An Alternative Approach for Nonlinear Latent Variable Models

REFERENCES

• Aiken , L. S. and West , S. G. 1991 . Multiple regression: Testing and interpreting interactions. Newbury Park, CA : Sage. .
   Google Scholar
• Arminger , G. and Muthén , B. 1998 . A Bayesian approach to nonlinear variable models using the Gibbs sampler and the Metropolis–Hastings algorithm. . Psychometrika , 63 : 271 – 310 .
   Web of Science ®Google Scholar
• Bauer , D. J. 2005 . A semiparametric approach to modeling nonlinear relations among latent variables. . Structural Equation Modeling , 4 : 513 – 535 .
   Web of Science ®Google Scholar
• Bentler , P. M. 1983 . Some contributions to efficient statistics in structural models: Specification and estimation of moment structures. . Psychometrika , 48 : 493 – 517 .
   Web of Science ®Google Scholar
• Bentler , P. M. 2000–2008 . EQS 6 structural equations program manual. Encino, CA : Multivariate Software. .
   Google Scholar
• Bentler , P. M. and Dijkstra , T. 1985 . “ Efficient estimation via linearization in structural models ” . In Multivariate analysis VI Edited by: Kirshnaiah , P. R. 9 – 42 . Amsterdam : North Holland .
   Google Scholar
• Bentler , P. M. and Weeks , D. G. 1980 . Linear structural equations with latent variable. . Psychometrika , 45 : 289 – 308 .
   Web of Science ®Google Scholar
• Bollen , K. A. 2002 . Latent variables in psychology and the social sciences. . Annual Review of Psychology , 53 : 605 – 634 .
   PubMed Web of Science ®Google Scholar
• Bollen , K. A. and Paxton , P. 1998a . Interactions of latent variables in structural equation models. . Structural Equation Modeling , 5 : 267 – 293 .
   Web of Science ®Google Scholar
• Bollen , K. A. and Paxton , P. 1998b . “ Two-stage least squares estimation of interaction effects ” . In Interaction and nonlinear effects in structural equation modeling Edited by: Schumacker , R. E. and Marcoulides , G. A. 125 – 151 . Hillsdale, NJ : Lawrence Erlbaum Associates .
   Google Scholar
• Browne , M. W. 1984 . Asymptotically distribution-free methods for the analysis of covariance structures. . British Journal of Mathematical and Statistical Psychology , 37 : 62 – 83 .
   PubMed Web of Science ®Google Scholar
• Coenders , G. , Batista-Foguet , J. M. and Saris , W. E. 2008 . Simple, efficient and distribution-free approach to interaction effects in complex structural equation models. . Quality & Quantity , 42 : 369 – 396 .
   Web of Science ®Google Scholar
• Cudeck , R. , Harring , J. R. and du Toit , S. H. C. 2009 . Marginal maximum likelihood estimation of a latent variable model with interaction. . Journal of Educational and Behavioral Statistics , 34 : 131 – 144 .
   Web of Science ®Google Scholar
• Dimitruk , P. , Schermelleh-Engel , K. , Kelava , A. and Moosbrugger , H. 2007 . Challenges in nonlinear structural equation modeling. . Methodology , 3 : 100 – 114 .
   Google Scholar
• Hargens , L. L. 2009 . Product-variable models of interaction effects and causal mechanisms. . Social Science Research , 38 : 19 – 28 .
   Google Scholar
• Jaccard , J. J. and Wan , C. K. 1996 . LISREL approaches to interaction effects in multiple regression. Thousand Oaks, CA : Sage. .
   Google Scholar
• Jöreskog , K. G. and Yang , F. 1996 . “ Nonlinear structural equation models: The Kenny–Judd model with interaction effects ” . In Advanced structural equation modeling: Issues and techniques Edited by: Marcoulides , G. A. and Schumacker , R. E. 57 – 88 . Mahwah, NJ : Lawrence Erlbaum Associates .
   Google Scholar
• Kenny , D. A. and Judd , C. M. 1984 . Estimating the nonlinear and interactive effects of latent variables. . Psychological Bulletin , 96 : 201 – 210 .
   Web of Science ®Google Scholar
• Klein , A. G. 2007 . QuasiML (Version 3.10) [Computer software]. Champaign, IL : Author .
   Google Scholar
• Klein , A. G. and Moosbrugger , H. 2000 . Maximum likelihood estimation of latent interaction effects with the LMS method. . Psychometrika , 65 : 457 – 474 .
   Web of Science ®Google Scholar
• Klein , A. G. and Muthén , B. O. 2007 . Quasi-maximum likelihood estimation of structural equation models with multiple interaction and quadratic effects. . Multivariate Behavioral Research , 42 : 647 – 673 .
   Web of Science ®Google Scholar
• Lee , S.-Y. 2007 . Structural equation modeling: A Bayesian approach. West Sussex, , UK : Wiley. .
   Google Scholar
• Lee , S.-Y. , Song , X.-Y. and Tang , N.-S. 2007 . Bayesian methods for analyzing structural equation models with covariates, interaction, and quadratic latent variables. . Structural Equation Modeling , 14 : 404 – 434 .
   Web of Science ®Google Scholar
• Lee , S.-Y. and Zhu , H. T. 2002 . Maximum likelihood estimation of nonlinear structural equation models. . Psychometrika , 67 : 189 – 210 .
   Web of Science ®Google Scholar
• Magnus , J. R. and Neudecker , H. 1988 . Matrix differential calculus with applications in statistics and econometrics. Chichester, , UK : Wiley. .
   Google Scholar
• Marsh , H. W. , Wen , Z. and Hau , K.-T. 2004 . Structural equation models of latent interactions: Evaluation of alternative estimation strategies and indicator construction. . Psychological Methods , 9 : 275 – 300 .
   PubMed Web of Science ®Google Scholar
• Meijer , E. 2005 . Matrix algebra for higher order moments. . Linear Algebra and its Applications , 410 : 112 – 134 .
   Google Scholar
• Mooijaart , A. 1985 . Factor analysis for non-normal variables. . Psychometrika , 50 : 323 – 342 .
   Web of Science ®Google Scholar
• Mooijaart , A. 2008 . “ Random polynomial and interaction latent variable models ” . In New Trends in Psychometrics Edited by: Shigemasu , K. , Okada , A. , Imaizumi , T. and Hoshino , T. 303 – 310 . Tokyo : Universal Academy Press .
   Google Scholar
• Mooijaart , A. and Satorra , A. 2009a . On insensitivity of the chi-square model test to nonlinear misspecification in structural equation models. . Psychometrika , 74 : 443 – 455 .
   Web of Science ®Google Scholar
• Mooijaart , A. and Satorra , A. 2009b, July . Testing for non-linear relationship in structural equation modeling. Paper presented at the International Meeting of the Psychometric Society, Cambridge, UK.
   Google Scholar
• Mulaik , S. A. 2009 . Linear causal modeling with structural equations. Boca Raton, FL : Chapman & Hall/CRC. .
   Google Scholar
• Muthén , B. O. and Asparouhov , T. 2003 . Modeling interactions between latent and observed continuous variables using maximum-likelihood estimatio. in Mplus . Mplus Web Notes , : 6 (version 1).
   Google Scholar
• Muthén , L. K. and Muthén , B. O. 1998–2007 . Mplus user's guide, , 5th ed. Los Angeles, CA : Muthén & Muthén .
   Google Scholar
• Ping , R. A. Jr. 1996 . Latent variable interaction and quadratic effect estimation: A two-step technique using structural equation analysis. . Psychological Bulletin , 119 : 166 – 175 .
   Web of Science ®Google Scholar
• Raykov , T. and Marcoulides , G. A. 2006 . A first course in structural equation modeling, , 2nd ed Mahwah, NJ : Lawrence Erlbaum Associates .
   Google Scholar
• Saris , W. E. , Batista-Foguet , J. M. and Coenders , G. 2007 . Selection of indicators for the interaction term in structural equation models with interaction. . Quality & Quantity , 41 : 55 – 72 .
   Web of Science ®Google Scholar
• Satorra , A. 1989 . Alternative test criteria in covariance structure analysis: A unified approach. . Psychometrika , 54 : 131 – 151 .
   Web of Science ®Google Scholar
• Satorra , A. and Bentler , P. M. 1994 . “ Corrections to test statistics and standard errors in covariance structure analysis ” . In Latent variables analysis: Applications for developmental research Edited by: von Eye , A. and Clogg , C. C. 399 – 419 . Thousand Oaks, CA : Sage .
   Google Scholar
• Schumacker , R. E. and Marcoulides , G. A. , eds. 1998 . Interaction and nonlinear effects in structural equation modeling. Mahwah, NJ : Lawrence Erlbaum Associates. .
   Google Scholar
• Sun , R. and Willson , V. L. 2009 . Evaluating intercept-slope interactions in latent growth modeling. . Structural Equation Modeling , 16 : 226 – 244 .
   Web of Science ®Google Scholar
• Wall , M. M. and Amemiya , Y. 2003 . A method of moment technique for fitting interaction effects in structural equation models. . The British Journal of Mathematical and Statistical Psychology , 56 : 47 – 63 .
   PubMed Web of Science ®Google Scholar
• Yuan , K.-H. and Bentler , P. M. 1998 . Normal theory based test statistics in structural equation modeling. . British Journal of Mathematical and Statistical Psychology , 51 : 289 – 309 .
   PubMed Web of Science ®Google Scholar