Confidence Intervals for a Semiparametric Approach to Modeling Nonlinear Relations among Latent Variables

REFERENCES

• Arminger , G. and Stein , P. 1997 . Finite mixtures of covariance structure models with regressors . Sociological Methods and Research , 26 : 148 – 182 .
   Web of Science ®Google Scholar
• Arminger , G. , Stein , P. and Wittenberg , J. 1999 . Mixtures of conditional mean and covariance structure models . Psychometrika , 64 : 475 – 494 .
   Web of Science ®Google Scholar
• Bauer , D. J. 2005 . A semiparametric approach to modeling nonlinear relations among latent variables . Structural Equation Modeling , 12 : 513 – 535 .
   Web of Science ®Google Scholar
• Bauer , D. J. , Baldasaro , R. E. and Gottfredson , N. C. Diagnostic procedures for detecting nonlinear relationships between latent variables . Structural Equation Modeling. , (in press)
   Google Scholar
• Bollen , K. A. 1989 . Structural equation models with latent variables. , New York, NY : Wiley .
   Google Scholar
• Dolan , C. V. and van der Maas , H. L. J. 1998 . Fitting multivariate normal finite mixtures subject to structural equation modeling . Psychometrika , 63 : 227 – 253 .
   Web of Science ®Google Scholar
• Efron , B. and Tibshirani , R. J. 1993 . An introduction to the bootstrap. , New York, NY : Chapman & Hall .
   Google Scholar
• Jaccard , J. and Wan , C. K. 1995 . Measurement error in the analysis of interaction effects between continuous predictors using multiple regression: Multiple indicator and structural equation approaches . Psychological Bulletin , 117 : 348 – 357 .
   Web of Science ®Google Scholar
• Jedidi , K. , Jagpal , H. S. and DeSarbo , W. S. 1997a . Finite-mixture structural equation models for response-based segmentation and unobserved heterogeneity . Marketing Science , 16 : 39 – 59 .
   Web of Science ®Google Scholar
• Jedidi , K. , Jagpal , H. S. and DeSarbo , W. S. 1997b . STEMM: A general finite mixture structural equation model . Journal of Classification , 14 : 23 – 50 .
   Web of Science ®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, Inc .
   Google Scholar
• Kelava , A. , Moosbrugger , H. , Dimitruk , P. and Schermelleh-Engel , K. 2008 . Multicollinearity and missing constraints: A comparison of three approaches for the analysis of latent nonlinear effects . Methodology , 4 : 51 – 66 .
   Google Scholar
• Kenny , D. A. and Judd , C. M. 1984 . Estimating the non-linear and interactive effects of latent variables . Psychological Bulletin , 96 : 201 – 210 .
   Web of Science ®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. and Zhu , H. T. 2000 . Statistical analysis of nonlinear structural equation models with continuous and polytomous data . British Journal of Mathematical and Statistical Psychology , 53 : 209 – 232 .
   PubMed Web of Science ®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
• Meredith , W. 1993 . Measurement invariance, factor analysis and factorial invariance . Psychometrika , 58 : 525 – 543 .
   Web of Science ®Google Scholar
• Mooijaart , A. and Bentler , R. 1986 . “ Random polynomial factor analysis ” . In Data analysis and informatics, IV: Proceedings of the fourth international symposium on data analysis and informatics , Edited by: Diday , E. , Jambu , M. , Lebart , L. , Pages , J. and Tomassone , R. 241 – 250 . North Holland, Amsterdam : Elsevier Science .
   Google Scholar
• Muthén , B. O. 2001 . “ Second-generation structural equation modeling with a combination of categorical and continuous latent variables: New opportunities for latent class/latent growth modeling ” . In New methods for the analysis of change , Edited by: Sayer , A. and Collins , L. 291 – 322 . Washington, DC : American Psychological Association .
   Google Scholar
• Muthén , B. O. and Shedden , K. 1999 . Finite mixture modeling with mixture outcomes using the EM algorithm . Biometrics , 55 : 463 – 469 .
   PubMed Web of Science ®Google Scholar
• Muthén , L. K. and Muthén , B. O. 2007 . Mplus user's guide, , 5th ed. , Los Angeles, CA : Author .
   Google Scholar
• Ping , R. A. 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
• SAS Institute Inc. 2008 . SAS® 9.2 Enhanced logging facilities. , Cary, NC : Author .
   Google Scholar
• Schumacker , R. E. and Marcoulides , G. A. , eds. 1998 . Interaction and nonlinear effects in structural equation models. , Mahwah, NJ : Lawrence Erlbaum Associates, Inc .
   Google Scholar
• Steiger , J. H. , Shapiro , A. and Browne , M. W. 1985 . On the multivariate asymptotic distribution of sequential chi-square statistics . Psychometrika , 50 : 253 – 264 .
   Web of Science ®Google Scholar
• Stroud , T. W. 1972 . Fixed alternatives and Wald's formulation of the noncentral asymptotic behavior of the likelihood ratio statistic . Annals of Mathematical Statistics , 43 : 447 – 454 .
   Google Scholar
• Titterington , D. M. , Smith , A. F. M. and Makov , U. E. 1985 . Statistical analysis of finite mixture distributions. , Chichester, , UK : Wiley .
   Google Scholar
• Wald , A. 1943 . Tests of statistical hypotheses concerning several parameters when the number of observations is large . Transactions of the American Mathematical Society , 54 : 426 – 482 .
   Google Scholar