Reporting Monte Carlo Studies in Structural Equation Modeling

REFERENCES

• American Psychological Association . 2010 . Publication manual of the American Psychological Association, , 6th ed. Washington , DC : Author. .
   Google Scholar
• Anderson , J. C. and Gerbing , D. W. 1984 . The effect of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis . Psychometrika , 49 : 155 – 173 .
   Web of Science ®Google Scholar
• Anderson , R. D. 1996 . An evaluation of the Satorra–Bentler distributional misspecification correction applied to the McDonald fit index . Structural Equation Modeling , 3 : 203 – 227 .
   Web of Science ®Google Scholar
• APA Publications and Communications Board Working Group on Journal Article Reporting Standards . 2008 . Reporting standards for research in psychology: Why do we need them? What might they be? . American Psychologist , 63 : 839 – 851 .
   PubMed Web of Science ®Google Scholar
• Arbuckle , J. 1995–2006 . Amos 7.0: User's guide Spring House , PA : Amos Development Corporation. .
   Google Scholar
• Aris , E. M. D. 2001 . Statistical causal models for categorical data Tilburg : Dutch University Press. . [Doctoral dissertation, Catholic University Brabant]
   Google Scholar
• Asparouhov , T. and Muthén , B. O. 2009 . Exploratory structural equation modeling . Structural Equation Modeling , 16 : 397 – 438 .
   Web of Science ®Google Scholar
• Bai , Y. and Poon , W.-Y. 2009 . Using Mx to analyze cross-level effects in two-level structural equation models . Structural Equation Modeling , 16 : 163 – 178 .
   Web of Science ®Google Scholar
• Bandalos , D. L. 2002 . The effects of item parceling on goodness-of-fit and parameter estimate bias in structural equation modeling . Structural Equation Modeling , 9 : 78 – 102 .
   Web of Science ®Google Scholar
• Bang , J. W. , Schumacker , R. E. and Schlieve , P. L. 1998 . Random-number generator validity in simulation studies: An investigation of normality . Educational and Psychological Measurement , 58 : 430 – 450 .
   Web of Science ®Google Scholar
• Boomsma , A. 1982 . “ The robustness of LISREL against small sample sizes in factor analysis models. ” . In Systems under indirect observation: Causality, structure, prediction Edited by: Jöreskog , K. G. and Wold , H. 149 – 173 . Amsterdam , , Netherlands : North-Holland. . Part I
   Google Scholar
• Boomsma , A. 1983 . On the robustness of LISREL (maximum likelihood estimation) against small sample size and non-normality Amsterdam : Sociometric Research Foundation. . [Doctoral dissertation, University of Groningen]
   Google Scholar
• Boomsma , A. 1985 . Nonconvergence, improper solutions, and starting values in LISREL maximum likelihood estimation . Psychometrika , 50 : 229 – 242 .
   Web of Science ®Google Scholar
• Boomsma , A. 2000 . Reporting analyses of covariance structures . Structural Equation Modeling , 7 : 461 – 483 .
   Web of Science ®Google Scholar
• Bradley , J. V. 1978 . Robustness? . British Journal of Mathematical and Statistical Psychology , 31 : 144 – 152 .
   Web of Science ®Google Scholar
• Calcagno , V. and De Mezancourt , C. 2010 . glmuti: An R package for easy automated model selection with (generalized) linear models . Journal of Statistical Software , 34 : 1 – 29 .
   Web of Science ®Google Scholar
• Chen , F. , Bollen , K. A. , Paxton , P. , Curran , P. J. and Kirby , J. 2001 . Improper solutions in structural equation modeling: Causes, consequences, and strategies . Sociological Methods & Research , 29 : 468 – 508 .
   Web of Science ®Google Scholar
• Chen , Q. , Kwok , O.-M. , Luo , W. and Wilson , V. L. 2010 . The impact of ignoring a level of nesting structure in multilevel growth mixture models: A Monte Carlo study . Structural Equation Modeling , 17 : 570 – 589 .
   Web of Science ®Google Scholar
• Cheung , G. W. and Rensvold , R. B. 2002 . Evaluating goodness-of-fit indexes for testing measurement invariance . Structural Equation Modeling , 9 : 233 – 255 .
   Web of Science ®Google Scholar
• Cheung , M. W.-L. 2009 . Constructing approximate confidence intervals for parameters with structural equation models . Structural Equation Modeling , 16 : 267 – 294 .
   Web of Science ®Google Scholar
• Cheung , M. W.-L. 2010 . Fixed-effects meta-analyses as multiple-group structural equation models . Structural Equation Modeling , 17 : 481 – 509 .
   Web of Science ®Google Scholar
• Cheung , M. W.-L. and Chan , W. 2005 . Meta-analytic structural equation modeling: A two-stage approach . Structural Equation Modeling , 16 : 28 – 53 .
   Google Scholar
• Cheung , M. W.-L. and Chan , W. 2009 . A two-stage approach to synthesizing covariance matrices in meta-analytic structural equation modeling . Psychological Methods , 10 : 40 – 64 .
   Google Scholar
• Cleveland , W. S. 1985 . The elements of graphing Monterey , CA : Wadsworth. .
   Google Scholar
• Cleveland , W. S. 1993 . Visualizing data Summit , NJ : Hobart. .
   Google Scholar
• Cohen , J. 1988 . Statistical power analysis for the behavioral sciences, , 2nd ed. Hillsdale , NJ : Erlbaum. .
   Google Scholar
• De Groot , A. D. 1969 . Methodology: Foundations of inference and research in the behavioral sciences The Hague , , Netherlands : Mouton. .
   Google Scholar
• Ding , L. , Velicer , W. F. and Harlow , L. L. 1995 . Effects of estimation methods, number of indicators per factor, and improper solutions on structural equation modeling fit indices . Structural Equation Modeling , 2 : 119 – 144 .
   Web of Science ®Google Scholar
• Enders , C. K. and Bandalos , D. L. 2001 . The relative performance of full information maximum likelihood estimation for missing data in structural equation models . Structural Equation Modeling , 8 : 430 – 457 .
   Web of Science ®Google Scholar
• Fan , X. 2003 . Power of latent growth modeling for detecting group differences in latent growth trajectory parameters . Structural Equation Modeling , 10 : 380 – 400 .
   Web of Science ®Google Scholar
• Fan , X. , Thompson , B. and Wang , L. 1999 . Effects of sample size, estimation methods, and model specification on structural equation modeling fit indexes . Structural Equation Modeling , 6 : 56 – 83 .
   Web of Science ®Google Scholar
• Fouladi , R. T. 2000 . Performance of modified test statistics in covariance and correlation structure analysis under conditions of multivariate nonnormality . Structural Equation Modeling , 7 : 356 – 410 .
   Web of Science ®Google Scholar
• Gagné , P. and Furlow , C. F. 2009 . Automating multiple software packages in simulation research for structural equation modeling and hierarchical linear modeling . Structural Equation Modeling , 16 : 179 – 185 .
   Web of Science ®Google Scholar
• Gentle , J. E. 2003 . Random number generation and Monte Carlo methods, , 2nd ed. New York , NY : Springer. .
   Google Scholar
• Gold , M. S. and Bentler , P. M. 2000 . Treatments of missing data: A Monte Carlo comparison of RBHDI, iterative stochastic regression imputation, and expectation-maximization . Structural Equation Modeling , 7 : 319 – 355 .
   Web of Science ®Google Scholar
• Green , S. , Thompson , M. S. and Poirer , J. 2001 . An adjusted Bonferroni method for elimination of parameters in specification addition searches . Structural Equation Modeling , 8 : 18 – 39 .
   Web of Science ®Google Scholar
• Hancock , G. R. , Lawrence , F. R. and Nevitt , J. 2000 . Type I error and power of latent mean methods and MANOVA in factorially invariant and noninvariant latent variable systems . Structural Equation Modeling , 7 : 534 – 556 .
   Web of Science ®Google Scholar
• Hancock , G. R. and Mueller , R. O. , eds. 2010 . The reviewer's guide to quantitative methods in the social sciences New York , NY : Routledge. .
   Google Scholar
• Hertzog , C. , Van Oertzen , T. , Ghisletta , P. and Lindenberger , U. 2008 . Evaluating the power of latent growth curve models to detect individual differences in change . Structural Equation Modeling , 15 : 541 – 563 .
   Web of Science ®Google Scholar
• Herzog , W. , Boomsma , A. and Reinecke , S. 2007 . The model-size effect on traditional and modified tests of covariance structures . Structural Equation Modeling , 14 : 361 – 390 .
   Web of Science ®Google Scholar
• Hoogland , J. J. 1999 . The robustness of estimation methods for covariance structure analysis , Doctoral dissertation Netherlands : University of Groningen. .
   Google Scholar
• Hox , J. J. 1995 . Amos, EQS, and LISREL for Windows: A comparative review . Structural Equation Modeling , 2 : 79 – 91 .
   Web of Science ®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
• Jöreskog , K. G. and Sörbom , D. 1996 . PRELIS 2: User's reference guide, , 3rd ed. Chicago , IL : Scientific Software International. .
   Google Scholar
• Kaplan , D. and George , R. 1995 . A study of power associated with testing factor mean differences under violations of factorial invariance . Structural Equation Modeling , 2 : 101 – 118 .
   Web of Science ®Google Scholar
• Kleijnen , J. P. C. 1974–1975 . Statistical techniques in simulation New York , NY : Dekker. . (two parts)
   Google Scholar
• Kleijnen , J. P. C. 1977 . Statistical tools for simulation practitioners New York , NY : Dekker. .
   Google Scholar
• Kolenikov , S. and Bollen , K. A. 2012 . Testing negative error variances: Is a Heywood case a symptom of misspecification? . Sociological Methods & Research , 41 : 124 – 167 . http://web.missouri.edu/∼kolenikovs/papers/heywood-12.pdf[The original version—with unruined highlighting—is online available at
   Web of Science ®Google Scholar
• Kopka , H. and Daly , P. W. 2004 . Guide to LaTeX, , 4th ed. Boston , MA : Addison-Wesley. .
   Google Scholar
• LaGrange , B. and Cole , D. A. 2008 . An expansion of the trait-state-occasion model: Accounting for shared method variance . Structural Equation Modeling , 15 : 241 – 271 .
   Web of Science ®Google Scholar
• Leite , W. L. 2007 . A comparison of latent growth models for constructs measured by multiple items . Structural Equation Modeling , 14 : 581 – 610 .
   Web of Science ®Google Scholar
• Lyhagen , J. 2007 . Estimating nonlinear structural equation models: EMM and the Kenny–Judd model . Structural Equation Modeling , 14 : 391 – 403 .
   Web of Science ®Google Scholar
• MacCallum , R. C. , Widaman , K. F. , Preacher , K. J. and Hong , S. 2001 . Sample size in factor analysis: The role of model error . Multivariate Behavioral Research , 36 : 611 – 637 .
   PubMed Web of Science ®Google Scholar
• Mai , P. , Wu , E. and Bentler , P. M. 2010 . EQS goes R: Simulations for SEM using the package REQS . Structural Equation Modeling , 17 : 333 – 349 .
   Web of Science ®Google Scholar
• Milne , A. A. 1991 . The complete Winnie-the-Pooh London : Dean. .
   Google Scholar
• Moulder , B. C. and Algina , J. 2002 . Comparison of methods for estimating and testing latent variable interactions . Structural Equation Modeling , 9 : 1 – 19 .
   Web of Science ®Google Scholar
• Murrell , P. 2005 . R graphics Boca Raton , FL : Chapman & Hall/CRC. .
   Google Scholar
• Muthén , B. O. 1998–2004 . Mplus technical appendices Los Angeles , CA : Muthén & Muthén. .
   Google Scholar
• Muthén , L. K. and Muthén , B. O. 1998–2010 . Mplus user's guide, , 6th ed. Los Angeles , CA : Muthén & Muthén. .
   Google Scholar
• Nylund , K. L. , Asparouhov , T. and Muthén , B. O. 2007 . Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo simulation study . Structural Equation Modeling , 14 : 535 – 569 .
   Web of Science ®Google Scholar
• Olsson , U. H. , Foss , T. , Troye , S. V. and Howell , R. D. 2000 . The performance of ML, GLS, and WLS estimation in structural equation modeling under conditions of misspecification and nonnormality . Structural Equation Modeling , 7 : 557 – 595 .
   Web of Science ®Google Scholar
• Panter , A. T. and Sterba , S. K. , eds. 2011 . Handbook of ethics in quantitative methodology New York , NY : Routledge. .
   Google Scholar
• Paxton , P. , Curran , P. J. , Bollen , K. A. , Kirby , J. and Chen , F. 2001 . Monte Carlo experiments: Design and implementation . Structural Equation Modeling , 8 : 287 – 312 .
   Web of Science ®Google Scholar
• Publication policy regarding Monte Carlo studies . 1979 . Psychometrika , 44 : 133 – 134 . Referring: Publication policy (1979)
   Google Scholar
• R Development Core Team . 1999–2010 . R: A language and environment for statistical computing Vienna , , Austria : R Foundation for Statistical Computing. . ISBN 3–900051-07–0
   Google Scholar
• Raykov , T. 2000 . On the large-sample bias, variance, and mean squared error of the conventional noncentrality parameter estimator of covariance structure models . Structural Equation Modeling , 7 : 431 – 441 .
   Web of Science ®Google Scholar
• Ren , L. , Dunson , D. , Lindroth , S. and Carin , L. 2010 . Dynamic nonparametric Bayesian models for analyzing music . Journal of the American Statistical Association , 105 : 458 – 472 .
   Web of Science ®Google Scholar
• Ripley , B. D. 1987 . Stochastic simulation New York , NY : Wiley. .
   Google Scholar
• Robey , R. R. and Barcikowski , R. S. 1992 . Type I error and the number of iterations in Monte Carlo studies of robustness . British Journal of Mathematical and Statistical Psychology , 45 : 283 – 288 .
   Web of Science ®Google Scholar
• Rosenthal , R. 1994 . Science and ethics in conducting, analyzing, and reporting psychological research . Psychological Science , 3 : 127 – 134 .
   Google Scholar
• Ryu , E. and West , S. G. 2009 . Level-specific evaluation of model fit in multilevel structural equation modeling . Structural Equation Modeling , 16 : 583 – 601 .
   Web of Science ®Google Scholar
• Schrage , L. 1979 . A more portable Fortran random number generator . ACM Transactions on Mathematical Software , 5 : 132 – 138 .
   Google Scholar
• Serlin , R. C. 2000 . Testing for robustness in Monte Carlo studies . Psychological Methods , 5 : 230 – 240 .
   PubMed Web of Science ®Google Scholar
• Shadish , W. R. , Cook , T. D. and Campbell , D. T. 2002 . Experimental and quasi-experimental designs for generalized causal inference Boston , MA : Houghton Mifflin. .
   Google Scholar
• Siemsen , E. and Bollen , K. A. 2007 . Least absolute deviation estimation in structural equation modeling . Sociological Methods & Research , 36 : 227 – 265 .
   Web of Science ®Google Scholar
• Sivo , S. A. and Wilson , V. I. 2000 . Modeling causal error structures in longitudinal panel data: A Monte Carlo study . Structural Equation Modeling , 7 : 174 – 205 .
   Web of Science ®Google Scholar
• Skrondal , A. 2000 . Design and analysis of Monte Carlo experiments: Attacking the conventional wisdom . Multivariate Behavioral Research , 35 : 137 – 167 .
   PubMed Web of Science ®Google Scholar
• Song , S.-Y. and Lee , S.-Y. 2002 . A Bayesian approach for multigroup nonlinear factor analysis . Structural Equation Modeling , 9 : 523 – 553 .
   Web of Science ®Google Scholar
• Song , W. T. and Schmeiser , B. W. 2009 . Omitting meaningless digits in point estimates: The probability guarantee of leading-digit rules . Operations Research , 57 : 109 – 117 .
   Web of Science ®Google Scholar
• Tufte , E. R. 1983 . The visual display of quantitative information Cheshire , CT : Graphics Press. .
   Google Scholar
• Ulam , S. M. 1991 . Adventures of a mathematician Berkeley , CA : University of California Press. .
   Google Scholar
• Wainer , H. 2005 . Graphic discovery: A trout in the milk and other visual adventures Princeton , NJ : Princeton University Press. .
   Google Scholar
• Wilcox , R. R. 2003 . Applying contemporary statistical techniques San Diego , CA : Academic Press. .
   Google Scholar
• Wilkinson L., & the Task Force on Statistical Inference . 1999 . Statistical methods in psychology journals: Guidelines and explanations . American Psychologist , 54 : 594 – 604 .
   Google Scholar
• Williams , J. and MacKinnon , D. P. 2008 . Resampling and distribution of the product methods for testing indirect effects in complex models . Structural Equation Modeling , 15 : 23 – 51 .
   PubMed Web of Science ®Google Scholar
• Ximénez , C. 2006 . A Monte Carlo study of recovery of weak factor loadings in confirmatory factor analysis . Structural Equation Modeling , 13 : 587 – 614 .
   Web of Science ®Google Scholar
• Yang-Wallentin , F. , Jöreskog , K. G. and Luo , H. 2010 . Confirmatory factor analysis of ordinal variables with misspecified models . Structural Equation Modeling , 17 : 392 – 423 .
   Web of Science ®Google Scholar