statistical modeling for the social and behavioral sciences , 1995 .

[6]  Martin R. Wolf,et al.  K3 User Guide , 2000 .

[7]  M. Browne.  Generalized Least Squares Estimators in the Analysis of Covariance Structures. , 1973 .

[8]  G. Arminger,et al.  Specification and Estimation of Mean- and Covariance-Structure Models , 1995 .

[9]  J. Wolfe.  A Monte Carlo Study of the Sampling Distribution of the Likelihood Ratio for Mixtures of Multinormal Distributions , 1971 .

[10]  G. McLachlan.  On Bootstrapping the Likelihood Ratio Test Statistic for the Number of Components in a Normal Mixture , 1987 .

[11]  Karl G. Jöreskog,et al.  LISREL 7: A guide to the program and applications , 1988 .

[12]  Michel Wedel,et al.  On Estimating Finite Mixtures of Multivariate Regression and Simultaneous Equation Models , 1996 .

[13]  W. DeSarbo,et al.  Finite-Mixture Structural Equation Models for Response-Based Segmentation and Unobserved Heterogeneity , 1997 .

[14]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[15]  Murray Aitkin,et al.  Statistical Modelling of Data on Teaching Styles , 1981 .

[16]  Geoffrey J. McLachlan,et al.  FITTING FINITE MIXTURE MODELS IN A REGRESSION CONTEXT , 1992 .

[17]  W. DeSarbo,et al.  A maximum likelihood methodology for clusterwise linear regression , 1988 .

[18]  K. Lange,et al.  EM algorithms without missing data , 1997, Statistical methods in medical research.

[19]  T. Louis.  Finding the Observed Information Matrix When Using the EM Algorithm , 1982 .

[20]  A. F. Smith,et al.  Statistical analysis of finite mixture distributions , 1986 .

[21]  P. Whittle,et al.  Latent Variables in Socio‐Economic Models , 1978 .

[22]  B. Lindsay,et al.  The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family , 1994 .

[23]  D. Rubin,et al.  Estimation and Hypothesis Testing in Finite Mixture Models , 1985 .