Evaluation of Structural Equation Mixture Models: Parameter Estimates and Correct Class Assignment

Structural equation mixture models (SEMMs) are latent class models that permit the estimation of a structural equation model within each class. Fitting SEMMs is illustrated using data from 1 wave of the Notre Dame Longitudinal Study of Aging. Based on the model used in the illustration, SEMM parameter estimation and correct class assignment are investigated in a large-scale simulation study. Design factors of the simulation study are (im)balanced class proportions, (im)balanced factor variances, sample size, and class separation. We compare the fit of models with correct and misspecified within-class structural relations. In addition, we investigate the potential to fit SEMMs with binary indicators. The structure of within-class distributions can be recovered under a wide variety of conditions, indicating the general potential and flexibility of SEMMs to test complex within-class models. Correct class assignment is limited.

[1]  K. Pearson Contributions to the Mathematical Theory of Evolution , 1894 .

[2]  K. Pearson Contributions to the Mathematical Theory of Evolution. II. Skew Variation in Homogeneous Material , 1895 .

[3]  T. W. Anderson,et al.  Classification into two Multivariate Normal Distributions with Different Covariance Matrices , 1962 .

[4]  V. Wood,et al.  An analysis of a short self-report measure of life satisfaction: correlation with rater judgments. , 1969, Journal of gerontology.

[5]  D. Hosmer A Comparison of Iterative Maximum Likelihood Estimates of the Parameters of a Mixture of Two Normal Distributions Under Three Different Types of Sample , 1973 .

[6]  G. Schwarz Estimating the Dimension of a Model , 1978 .

[7]  A. Cohen,et al.  Finite Mixture Distributions , 1982 .

[8]  T. Kamarck,et al.  A global measure of perceived stress. , 1983, Journal of health and social behavior.

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

[10]  Satya N. Mishra,et al.  Overlapping coefficient: the generalized t approach , 1986 .

[11]  S. Sclove Application of model-selection criteria to some problems in multivariate analysis , 1987 .

[12]  E. Ziegel Modern Mathematical Statistics , 1989 .

[13]  R. Ursano,et al.  The Impact of a Military Air Disaster on The Health of Assistance Workers: A Prospective Study , 1989, The Journal of nervous and mental disease.

[14]  A. Raftery,et al.  Model-based Gaussian and non-Gaussian clustering , 1993 .

[15]  K. Land,et al.  AGE, CRIMINAL CAREERS, AND POPULATION HETEROGENEITY: SPECIFICATION AND ESTIMATION OF A NONPARAMETRIC, MIXED POISSON MODEL* , 1993 .

[16]  A. Agresti Categorical data analysis , 1993 .

[17]  W. Meredith Measurement invariance, factor analysis and factorial invariance , 1993 .

[18]  G. Celeux,et al.  An entropy criterion for assessing the number of clusters in a mixture model , 1996 .

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

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

[21]  Kamel Jedidi,et al.  STEMM: A General Finite Mixture Structural Equation Model , 1997 .

[22]  Gerhard Arminger,et al.  Finite Mixtures of Covariance Structure Models with Regressors , 1997 .

[23]  Han L. J. van der Maas,et al.  Fitting multivariage normal finite mixtures subject to structural equation modeling , 1998 .

[24]  Adrian E. Raftery,et al.  MCLUST: Software for Model-Based Cluster Analysis , 1999 .

[25]  B. Muthén,et al.  Finite Mixture Modeling with Mixture Outcomes Using the EM Algorithm , 1999, Biometrics.

[26]  Gerhard Arminger,et al.  Mixtures of conditional mean- and covariance-structure models , 1999 .

[27]  B. Muthén,et al.  Integrating person-centered and variable-centered analyses: growth mixture modeling with latent trajectory classes. , 2000, Alcoholism, clinical and experimental research.

[28]  Geoffrey J. McLachlan,et al.  Finite Mixture Models , 2019, Annual Review of Statistics and Its Application.

[29]  D. Rubin,et al.  Testing the number of components in a normal mixture , 2001 .

[30]  Toni L. Bisconti,et al.  The Mediational Effect of Hardiness on Social Support and Optimal Outcomes in Later Life , 2001 .

[31]  Adrian E. Raftery,et al.  Model-Based Clustering, Discriminant Analysis, and Density Estimation , 2002 .

[32]  Bengt,et al.  Latent Variable Analysis With Categorical Outcomes : Multiple-Group And Growth Modeling In Mplus , 2002 .

[33]  Jay Magidson,et al.  Latent class models for classification , 2003, Comput. Stat. Data Anal..

[34]  Adrian E. Raftery,et al.  Enhanced Model-Based Clustering, Density Estimation, and Discriminant Analysis Software: MCLUST , 2003, J. Classif..

[35]  Neal O. Jeffries A note on 'Testing the number of components in a normal mixture' , 2003 .

[36]  Daniel J Bauer,et al.  The integration of continuous and discrete latent variable models: potential problems and promising opportunities. , 2004, Psychological methods.

[37]  D. Steinley Properties of the Hubert-Arabie adjusted Rand index. , 2004, Psychological methods.

[38]  Roger E. Millsap,et al.  Assessing Factorial Invariance in Ordered-Categorical Measures , 2004 .

[39]  B. Muthén,et al.  Investigating population heterogeneity with factor mixture models. , 2005, Psychological methods.

[40]  Douglas Thain,et al.  Distributed computing in practice: the Condor experience , 2005, Concurr. Pract. Exp..

[41]  M. Neale,et al.  Distinguishing Between Latent Classes and Continuous Factors: Resolution by Maximum Likelihood? , 2006, Multivariate behavioral research.

[42]  B. Muthén,et al.  Performance of Factor Mixture Models as a Function of Model Size, Covariate Effects, and Class-Specific Parameters. , 2007 .

[43]  B. Muthén,et al.  Deciding on the Number of Classes in Latent Class Analysis and Growth Mixture Modeling: A Monte Carlo Simulation Study , 2007 .

[44]  Adrian E. Raftery,et al.  MCLUST Version 3 for R: Normal Mixture Modeling and Model-Based Clustering † , 2007 .

[45]  S. Reise,et al.  Detecting Mixtures From Structural Model Differences Using Latent Variable Mixture Modeling: A Comparison of Relative Model Fit Statistics , 2007 .

[46]  Gitta Lubke,et al.  Distinguishing Between Latent Classes and Continuous Factors with Categorical Outcomes: Class Invariance of Parameters of Factor Mixture Models , 2008, Multivariate behavioral research.

[47]  P. Deb Finite Mixture Models , 2008 .