University of Groningen Dimensionality assesment with ...Measurement bias and multidimen-sionality; an illustration of bias detection in multidimensional measurement models. Advances

University of Groningen

Dimensionality assesment with factor analysis methodsBarendse, Mariska

IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.

Document VersionPublisher's PDF, also known as Version of record

Publication date:2015

Link to publication in University of Groningen/UMCG research database

Citation for published version (APA):Barendse, M. (2015). Dimensionality assesment with factor analysis methods. [S.n.].

CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).

Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.

Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.

Download date: 06-04-2021

https://research.rug.nl/en/publications/dimensionality-assesment-with-factor-analysis-methods(16a8c55b-1c6d-4465-a5e0-267480751fe4).html

161160

exploratory methods such as non–parametric item response theory (IRT)

models. It would also be interesting to compare the nonlinear models

presented in Chapters 5 and 6 with the IRT models as presented by

Molenaar (2012), who tested nonnormality (including interaction effects).

In addition, one could compare the multilevel models studied in Chapter

3 with the Bayesian or frequentist IRT oriented multilevel models (e.g.,

Verhagen, 2012).

161

Bibliography

Agresti, A. (2002). Categorical Data Analysis. New York: Wiley-Interscience.

Agresti, A. & Yang, M.-C. (1987). An empirical investigation of some effects ofsparseness in contingency tables. Computational Statistics & Data Analysis,5 (1), 9–21.

Asparouhov, T. & Muthén, B. O. (2006). Robust chi square difference testingwith mean and variance adjusted test statistics. Mplus Web Notes: No. 10.Retrieved from http://www.statmodel.com/download/webnotes/webnote10.pdf.

Asparouhov, T. & Muthén, B. O. (2007). Computationally efficient estimationof multilevel high-dimensional latent variable models. In Proceedings ofthe 2007 JSM meeting in Salt Lake City, Utah, Section on Statistics inEpidemiology, (pp. 2531–2535).

Asparouhov, T. & Muthén, B. O. (2010a). Computing the strictly positiveSatorra-Bentler chi–square test in Mplus. Mplus Web Notes: No. 12. Re-trieved from http://www.statmodel.com/download/webnotes/webnote12.pdf.

Asparouhov, T. & Muthén, B. O. (2010b). Simple second order chi-square cor-rection. Mplus Technical Appendix. Retrieved from http://www. statmodel.com/download/WLSMV new chi21. pdf.

Barendse, M. T., Oort, F. J., & Garst, G. J. A. (2010). Using restricted factoranalysis with latent moderated structures to detect uniform and nonuniformmeasurement bias; a simulation study. Advances in Statistical Analysis,94 (2), 117–127.

Barendse, M. T., Oort, F. J., & Timmerman, M. E. (2014). Using exploratoryfactor analysis to determine the dimensionality of discrete responses. Struc-tural Equation Modeling: A Multidisciplinary Journal, (ahead-of-print), 1–15.

Barendse, M. T., Oort, F. J., Werner, C. S., Ligtvoet, R., & Schermelleh-Engel,K. (2012). Measurement bias detection through factor analysis. StructuralEquation Modeling: A Multidisciplinary Journal, 19 (4), 561–579.

162 162

Bartholomew, D. J. & Leung, S. O. (2002). A goodness of fit test for sparse2p contingency tables. British Journal of Mathematical and Statistical Psy-chology, 55 (1), 1–15.

Beauducel, A. (2001). On the generalizability of factors: The influence ofchanging contexts of variables on different methods of factor extraction.Methods of Psychological Research Online, 6 (1), 69–96.

Beauducel, A. & Herzberg, P. Y. (2006). On the performance of maximumlikelihood versus means and variance adjusted weighted least squares esti-mation in cfa. Structural Equation Modeling: A Multidisciplinary Journal,13 (2), 186–203.

Bohrnstedt, G. W. & Goldberger, A. S. (1969). On the exact covariance ofproducts of random variables. Journal of the American Statistical Associa-tion, 64 (328), 1439–1442.

Boker, S., Neale, M., Maes, H., Wilde, M., Spiegel, M., Brick, T., Spies, J.,Estabrook, R., Kenny, S., Bates, T., et al. (2011). OpenMx: An open sourceextended structural equation modeling framework. Psychometrika, 76 (2),306–317.

Bollen, K. A. (1989). Structural Equations with Latent Variables. New York:John Wiley & Sons.

Boulton, A. J. (2011). Fit Index Sensitivity in Multilevel Structural EquationModeling. PhD thesis, Docteral dissertation Kansas, University of Kansas.

Briggs, N. E. & MacCallum, R. C. (2003). Recovery of weak common factorsby maximum likelihood and ordinary least squares estimation. MultivariateBehavioral Research, 38 (1), 25–56.

Browne, M. W. (1984). Asymptotically distribution–free methods for the anal-ysis of covariance structures. British Journal of Mathematical and StatisticalPsychology, 37 (1), 62–83.

Browne, M. W. (1995). Covariance structures. In Topics in Applied Multi-variate Analysis, (pp. 72–141). ID M. Hawkins. Cambridge, UK: CambridgeUniversity.

Browne, M. W. (2001). An overview of analytic rotation in exploratory factoranalysis. Multivariate Behavioral Research, 36 (1), 111–150.

Browne, M. W. & Cudeck, R. (1992). Alternative ways of assessing model fit.Sociological Methods & Research, 21 (2), 230–258.

163162

Bartholomew, D. J. & Leung, S. O. (2002). A goodness of fit test for sparse2p contingency tables. British Journal of Mathematical and Statistical Psy-chology, 55 (1), 1–15.

Beauducel, A. (2001). On the generalizability of factors: The influence ofchanging contexts of variables on different methods of factor extraction.Methods of Psychological Research Online, 6 (1), 69–96.

Beauducel, A. & Herzberg, P. Y. (2006). On the performance of maximumlikelihood versus means and variance adjusted weighted least squares esti-mation in cfa. Structural Equation Modeling: A Multidisciplinary Journal,13 (2), 186–203.

Bohrnstedt, G. W. & Goldberger, A. S. (1969). On the exact covariance ofproducts of random variables. Journal of the American Statistical Associa-tion, 64 (328), 1439–1442.

Boker, S., Neale, M., Maes, H., Wilde, M., Spiegel, M., Brick, T., Spies, J.,Estabrook, R., Kenny, S., Bates, T., et al. (2011). OpenMx: An open sourceextended structural equation modeling framework. Psychometrika, 76 (2),306–317.

Bollen, K. A. (1989). Structural Equations with Latent Variables. New York:John Wiley & Sons.

Boulton, A. J. (2011). Fit Index Sensitivity in Multilevel Structural EquationModeling. PhD thesis, Docteral dissertation Kansas, University of Kansas.

Briggs, N. E. & MacCallum, R. C. (2003). Recovery of weak common factorsby maximum likelihood and ordinary least squares estimation. MultivariateBehavioral Research, 38 (1), 25–56.

Browne, M. W. (1984). Asymptotically distribution–free methods for the anal-ysis of covariance structures. British Journal of Mathematical and StatisticalPsychology, 37 (1), 62–83.

Browne, M. W. (1995). Covariance structures. In Topics in Applied Multi-variate Analysis, (pp. 72–141). ID M. Hawkins. Cambridge, UK: CambridgeUniversity.

Browne, M. W. (2001). An overview of analytic rotation in exploratory factoranalysis. Multivariate Behavioral Research, 36 (1), 111–150.

Browne, M. W. & Cudeck, R. (1992). Alternative ways of assessing model fit.Sociological Methods & Research, 21 (2), 230–258.

163

Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences. Hills-dale, New Jersey: Lawrence Erlbaum Associates.

Conway, J. M. & Huffcutt, A. I. (2003). A review and evaluation of exploratoryfactor analysis practices in organizational research. Organizational ResearchMethods, 6 (2), 147–168.

D’Haenens, E., Van Damme, J., & Onghena, P. (2010). Multilevel exploratoryfactor analysis: illustrating its surplus value in educational effectivenessresearch. School Effectiveness and School Improvement, 21 (2), 209–235.

Dolan, C. V. (1994). Factor analysis of variables with 2, 3, 5 and 7 responsecategories: A comparison of categorical variable estimators using simulateddata. British Journal of Mathematical and Statistical Psychology, 47 (2),309–326.

Fabrigar, L. R., Wegener, D. T., MacCallum, R. C., & Strahan, E. J. (1999).Evaluating the use of exploratory factor analysis in psychological research.Psychological Methods, 4 (3), 272–299.

Flora, D. B. & Curran, P. J. (2004). An empirical evaluation of alternativemethods of estimation for confirmatory factor analysis with ordinal data.Psychological Methods, 9 (4), 466–491.

Gaskin, C. J. & Happell, B. (2014). On exploratory factor analysis: A reviewof recent evidence, an assessment of current practice, and recommendationsfor future use. International Journal of Nursing Studies, 51 (3), 511–521.

Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2013). BayesianData Analysis. Texts in statistical science series. London, United Kingkom:Chapman & Hall/CRC.

Gelman, A. & Rubin, D. B. (1992). Inference from iterative simulation usingmultiple sequences. Statistical Science, 457–472.

Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches tothe calculation of posterior moments. In Bayesian Statistics, (pp. 169–193).JM Bernardo, JO Berger, AP Dawid, AFM Smith (Eds.) University Press.

Gonzalez-Roma, V., Hernandez, A., & Gomez-Benito, J. (2006). Power andtype i error of the mean and covariance structure analysis model for de-tecting differential item functioning in graded response items. MultivariateBehavioral Research, 41 (1), 29–53.

Hayashi, K., Bentler, P. M., & Yuan, K.-H. (2007). On the likelihood ratio testfor the number of factors in exploratory factor analysis. Structural EquationModeling: A Multidisciplinary Journal, 14 (3), 505–526.

164 164

Hernández, A. & González-Romá, V. (2003). Evaluating the multiple-groupmean and covariance structure analysis model for the detection of differentialitem functioning in polytomous ordered items. Psicothema, 15 (2), 322–327.

Holgado-Tello, F. P., Chacón-Moscoso, S., Barbero-Garćıa, I., & Vila-Abad,E. (2010). Polychoric versus pearson correlations in exploratory and con-firmatory factor analysis of ordinal variables. Quality & Quantity, 44 (1),153–166.

Hooper, D., Coughlan, J., & Mullen, M. (2008). Structural equation mod-elling: Guidelines for determining model fit. Electronic Journal of BusinessResearch Methods, 6 (1), 53–60.

Hu, L. & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariancestructure analysis: Conventional criteria versus new alternatives. StructuralEquation Modeling: A Multidisciplinary Journal, 6 (1), 1–55.

Jak, S., Oort, F. J., & Dolan, C. V. (2010). Measurement bias and multidimen-sionality; an illustration of bias detection in multidimensional measurementmodels. Advances in Statistical Analysis, 94 (2), 129–137.

Jak, S., Oort, F. J., & Dolan, C. V. (2013). A test for cluster bias: Detect-ing violations of measurement invariance across clusters in multilevel data.Structural Equation Modeling: A Multidisciplinary Journal, 20 (2), 265–282.

Jak, S., Oort, F. J., & Dolan, C. V. (2014). Measurement bias in multileveldata. Structural Equation Modeling: A Multidisciplinary Journal, 21 (1),31–39.

Johnson, D. R. & Creech, J. C. (1983). Ordinal measures in multiple indicatormodels: A simulation study of categorization error. American SociologicalReview, 48 (3), 398–407.

Jöreskog, K. G. (1990). New developments in LISREL: Analysis of ordinalvariables using polychoric correlations and weighted least squares. Quality& Quantity, 24 (4), 387–404.

Jöreskog, K. G. (1994). On the estimation of polychoric correlations and theirasymptotic covariance matrix. Psychometrika, 59 (3), 381–389.

Jöreskog, K. G. & Moustaki, I. (2001). Factor analysis of ordinal variables: Acomparison of three approaches. Multivariate Behavioral Research,, 36 (3),347–387.

Katsikatsou, M., Moustaki, I., Yang-Wallentin, F., & Jöreskog, K. G. (2012).Pairwise likelihood estimation for factor analysis models with ordinal data.Computational Statistics & Data Analysis, 56 (12), 4243–4258.

165164

Hernández, A. & González-Romá, V. (2003). Evaluating the multiple-groupmean and covariance structure analysis model for the detection of differentialitem functioning in polytomous ordered items. Psicothema, 15 (2), 322–327.

Holgado-Tello, F. P., Chacón-Moscoso, S., Barbero-Garćıa, I., & Vila-Abad,E. (2010). Polychoric versus pearson correlations in exploratory and con-firmatory factor analysis of ordinal variables. Quality & Quantity, 44 (1),153–166.

Hooper, D., Coughlan, J., & Mullen, M. (2008). Structural equation mod-elling: Guidelines for determining model fit. Electronic Journal of BusinessResearch Methods, 6 (1), 53–60.

Hu, L. & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariancestructure analysis: Conventional criteria versus new alternatives. StructuralEquation Modeling: A Multidisciplinary Journal, 6 (1), 1–55.

Jak, S., Oort, F. J., & Dolan, C. V. (2010). Measurement bias and multidimen-sionality; an illustration of bias detection in multidimensional measurementmodels. Advances in Statistical Analysis, 94 (2), 129–137.

Jak, S., Oort, F. J., & Dolan, C. V. (2013). A test for cluster bias: Detect-ing violations of measurement invariance across clusters in multilevel data.Structural Equation Modeling: A Multidisciplinary Journal, 20 (2), 265–282.

Jak, S., Oort, F. J., & Dolan, C. V. (2014). Measurement bias in multileveldata. Structural Equation Modeling: A Multidisciplinary Journal, 21 (1),31–39.

Johnson, D. R. & Creech, J. C. (1983). Ordinal measures in multiple indicatormodels: A simulation study of categorization error. American SociologicalReview, 48 (3), 398–407.

Jöreskog, K. G. (1990). New developments in LISREL: Analysis of ordinalvariables using polychoric correlations and weighted least squares. Quality& Quantity, 24 (4), 387–404.

Jöreskog, K. G. (1994). On the estimation of polychoric correlations and theirasymptotic covariance matrix. Psychometrika, 59 (3), 381–389.

Jöreskog, K. G. & Moustaki, I. (2001). Factor analysis of ordinal variables: Acomparison of three approaches. Multivariate Behavioral Research,, 36 (3),347–387.

Katsikatsou, M., Moustaki, I., Yang-Wallentin, F., & Jöreskog, K. G. (2012).Pairwise likelihood estimation for factor analysis models with ordinal data.Computational Statistics & Data Analysis, 56 (12), 4243–4258.

165

Klein, A. G. (2007). Quasi–ML 3.10–quick reference manual. UnpublishedPaper, The University of Western Ontario.

Klein, A. G. & Moosbrugger, H. (2000). Maximum likelihood estimation oflatent interaction effects with the LMS method. Psychometrika, 65 (4), 457–474.

Klein, A. G. & Muthén, B. O. (2007). Quasi–maximum likelihood estimation ofstructural equation models with multiple interaction and quadratic effects.Multivariate Behavioral Research, 42 (4), 647–673.

Lee, S.-Y. (2007). Structural Equation Modeling: A Bayesian Approach. Chich-ester, United Kingkom: John Wiley & Sons.

Lee, S.-Y., Poon, W.-Y., & Bentler, P. (1990). Full maximum likelihood anal-ysis of structural equation models with polytomous variables. Statistics &Probability Letters, 9 (1), 91–97.

Lee, S.-Y. & Song, X.-Y. (2012). Basic and Advanced Bayesian StructuralEquation Modeling: With Applications in the Medical and Behavioral Sci-ences. Chichester, United Kingkom: John Wiley & Sons.

Lord, F. & Novick, M. (1968). Statistical Theories of Mental Test Scores.Oxford, England: Addison-Wesley.

Lunn, D., Spiegelhalter, D., Thomas, A., & Best, N. (2009). The BUGSproject: Evolution, critique and future directions. Statistics in Medicine,28 (25), 3049–3067.

MacCallum, R. C., Browne, M. W., & Sugawara, H. M. (1996). Power anal-ysis and determination of sample size for covariance structure modeling.Psychological Methods, 1 (2), 130.

MacCallum, R. C., Widaman, K. F., Preacher, K. J., & Hong, S. (2001). Sam-ple size in factor analysis: The role of model error. Multivariate BehavioralResearch, 36 (4), 611–637.

MacCallum, R. C., Widaman, K. F., Zhang, S., & Hong, S. (1999). Samplesize in factor analysis. Psychological Methods, 4 (1), 84.

MacCallum, R. C., Zhang, S., Preacher, K. J., & Rucker, D. D. (2002). On thepractice of dichotomization of quantitative variables. Psychological Methods,7 (1), 19–40.

Marsh, H. W., Hau, K.-T., & Wen, Z. (2004). In search of golden rules:Comment on hypothesis-testing approaches to setting cutoff values for fitindexes and dangers in overgeneralizing Hu and Bentler’s (1999) findings.Structural Equation Modeling: A Multidisciplinary Journal, 11 (3), 320–341.

166 166

Maydeu-Olivares, A. (2006). Limited information estimation and testing ofdiscretized multivariate normal structural models. Psychometrika, 71 (1),57–77.

Maydeu-Olivares, A. & Joe, H. (2006). Limited information goodness-of-fittesting in multidimensional contingency tables. Psychometrika, 71 (4), 713–732.

Meade, A. W. & Lautenschlager, G. J. (2004). A monte-carlo study of confir-matory factor analytic tests of measurement equivalence/invariance. Struc-tural Equation Modeling: A Multidisciplinary Journal, 11 (1), 60–72.

Mellenbergh, G. J. (1989). Item bias and item response theory. InternationalJournal of Educational Research, 13 (2), 127–143.

Meredith, W. (1993). Measurement invariance, factor analysis and factorialinvariance. Psychometrika, 58 (4), 525–543.

Molenaar, D. (2012). Testing distributional assumptions in psychometric mea-surement models with substantive applications in psychology. PhD thesis,Docteral dissertation Amsterdam, University of Amsterdam.

Moosbrugger, H., Schermelleh-Engel, K., Kelava, A., & Klein, A. G. (2009).Testing multiple nonlinear effects in structural equation modeling: A com-parison of alternative estimation approaches. In Structural equation model-ing in educational research: Concepts and applications, (pp. 103–136). SensePublishers, Rotterdam.

Moustaki, I. (2003). A general class of latent variable models for ordinalmanifest variables with covariate effects on the manifest and latent variables.British Journal of Mathematical and Statistical Psychology, 56 (2), 337–357.

MRC Biostatistics Unit (2006). Dic: Deviance Information Criterion.http://www.mrc-bsu.cam.ac.uk/software/bugs/the-bugs-project-dic/. Ap-proached at 30 July 2014.

Muthén, B. O. (1984). A general structural equation model with dichotomous,ordered categorical, and continuous latent variable indicators. Psychome-trika, 49 (1), 115–132.

Muthén, B. O. (1989a). Latent variable modeling in heterogeneous popula-tions. Psychometrika, 54 (4), 557–585.

Muthén, B. O. (1989b). Multiple-group structural modelling with non-normalcontinuous variables. British Journal of Mathematical and Statistical Psy-chology, 42 (1), 55–62.

167166

Maydeu-Olivares, A. (2006). Limited information estimation and testing ofdiscretized multivariate normal structural models. Psychometrika, 71 (1),57–77.

Maydeu-Olivares, A. & Joe, H. (2006). Limited information goodness-of-fittesting in multidimensional contingency tables. Psychometrika, 71 (4), 713–732.

Meade, A. W. & Lautenschlager, G. J. (2004). A monte-carlo study of confir-matory factor analytic tests of measurement equivalence/invariance. Struc-tural Equation Modeling: A Multidisciplinary Journal, 11 (1), 60–72.

Mellenbergh, G. J. (1989). Item bias and item response theory. InternationalJournal of Educational Research, 13 (2), 127–143.

Meredith, W. (1993). Measurement invariance, factor analysis and factorialinvariance. Psychometrika, 58 (4), 525–543.

Molenaar, D. (2012). Testing distributional assumptions in psychometric mea-surement models with substantive applications in psychology. PhD thesis,Docteral dissertation Amsterdam, University of Amsterdam.

Moosbrugger, H., Schermelleh-Engel, K., Kelava, A., & Klein, A. G. (2009).Testing multiple nonlinear effects in structural equation modeling: A com-parison of alternative estimation approaches. In Structural equation model-ing in educational research: Concepts and applications, (pp. 103–136). SensePublishers, Rotterdam.

Moustaki, I. (2003). A general class of latent variable models for ordinalmanifest variables with covariate effects on the manifest and latent variables.British Journal of Mathematical and Statistical Psychology, 56 (2), 337–357.

MRC Biostatistics Unit (2006). Dic: Deviance Information Criterion.http://www.mrc-bsu.cam.ac.uk/software/bugs/the-bugs-project-dic/. Ap-proached at 30 July 2014.

Muthén, B. O. (1984). A general structural equation model with dichotomous,ordered categorical, and continuous latent variable indicators. Psychome-trika, 49 (1), 115–132.

Muthén, B. O. (1989a). Latent variable modeling in heterogeneous popula-tions. Psychometrika, 54 (4), 557–585.

Muthén, B. O. (1989b). Multiple-group structural modelling with non-normalcontinuous variables. British Journal of Mathematical and Statistical Psy-chology, 42 (1), 55–62.

167

Muthén, B. O. (1994). Multilevel covariance structure analysis. SociologicalMethods & Research, 22 (3), 376–398.

Muthén, B. O. (1998-2004). Mplus technical appendices. Unpublished technicalreport. Retrieved from https://www.statmodel.com/download/techappen.pdf.

Muthén, B. O. & Asparouhov, T. (2003). Modeling interactions be-tween latent and observed continuous variables using maximum-likelihoodestimation in Mplus. Mplus Web Notes: No. 6. Retrieved fromhttp://statmodel2.com/download/webnotes/webnote6.pdf.

Muthén, B. O. & Asparouhov, T. (2012). Bayesian structural equation mod-eling: a more flexible representation of substantive theory. PsychologicalMethods, 17 (3), 313.

Muthén, B. O. & Asparouhov, T. (2013). BSEM measurement in-variance analysis. Mplus Web Notes: No. 6. Retrieved fromhttps://www.statmodel.com/examples/webnotes/webnote17.pdf.

Muthén, B. O., Du Toit, S. H., & Spisic, D. (1997). Robust inference usingweighted least squares and quadratic estimating equations in latent variablemodeling with categorical and continuous outcomes. Unpublished technicalreport. Retrieved fromhttp://pages.gseis.ucla.edu/faculty/muthen/articles/Article 075.pdf.

Muthén, B. O. & Kaplan, D. (1985). A comparison of some methodologiesfor the factor analysis of non-normal likert variables. British Journal ofMathematical and Statistical Psychology, 38 (2), 171–189.

Muthén, B. O. & Kaplan, D. (1992). A comparison of some methodologies forthe factor analysis of non-normal likert variables: A note on the size of themodel. British Journal of Mathematical and Statistical Psychology, 45 (1),19–30.

Muthén, L. K. & Muthén, B. O. (2007). Mplus: Statistical analysis with latentvariables: User’s guide. Muthén & Muthén.

Muthén, L. K. & Muthén, B. O. (2010). Mplus: Statistical analysis with latentvariables: User’s guide. Muthén & Muthén.

Navas-Ara, M. J. & Gómez-Benito, J. (2002). Effects of ability scale pu-rification on the identification of DIF. European Journal of PsychologicalAssessment, 18 (1), 9.

Neale, M. C., Boker, S. M., Xie, G., & Maes, H. H. (2002). Mx: Statisticalmodeling. Richmond: Virginia Commonwealth University, Department ofPsychiatry.

168 168

Olsson, U. (1979). Maximum likelihood estimation of the polychoric correlationcoefficient. Psychometrika, 44 (4), 443–460.

Olsson, U. H., Foss, T., & Breivik, E. (2004). Two equivalent discrepancyfunctions for maximum likelihood estimation: Do their test statistics followa non-central chi-square distribution under model misspecification? Socio-logical Methods & Research, 32 (4), 453–500.

Olsson, U. H., Troye, S. V., & Howell, R. D. (1999). Theoretic fit and empiricalfit: The performance of maximum likelihood versus generalized least squaresestimation in structural equation models. Multivariate Behavioral Research,34 (1), 31–58.

Oort, F. J. (1991). Theory of violators: Assessing unidimensionality of psycho-logical measures. In W. K. F. Steyer, R. & W. K. F. (Eds.), Psychometricmethodology (pp. 377–381). Stuttgart, Germany: Gustav Fischer.

Oort, F. J. (1992). Using restricted factor analysis to detect item bias.Methodika, 6, 150–166.

Oort, F. J. (1996). Using Restricted Factor Analysis in Test Construction.PhD thesis, Docteral dissertation Amsterdam, University of Amsterdam.

Oort, F. J. (1998). Simulation study of item bias detection with restrictedfactor analysis. Structural Equation Modeling: A Multidisciplinary Journal,5 (2), 107–124.

Oort, F. J. (2011). Likelihood-based confidence intervals in exploratory factoranalysis. Structural Equation Modeling: A Multidisciplinary Journal, 18 (3),383–396.

Plummer, M., Best, N., Cowles, K., & Vines, K. (2006). CODA: Convergencediagnosis and output analysis for MCMC. R News, 6 (1), 7–11.

Preacher, K. J. & MacCallum, R. C. (2003). Repairing Tom Swift’s elec-tric factor analysis machine. Understanding Statistics: Statistical Issues inPsychology, Education, and the Social Sciences, 2 (1), 13–43.

R Core Team (2014). R: A Language and Environment for Statistical Com-puting. Vienna, Austria: R Foundation for Statistical Computing.

R Development Core Team (2010). R: A Language and Environment for Statis-tical Computing. Vienna, Austria: R Foundation for Statistical Computing.

Rabe-Hesketh, S., Skrondal, A., & Pickles, A. (2004). Generalized multilevelstructural equation modeling. Psychometrika, 69 (2), 167–190.

169168

Olsson, U. (1979). Maximum likelihood estimation of the polychoric correlationcoefficient. Psychometrika, 44 (4), 443–460.

Olsson, U. H., Foss, T., & Breivik, E. (2004). Two equivalent discrepancyfunctions for maximum likelihood estimation: Do their test statistics followa non-central chi-square distribution under model misspecification? Socio-logical Methods & Research, 32 (4), 453–500.

Olsson, U. H., Troye, S. V., & Howell, R. D. (1999). Theoretic fit and empiricalfit: The performance of maximum likelihood versus generalized least squaresestimation in structural equation models. Multivariate Behavioral Research,34 (1), 31–58.

Oort, F. J. (1991). Theory of violators: Assessing unidimensionality of psycho-logical measures. In W. K. F. Steyer, R. & W. K. F. (Eds.), Psychometricmethodology (pp. 377–381). Stuttgart, Germany: Gustav Fischer.

Oort, F. J. (1992). Using restricted factor analysis to detect item bias.Methodika, 6, 150–166.

Oort, F. J. (1996). Using Restricted Factor Analysis in Test Construction.PhD thesis, Docteral dissertation Amsterdam, University of Amsterdam.

Oort, F. J. (1998). Simulation study of item bias detection with restrictedfactor analysis. Structural Equation Modeling: A Multidisciplinary Journal,5 (2), 107–124.

Oort, F. J. (2011). Likelihood-based confidence intervals in exploratory factoranalysis. Structural Equation Modeling: A Multidisciplinary Journal, 18 (3),383–396.

Plummer, M., Best, N., Cowles, K., & Vines, K. (2006). CODA: Convergencediagnosis and output analysis for MCMC. R News, 6 (1), 7–11.

Preacher, K. J. & MacCallum, R. C. (2003). Repairing Tom Swift’s elec-tric factor analysis machine. Understanding Statistics: Statistical Issues inPsychology, Education, and the Social Sciences, 2 (1), 13–43.

R Core Team (2014). R: A Language and Environment for Statistical Com-puting. Vienna, Austria: R Foundation for Statistical Computing.

R Development Core Team (2010). R: A Language and Environment for Statis-tical Computing. Vienna, Austria: R Foundation for Statistical Computing.

Rabe-Hesketh, S., Skrondal, A., & Pickles, A. (2004). Generalized multilevelstructural equation modeling. Psychometrika, 69 (2), 167–190.

169

Raftery, A. E. & Lewis, S. M. (1992). [practical markov chain monte carlo]:Comment: One long run with diagnostics: Implementation strategies formarkov chain monte carlo. Statistical Science, 7, 493–497.

Raftery, A. E. & Lewis, S. M. (1995). The number of iterations, convergencediagnostics and generic metropolis algorithms. In Practical Markov ChainMonte Carlo (W.R. Gilks, D.J. Spiegelhalter and, (pp. 115–130). London,United Kingkom: Chapman and Hall.

Reiser, M. & Lin, Y. (1999). A goodness-of-fit test for the latent class modelwhen expected frequencies are small. Sociological Methodology, 29 (1), 81–111.

Reiser, M. & VandenBerg, M. (1994). Validity of the chi-square test in dichoto-mous variable factor analysis when expected frequencies are small. BritishJournal of Mathematical and Statistical Psychology, 47 (1), 85–107.

Rhemtulla, M., Brosseau-Liard, P. E., & Savalei, V. (2012). When can categor-ical variables be treated as continuous? a comparison of robust continuousand categorical sem estimation methods under suboptimal conditions. Psy-chological Methods, 17 (3), 354–373.

Rigdon, E. E. & Ferguson Jr, C. E. (1991). The performance of the polychoriccorrelation coefficient and selected fitting functions in confirmatory factoranalysis with ordinal data. Journal of Marketing Research, 491–497.

Roberts, G. O. (1996). Markov chain concepts related to sampling algorithms.In W. R. Gilks, S. Richardson, & D. J. Spiegelhalter (Eds.), Markov chainMonte Carlo in practice (pp. 45–57). London, United Kingkom: Springer.

Rosseel, Y. (2012). lavaan: An R package for structural equation modeling.Journal of Statistical Software, 48 (2), 1–36.

Ryu, E. & West, S. G. (2009). Level-specific evaluation of model fit in multi-level structural equation modeling. Structural Equation Modeling: A Mul-tidisciplinary Journal, 16 (4), 583–601.

Satorra, A. & Bentler, P. M. (1994). Corrections to test statistics and standarderrors in covariance structure analysis. In A. van Eye & C. C. C. (Eds.)(Eds.), Latent Variables Analysis: Applications to Developmental Research(pp. 399–419). Sage Publications, Inc; Thousand Oaks, CA.

Satorra, A. & Bentler, P. M. (2001). A scaled difference chi-square test statisticfor moment structure analysis. Psychometrika, 66 (4), 507–514.

Satorra, A. & Bentler, P. M. (2010). Ensuring positiveness of the scaled dif-ference chi-square test statistic. Psychometrika, 75 (2), 243–248.

170 170

Schermelleh-Engel, K., Werner, C. S., Klein, A. G., & Moosbrugger, H. (2010).Nonlinear structural equation modeling: is partial least squares an alterna-tive? Advances in Statistical Analysis, 94 (2), 167–184.

Schmitt, N. & Kuljanin, G. (2008). Measurement invariance: Review of prac-tice and implications. Human Resource Management Review, 18 (4), 210–222.

Sivo, S. A., Fan, X., Witta, E. L., & Willse, J. T. (2006). The search for” op-timal” cutoff properties: Fit index criteria in structural equation modeling.The Journal of Experimental Education, 74 (3), 267–288.

Snijders, T. & Bosker, R. (1999). Multilevel Analysis: An Introduction to Basicand Advanced Multilevel Modeling. Oaks, CA: Sage.

Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & Van Der Linde, A. (2002).Bayesian measures of model complexity and fit. Journal of the Royal Sta-tistical Society: Series B (Statistical Methodology), 64 (4), 583–639.

Spilt, J. L., Koomen, H. M., & Jak, S. (2012). Are boys better off with maleand girls with female teachers? a multilevel investigation of measurementinvariance and gender match in teacher–student relationship quality. Journalof School Psychology, 50 (3), 363–378.

Steiger, J. H., Shapiro, A., & Browne, M. W. (1985). On the multivariateasymptotic distribution of sequential chi-square statistics. Psychometrika,50 (3), 253–263.

Tanner, M. A. & Wong, W. H. (1987). The calculation of posterior distribu-tions by data augmentation. Journal of the American Statistical Association,82 (398), 528–540.

Tate, R. (2003). A comparison of selected empirical methods for assessing thestructure of responses to test items. Applied Psychological Measurement,27 (3), 159–203.

Ten Holt, J. C., van Duijn, M. A., & Boomsma, A. (2010). Scale constructionand evaluation in practice: A review of factor analysis versus item responsetheory applications. Psychological Test and Assessment Modeling, 52 (3),272–297.

Vandenberg, R. J. & Lance, C. E. (2000). A review and synthesis of themeasurement invariance literature: Suggestions, practices, and recommen-dations for organizational research. Organizational Research Methods, 3 (1),4–70.

171170

Schermelleh-Engel, K., Werner, C. S., Klein, A. G., & Moosbrugger, H. (2010).Nonlinear structural equation modeling: is partial least squares an alterna-tive? Advances in Statistical Analysis, 94 (2), 167–184.

Schmitt, N. & Kuljanin, G. (2008). Measurement invariance: Review of prac-tice and implications. Human Resource Management Review, 18 (4), 210–222.

Sivo, S. A., Fan, X., Witta, E. L., & Willse, J. T. (2006). The search for” op-timal” cutoff properties: Fit index criteria in structural equation modeling.The Journal of Experimental Education, 74 (3), 267–288.

Snijders, T. & Bosker, R. (1999). Multilevel Analysis: An Introduction to Basicand Advanced Multilevel Modeling. Oaks, CA: Sage.

Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & Van Der Linde, A. (2002).Bayesian measures of model complexity and fit. Journal of the Royal Sta-tistical Society: Series B (Statistical Methodology), 64 (4), 583–639.

Spilt, J. L., Koomen, H. M., & Jak, S. (2012). Are boys better off with maleand girls with female teachers? a multilevel investigation of measurementinvariance and gender match in teacher–student relationship quality. Journalof School Psychology, 50 (3), 363–378.

Steiger, J. H., Shapiro, A., & Browne, M. W. (1985). On the multivariateasymptotic distribution of sequential chi-square statistics. Psychometrika,50 (3), 253–263.

Tanner, M. A. & Wong, W. H. (1987). The calculation of posterior distribu-tions by data augmentation. Journal of the American Statistical Association,82 (398), 528–540.

Tate, R. (2003). A comparison of selected empirical methods for assessing thestructure of responses to test items. Applied Psychological Measurement,27 (3), 159–203.

Ten Holt, J. C., van Duijn, M. A., & Boomsma, A. (2010). Scale constructionand evaluation in practice: A review of factor analysis versus item responsetheory applications. Psychological Test and Assessment Modeling, 52 (3),272–297.

Vandenberg, R. J. & Lance, C. E. (2000). A review and synthesis of themeasurement invariance literature: Suggestions, practices, and recommen-dations for organizational research. Organizational Research Methods, 3 (1),4–70.

171

Varin, C. (2008). On composite marginal likelihoods. Advances in StatisticalAnalysis, 92 (1), 1–28.

Varin, C., Reid, N. M., & Firth, D. (2011). An overview of composite likelihoodmethods. Statistica Sinica, 21 (1), 5–42.

Vasdekis, V. G., Cagnone, S., & Moustaki, I. (2012). A composite likelihoodinference in latent variable models for ordinal longitudinal responses. Psy-chometrika, 77 (3), 425–441.

Verhagen, A. J. (2012). Bayesian Item Response Theory Models for Measur-ment Variance. PhD thesis, Docteral dissertation Twenty, University ofTwente.

Wirth, R. & Edwards, M. C. (2007). Item factor analysis: current approachesand future directions. Psychological methods, 12 (1), 58.

Woods, C. M. & Grimm, K. J. (2011). Testing for nonuniform differentialitem functioning with multiple indicator multiple cause models. AppliedPsychological Measurement, 35 (5), 339–361.

Xi, N. (2011). A composite likelihood approach for factor analyzing ordinaldata. PhD thesis, Docteral dissertation Columbus, OH: Ohio State Univer-sity.

Yang-Wallentin, F., Jöreskog, K. G., & Luo, H. (2010). Confirmatory factoranalysis of ordinal variables with misspecified models. Structural EquationModeling: A Multidisciplinary Journal, 17 (3), 392–423.

Yu, C.-Y. (2002). Evaluating cutoff criteria of model fit indices for latentvariable models with binary and continuous outcomes. PhD thesis, Docteraldissertation Los Angeles, University of California.

Yuan, K.-H. & Bentler, P. M. (1998). Normal theory based test statistics instructural equation modelling. British Journal of Mathematical and Statis-tical Psychology, 51 (2), 289–309.

Yuan, K.-H. & Bentler, P. M. (2000). Three likelihood-based methods for meanand covariance structure analysis with nonnormal missing data. SociologicalMethodology, 30 (1), 165–200.

Zhang, J. & Stout, W. (1999). Conditional covariance structure of generalizedcompensatory multidimensional items. Psychometrika, 64 (2), 129–152.

172 172

Documents

University of Groningen Dimensionality assesment with ...Measurement bias and multidimen-sionality; an illustration of bias detection in multidimensional measurement models. Advances