Testing non-nested structural equation models

In this article, we apply Vuong's (1989) likelihood ratio tests of nonnested models to the comparison of nonnested structural equation models (SEMs). Similar tests have been previously applied in SEM contexts (especially to mixture models), though the nonstandard output required to conduct the tests has limited their use and study. We review the theory underlying the tests and show how they can be used to construct interval estimates for differences in nonnested information criteria. Through both simulation and application, we then study the tests' performance in nonmixture SEMs and describe their general implementation via free R packages. The tests offer researchers a useful tool for nonnested SEM comparison, with barriers to test implementation now removed. (PsycINFO Database Record

[1]  S. Hershberger,et al.  A Simple Rule for Generating Equivalent Models in Covariance Structure Modeling. , 1990, Multivariate behavioral research.

[2]  W. Greene,et al.  Accounting for Excess Zeros and Sample Selection in Poisson and Negative Binomial Regression Models , 1994 .

[3]  Yves Rosseel,et al.  lavaan: An R Package for Structural Equation Modeling , 2012 .

[4]  Edgar C. Merkle,et al.  The problem of model selection uncertainty in structural equation modeling. , 2012, Psychological methods.

[5]  Sehee Hong,et al.  PROTECTIVE FACTORS AGAINST SUBSTANCE USE AMONG ASIAN AMERICAN YOUTH: A TEST OF THE PEER CLUSTER THEORY , 2002 .

[6]  D. Rivers,et al.  Model Selection Tests for Nonlinear Dynamic Models , 2002 .

[7]  Alexander Shapiro,et al.  Normal Versus Noncentral Chi-square Asymptotics of Misspecified Models , 2009, Multivariate behavioral research.

[8]  D. Wegener,et al.  The problem of equivalent models in applications of covariance structure analysis. , 1993, Psychological bulletin.

[9]  Gerry Leversha,et al.  Statistical inference (2nd edn), by Paul H. Garthwaite, Ian T. Jolliffe and Byron Jones. Pp.328. £40 (hbk). 2002. ISBN 0 19 857226 3 (Oxford University Press). , 2003, The Mathematical Gazette.

[10]  Barbara M. Byrne,et al.  Burnout: Testing for the Validity, Replication, and Invariance of Causal Structure Across Elementary, Intermediate, and Secondary Teachers , 1994 .

[11]  Q. Vuong.  Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses , 1989 .

[12]  L. V. Jones,et al.  A sensible formulation of the significance test. , 2000, Psychological methods.

[13]  T. W. Anderson,et al.  Asymptotic Chi-Square Tests for a Large Class of Factor Analysis Models , 1990 .

[14]  T. Little,et al.  Abstract: Taking Into Account Sampling Variability of Model Selection Indices: A Parametric Bootstrap Approach , 2013, Multivariate Behavioral Research.

[15]  Adrian E. Raftery,et al.  Bayesian Model Averaging: A Tutorial , 2016 .

[16]  B. Muthén.  A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators , 1984 .

[17]  Roy Levy,et al.  A Framework of Statistical Tests For Comparing Mean and Covariance Structure Models , 2007, Multivariate behavioral research.

[18]  Barbara M. Byrne,et al.  Structural equation modeling with EQS : basic concepts, applications, and programming , 2000 .

[19]  Naoya Katayama.  Portmanteau likelihood ratio tests for model selection , 2008 .

[20]  Adrian E. Raftery,et al.  Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors , 1999 .

[21]  Deniz Senturk-Doganaksoy,et al.  Explanatory Item Response Models: A Generalized Linear and Nonlinear Approach , 2006, Technometrics.

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

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

[24]  R. Golden.  Discrepancy Risk Model Selection Test theory for comparing possibly misspecified or nonnested models , 2003 .

[25]  Victoria Savalei,et al.  Understanding Robust Corrections in Structural Equation Modeling , 2014 .

[26]  K. Holzinger,et al.  A study in factor analysis : the stability of a bi-factor solution , 1939 .

[27]  A. Shapiro,et al.  On the multivariate asymptotic distribution of sequential Chi-square statistics , 1985 .

[28]  H. Akaike.  A new look at the statistical model identification , 1974 .

[29]  Albert Satorra,et al.  Testing model nesting and equivalence. , 2008, Psychological methods.

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

[31]  M. Frese,et al.  Making Things Happen : Reciprocal Relationships between Work Characteristics and Personal Initiative ( PI ) in a Four-Wave Longitudinal Structural Equation Model , 2008 .

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

[33]  A. Satorra,et al.  Corrections to test statistics and standard errors in covariance structure analysis. , 1994 .

[34]  Gregory R. Hancock,et al.  An Extended Model Comparison Framework for Covariance and Mean Structure Models, Accommodating Multiple Groups and Latent Mixtures , 2011 .

[35]  Paul Wilson,et al.  The misuse of the Vuong test for non-nested models to test for zero-inflation , 2015 .

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

[37]  Myrsini Katsikatsou,et al.  Pairwise likelihood estimation for factor analysis models with ordinal data , 2012, Comput. Stat. Data Anal..

[38]  Golden,et al.  Statistical Tests for Comparing Possibly Misspecified and Nonnested Models. , 2000, Journal of mathematical psychology.

[39]  John Todman,et al.  Should We Stay or Should We Go? A Social Psychological Model of Schisms in Groups , 2002 .

[40]  Patrick Miller,et al.  SIMulated Structural Equation Modeling , 2015 .

[41]  R. A. Leibler,et al.  On Information and Sufficiency , 1951 .

[42]  Todd E. Clark,et al.  Tests of Equal Forecast Accuracy for Overlapping Models , 2011 .

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

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