Hypothesis Testing and Model Comparison in Two-level Structural Equation Models

One basic and important problem in two-level structural equation modeling is to find a good model for the observed sample data. This article demonstrates the use of the well-known Bayes factor in the Bayesian literature for hypothesis testing and model comparison in general two-level structural equation models. It is shown that the proposed methodology is flexible, and can be applied to situations with a wide variety of nonnested models. Moreover, some problems encountered in using existing methods for goodness-of-fit assessment of the proposed model can be alleviated. An illustrative example with some real data from an AIDS care study is presented.

[1]  L. Wasserman,et al.  Computing Bayes Factors by Combining Simulation and Asymptotic Approximations , 1997 .

[2]  Sik-Yum Lee,et al.  Constrained maximum likelihood estimation of two-level covariance structure model via EM type algorithms , 1999 .

[3]  P. Bentler,et al.  Significance Tests and Goodness of Fit in the Analysis of Covariance Structures , 1980 .

[4]  A. Raftery.  Choosing Models for Cross-Classifications , 1986 .

[5]  A. O'Hagan,et al.  Fractional Bayes factors for model comparison , 1995 .

[6]  S Y Lee,et al.  Bayesian estimation and test for factor analysis model with continuous and polytomous data in several populations. , 2001, The British journal of mathematical and statistical psychology.

[7]  Harvey Goldstein,et al.  Balanced versus unbalanced designs for linear structural relations in two‐level data , 1989 .

[8]  A. Gelfand,et al.  Bayesian Model Choice: Asymptotics and Exact Calculations , 1994 .

[9]  J A Stein,et al.  The effects of establishment practices, knowledge and attitudes on condom use among Filipina sex workers. , 1998, AIDS care.

[10]  L. Tierney,et al.  Fully Exponential Laplace Approximations to Expectations and Variances of Nonpositive Functions , 1989 .

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

[12]  Sik-Yum Lee,et al.  Multilevel analysis of structural equation models , 1990 .

[13]  Edgar F. Borgatta,et al.  Sociological Methodology, 1969. , 1969 .

[14]  B. Carlin,et al.  Bayesian Model Choice Via Markov Chain Monte Carlo Methods , 1995 .

[15]  B. Muthén,et al.  Multilevel Covariance Structure Analysis , 1994 .

[16]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[17]  R. Kass,et al.  Approximate Bayes Factors and Orthogonal Parameters, with Application to Testing Equality of Two Binomial Proportions , 1992 .

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

[19]  Harvey Goldstein,et al.  A general model for the analysis of multilevel data , 1988 .

[20]  W. Poon,et al.  Two-level analysis of covariance structures for unbalanced designs with small level-one samples. , 1992, The British journal of mathematical and statistical psychology.

[21]  D. G. Weeks,et al.  Linear structural equations with latent variables , 1980 .

[22]  Wai-Yin Poon,et al.  ANALYSIS OF TWO-LEVEL STRUCTURAL EQUATION MODELS VIA EM TYPE ALGORITHMS , 1998 .

[23]  Yeow Meng Thum,et al.  Hierarchical Linear Models for Multivariate Outcomes , 1997 .

[24]  J. Berger,et al.  The Intrinsic Bayes Factor for Model Selection and Prediction , 1996 .

[25]  J. Berger,et al.  Testing a Point Null Hypothesis: The Irreconcilability of P Values and Evidence , 1987 .

[26]  Nicholas T. Longford,et al.  Factor analysis for clustered observations , 1992 .

[27]  Karl G. Jöreskog,et al.  Lisrel 8: Structural Equation Modeling With the Simplis Command Language , 1993 .

[28]  Adrian E. Raftery,et al.  Bayesian Model Selection in Structural Equation Models , 1992 .

[29]  Stephen W. Raudenbush,et al.  Maximum likelihood estimation for unbalanced multilevel covariance structure models via the EM algorithm , 1995 .

[30]  L. Wasserman,et al.  Practical Bayesian Density Estimation Using Mixtures of Normals , 1997 .

[31]  S. Chib.  Marginal Likelihood from the Gibbs Output , 1995 .

[32]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

[33]  P. Green,et al.  On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion) , 1997 .

[34]  Roderick P. McDonald,et al.  A general model for two-level data with responses missing at random , 1993 .

[35]  Bengt Muthén,et al.  Multilevel Factor Analysis of Class and Student Achievement Components , 1991 .

[36]  David Draper,et al.  Assessment and Propagation of Model Uncertainty , 2011 .

[37]  Xin-Yuan Song,et al.  Bayesian Estimation and Model Selection of Multivariate Linear Model with Polytomous Variables , 2002, Multivariate behavioral research.

[38]  H. Goldstein.  Multilevel mixed linear model analysis using iterative generalized least squares , 1986 .

[39]  P. Green.  Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[40]  M. Escobar,et al.  Bayesian Density Estimation and Inference Using Mixtures , 1995 .

[41]  S. Raudenbush,et al.  Chapter 10: Methodological Advances in Analyzing the Effects of Schools and Classrooms on Student Learning , 1988 .

[42]  L. Tierney,et al.  Accurate Approximations for Posterior Moments and Marginal Densities , 1986 .

[43]  A. Raftery.  Bayesian Model Selection in Social Research , 1995 .