A Unified Approach to Multi-group Structural Equation Modeling with Nonstandard Samples

To appear in: G. A. Marcoulides & R. E. Schumacker (Eds.) Advanced Structural Equation Modeling: New Developments and Techniques Mahwah, NJ: Erlbaum. A Unified Approach to Multi-group Structural Equation Modeling with Nonstandard Samples ∗ Ke-Hai Yuan University of North Texas and Peter M. Bentler University of California, Los Angeles February 21, 2000 This project was supported by a University of North Texas Faculty Research Grant Program and Grants DA01070 and DA00017 from the National Institute on Drug Abuse.

[1]  Ke-Hai Yuan,et al.  Asymptotics of Estimating Equations under Natural Conditions , 1998 .

[2]  A. Satorra,et al.  A scaled difference chi-square test statistic for moment structure analysis , 1999 .

[3]  Michael E. Sobel,et al.  Pseudo-Maximum Likelihood Estimation of Mean and Covariance Structures with Missing Data , 1990 .

[4]  Karl G. Jöreskog,et al.  Lisrel 8: User's Reference Guide , 1997 .

[5]  P. Allison Estimation of Linear Models with Incomplete Data , 1987 .

[6]  J. Magnus,et al.  Matrix Differential Calculus with Applications in Statistics and Econometrics (Revised Edition) , 1999 .

[7]  Robert C. Gardner,et al.  On the growth of structural equation modeling in psychological journals , 1996 .

[8]  P. Bentler,et al.  Multiple population covariance structure analysis under arbitrary distribution theory , 1987 .

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

[10]  James L. Arbuckle,et al.  Full Information Estimation in the Presence of Incomplete Data , 1996 .

[11]  K. Yuan,et al.  Robust mean and covariance structure analysis. , 1998, The British journal of mathematical and statistical psychology.

[12]  L. Wolfle,et al.  Annotated bibliography of structural equation modelling: technical work. , 1991, The British journal of mathematical and statistical psychology.

[13]  R. Maronna Robust $M$-Estimators of Multivariate Location and Scatter , 1976 .

[14]  David E. Tyler Robustness and efficiency properties of scatter matrices , 1983 .

[15]  Geert Molenberghs,et al.  Likelihood Based Frequentist Inference When Data Are Missing at Random , 1998 .

[16]  K. Yuan,et al.  5. Three Likelihood-Based Methods for Mean and Covariance Structure Analysis with Nonnormal Missing Data , 2000 .

[17]  S. Kotz,et al.  Symmetric Multivariate and Related Distributions , 1989 .

[18]  Bengt Muthén,et al.  Multiple-group structural modelling with non-normal continuous variables. , 1989 .

[19]  P M Bentler,et al.  Robust transformation with applications to structural equation modelling. , 2000, The British journal of mathematical and statistical psychology.

[20]  S. Zeger,et al.  Longitudinal data analysis using generalized linear models , 1986 .

[21]  Albert Satorra,et al.  Scaled and Adjusted Restricted Tests in Multi Sample Analysis of Moment Structures , 1999 .

[22]  Sik-Yum Lee,et al.  Sensitivity analysis of structural equation models , 1996 .

[23]  R. Muirhead Aspects of Multivariate Statistical Theory , 1982, Wiley Series in Probability and Statistics.

[24]  R. Little,et al.  Editing and Imputation for Quantitative Survey Data , 1987 .

[25]  P. Bentler,et al.  Covariance structure analysis: statistical practice, theory, and directions. , 1996, Annual review of psychology.

[26]  D. Sörbom A GENERAL METHOD FOR STUDYING DIFFERENCES IN FACTOR MEANS AND FACTOR STRUCTURE BETWEEN GROUPS , 1974 .

[27]  Noel G. Cadigan,et al.  Local influence in structural equation models , 1995 .

[28]  Peter M. Bentler,et al.  Estimation of Contamination Parameters and Identification of Outliers in Multivariate Data , 1988 .

[29]  P. Green Iteratively reweighted least squares for maximum likelihood estimation , 1984 .

[30]  Y Kano,et al.  Can test statistics in covariance structure analysis be trusted? , 1992, Psychological bulletin.

[31]  R. Little Robust Estimation of the Mean and Covariance Matrix from Data with Missing Values , 1988 .

[32]  J. Aitchison,et al.  Maximum-Likelihood Estimation of Parameters Subject to Restraints , 1958 .

[33]  P. Rousseeuw,et al.  Unmasking Multivariate Outliers and Leverage Points , 1990 .

[34]  Kenneth A. Bollen,et al.  OBSERVATIONAL RESIDUALS IN FACTOR ANALYSIS AND STRUCTURAL EQUATION MODELS , 1991 .

[35]  E. Ziegel,et al.  Basic Principles of Structural Equation Modelling , 1996 .

[36]  Yutaka Tanaka,et al.  Influence in covariance structure analysis : with an application to confirmatory factor analysis , 1991 .

[37]  Rex B. Kline,et al.  Principles and Practice of Structural Equation Modeling , 1998 .

[38]  Y. Kano Consistency Property of Elliptic Probability Density Functions , 1994 .

[39]  Jeremy MG Taylor,et al.  Robust Statistical Modeling Using the t Distribution , 1989 .

[40]  N M Laird,et al.  Missing data in longitudinal studies. , 1988, Statistics in medicine.

[41]  George R. Franke,et al.  Structural Equation Modeling with EQS and EQS/Windows , 1995 .

[42]  G. A. Marcoulides,et al.  Advanced structural equation modeling : issues and techniques , 1996 .

[43]  P. Bentler,et al.  ML Estimation of Mean and Covariance Structures with Missing Data Using Complete Data Routines , 1999 .

[44]  R. P. McDonald,et al.  Structural Equations with Latent Variables , 1989 .

[45]  Richard G. Lomax,et al.  A Beginner's Guide to Structural Equation Modeling , 2022 .

[46]  Ke-Hai Yuan,et al.  Robust mean and covariance structure analysis through iteratively reweighted least squares , 2000 .

[47]  P. Bentler,et al.  The weight matrix in asymptotic distribution-free methods , 1985 .

[48]  J. T. Austin,et al.  Theoretical and technical contributions to structural equation modeling: An updated annotated bibliography , 1996 .

[49]  K. Yuan,et al.  9. Structural Equation Modeling with Robust Covariances , 1998 .

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

[51]  Roderick J. A. Little,et al.  Statistical Analysis with Missing Data , 1988 .

[52]  S. West,et al.  The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis. , 1996 .

[53]  Bengt Muthén,et al.  On structural equation modeling with data that are not missing completely at random , 1987 .

[54]  Sik-Yum Lee,et al.  Estimation for structural equation models with missing data , 1986 .

[55]  R. Hoyle Structural equation modeling: concepts, issues, and applications , 1997 .

[56]  Peter M. Bentler,et al.  EQS : structural equations program manual , 1989 .

[57]  M. Browne Asymptotically distribution-free methods for the analysis of covariance structures. , 1984, The British journal of mathematical and statistical psychology.