References
- Akaike, H. (1974). A new look at the statistical model dentification. IEEE Transactions on Automatic Control, 19(6), 716–723. https://doi.org/https://doi.org/10.1109/TAC.1974.1100705
- Asparouhov, T., & Muthén, B. (2009). Exploratory structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 16(3), 397–438. https://doi.org/https://doi.org/10.1080/10705510903008204
- Battauz, M. (2019). Regularized estimation of the nominal response model. Multivariate Behavioral Research. https://doi.org/https://doi.org/10.1080/00273171.2019.1681252
- Bauer, D. J., Belzak, W. C. M., & Cole, V. T. (2020). Simplifying the assessment of measurement invariance over multiple background variables: Using regularized moderated nonlinear factor analysis to detect differential item functioning. Structural Equation Modeling: A Multidisciplinary Journal, 27(1), 43–55. https://doi.org/https://doi.org/10.1080/10705511.2019.1642754
- Beauducel, A., & Herzberg, P. Y. (2006). On the performance of maximum likelihood versus means and variance adjusted weighted least squares estimation in cfa. Structural Equation Modeling: A Multidisciplinary Journal, 13(2), 186–203. https://doi.org/https://doi.org/10.1207/s15328007sem1302_2
- Bernaards, C. A., & Jennrich, R. I. (2005). Gradient projection algorithms and software for arbitrary rotation criteria in factor analysis. Educational and Psychological Measurement, 65(5), 676–696. https://doi.org/https://doi.org/10.1177/0013164404272507
- Bock, R. D., Gibbons, R., & Muraki, E. (1988). Full-information item factor analysis. Applied Psychological Measurement, 12(3), 261–280. https://doi.org/https://doi.org/10.1177/014662168801200305
- Bollen, K. A. (1989). Structural equations with latent variables. Wiley-Interscience.
- Bühlmann, P., & van de Geer, S. (2011). Statistics for high-dimensional data. Springer.
- Chang, Y.-W., Hsu, N.-J., & Tsai, R.-C. (2017). Unifying differential item functioning in factor analysis for categorical data under a discretization of a normal variant. Psychometrika, 82(2), 382–406. https://doi.org/https://doi.org/10.1007/s11336-017-9562-0
- Chen, Y., Liu, J., Xu, G., & Ying, Z. (2015). Statistical analysis of Q-matrix based diagnostic Classification Models. Journal of the American Statistical Association, 110(510), 850–866. https://doi.org/https://doi.org/10.1080/01621459.2014.934827
- Christoffersson, A. (1975). Factor analysis of dichotomized variables. Psychometrika, 40(1), 5–32. https://doi.org/https://doi.org/10.1007/BF02291477
- Christoffersson, A., & Gunsj, A. (1996). A short note on the estimation of the asymptotic covariance matrix for polychoric correlations. Psychometrika, 61(1), 173–175. https://doi.org/https://doi.org/10.1007/BF02296965
- Crawford, C., & Ferguson, G. (1970). A general rotation criterion and its use in orthogonal rotation. Psychometrika, 35(3), 321–332. https://doi.org/https://doi.org/10.1007/BF02310792
- DiStefano, C. (2002). The impact of categorization with confirmatory factor analysis. Structural Equation Modeling: A Multidisciplinary Journal, 9(3), 327–346. https://doi.org/https://doi.org/10.1207/S15328007SEM0903_2
- Dolan, C. V. (1994). Factor analysis of variables with 2, 3, 5 and 7 response categories: A comparison of categorical variable estimators using simulated data. British Journal of Mathematical and Statistical Psychology, 47(2), 309–326. https://doi.org/https://doi.org/10.1111/j.2044-8317.1994.tb01039.x
- Fan, J., & Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association, 96(456), 1348–1360. https://doi.org/https://doi.org/10.1198/016214501753382273
- Fan, J., & Lv, J. (2010). A selective overview of variable selection in high dimensional feature space. Statistica Sinica, 20(1), 101–148.
- Finch, W. H., & Miller, J. E. (2020). A comparison of regularized maximum-likelihood, regularized 2-stage least squares, and maximum-likelihood estimation with misspecified models, small samples, and weak factor structure. Multivariate Behavioral Research.
- Flora, D. B., & Curran, P. J. (2004). An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data. Psychological Methods, 9(4), 466–491. https://doi.org/https://doi.org/10.1037/1082-989X.9.4.466
- Forero, C. G., Maydeu-Olivares, A., & Gallardo-Pujol, D. (2009). Factor analysis with ordinal indicators: A Monte Carlo study comparing DWLS and ULS estimation. Structural Equation Modeling: A Multidisciplinary Journal, 16(4), 625–641. https://doi.org/https://doi.org/10.1080/10705510903203573
- Friedman, J., Hastie, T., & Tibshirani, R. (2010). Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33(1), 1–22. https://doi.org/https://doi.org/10.18637/jss.v033.i01
- Gao, X., & Song, P. X.-K. (2010). Composite likelihood Bayesian information criteria for model selection in high-dimensional data. Journal of the American Statistical Association, 105(492), 1531–1540. https://doi.org/https://doi.org/10.1198/jasa.2010.tm09414
- Geman, S., Bienenstock, E., & Doursat, R. (1992). Neural networks and the bias/variance dilemma. Neural Computation, 4(1), 1–58. https://doi.org/https://doi.org/10.1162/neco.1992.4.1.1
- Genz, A., & Bretz, F. (2009). Computation of multivariate normal and t probabilities. Springer Science & Business Media.
- Hastie, T., Tibshirani, R., & Wainwright, M. (2015). Statistical learning with sparsity: The lasso and generalizations. Chapman and Hall/CRC.
- Hershberger, S. L. (2003). The growth of structural equation modeling: 1994–2001. Structural Equation Modeling: A Multidisciplinary Journal, 10(1), 35–46. https://doi.org/https://doi.org/10.1207/S15328007SEM1001_2
- Hirose, K., & Yamamoto, M. (2014). Estimation of an oblique structure via penalized likelihood factor analysis. Computational Statistics & Data Analysis, 79, 120–132. https://doi.org/https://doi.org/10.1016/j.csda.2014.05.011
- Hirose, K., & Yamamoto, M. (2015). Sparse estimation via nonconcave penalized likelihood in factor analysis model. Statistics and Computing, 25(5), 863–875. https://doi.org/https://doi.org/10.1007/s11222-014-9458-0
- Huang, P.-H. (2018). A penalized likelihood method for multi-group structural equation modeling. The British Journal of Mathematical and Statistical Psychology, 71(3), 499–522. https://doi.org/https://doi.org/10.1111/bmsp.12130
- Huang, P.-H. (2020). lslx: Semi-confirmatory structural equation modeling via penalized likelihood. Journal of Statistical Software, 93(7), 1–37. https://doi.org/https://doi.org/10.18637/jss.v093.i07
- Huang, P.-H., Chen, H., & Weng, L.-J. (2017). A penalized likelihood method for structural equation modeling. Psychometrika, 82(2), 329–354. https://doi.org/https://doi.org/10.1007/s11336-017-9566-9
- Jacobucci, R., Grimm, K. J., & McArdle, J. J. (2016). Regularized structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 23(4), 555–566. https://doi.org/https://doi.org/10.1080/10705511.2016.1154793
- Johnson, D. R., & Creech, J. C. (1983). Ordinal measures in multiple indicator models: A simulation study of categorization error. American Sociological Review, 48(3), 398–407. https://doi.org/https://doi.org/10.2307/2095231
- Jöreskog, K. G. (1990). New developments in LISREL: Analysis of ordinal variables using polychoric correlations and weighted least squares. Quality and Quantity, 24, 387–404.
- Jreskog, K. (1994). On the estimation of polychoric correlations and their asymptotic covariance matrix. Psychometrika, 59(3), 381–389.
- Katsikatsou, M., & Moustaki, I. (2016). Pairwise likelihood ratio tests and model selection criteria for structural equation models with ordinal variables. Psychometrika, 81(4), 1046–1068. https://doi.org/https://doi.org/10.1007/s11336-016-9523-z
- 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. https://doi.org/https://doi.org/10.1016/j.csda.2012.04.010
- Knol, D. L., & Berger, M. P. (1991). Empirical comparison between factor analysis and multidimensional item response models. Multivariate Behavioral Research, 26(3), 457–477. https://doi.org/https://doi.org/10.1207/s15327906mbr2603_5
- Konishi, S., & Kitagawa, G. (1996). Generalised information criteria in model selection. Biometrika, 83(4), 875–890. https://doi.org/https://doi.org/10.1093/biomet/83.4.875
- Lee, S.-Y., Poon, W.-Y., & Bentler, P. M. (1990a). Full maximum likelihood analysis of structural equation models with polytomous variables. Statistics & Probability Letters, 9(1), 91–97.
- Lee, S.-Y., Poon, W.-Y., & Bentler, P. M. (1990b). A three-stage estimation procedure for structural equation models with polytomous variables. Psychometrika, 55(1), 45–51. https://doi.org/https://doi.org/10.1007/BF02294742
- Li, C.-H. (2016a). Confirmatory factor analysis with ordinal data: Comparing robust maximum likelihood and diagonally weighted least squares. Behavior Research Methods, 48(3), 936–949. https://doi.org/https://doi.org/10.3758/s13428-015-0619-7
- Li, C.-H. (2016b). The performance of ML, DWLS, and ULS estimation with robust corrections in structural equation models with ordinal variables. Psychological Methods, 21(3), 369–387. https://doi.org/https://doi.org/10.1037/met0000093
- Liang, X., & Jacobucci, R. (2019). Regularized structural equation modeling to detect measurement bias: Evaluation of lasso, adaptive lasso, and elastic net. Structural Equation Modeling: A Multidisciplinary Journal, 27(5), 722–734. .
- Lord, F. M., & Novick, M. R. (1968). Statistical theories of mental test scores. Addison-Wesley.
- Marsh, H. W., Lüdtke, O., Muthén, B., Asparouhov, T., Morin, A. J. S., Trautwein, U., & Nagengast, B. (2010). A new look at the big five factor structure through exploratory structural equation modeling. Psychological Assessment, 22(3), 471–491. https://doi.org/https://doi.org/10.1037/a0019227
- Marsh, H. W., Lüdtke, O., Nagengast, B., Morin, A. J. S., & Davier, M. v. (2013). Why item parcels are (almost) never appropriate: Two wrongs do not make a right-camouflaging misspecification with item parcels in CFA models. Psychological Methods, 18(3), 257–284. https://doi.org/https://doi.org/10.1037/a0032773
- Maydeu-Olivares, A. (2001). Limited information estimation and testing of Thurstonian models for paired comparison data under multiple judgment sampling. Psychometrika, 66(2), 209–227. https://doi.org/https://doi.org/10.1007/BF02294836
- McArdle, J. J., & McDonald, R. P. (1984). Some algebraic properties of the reticular action model for moment structures. British Journal of Mathematical and Statistical Psychology, 37(2), 234–251. https://doi.org/https://doi.org/10.1111/j.2044-8317.1984.tb00802.x
- Muthén, B. (1978). Contributions to factor analysis of dichotomous variables. Psychometrika, 43(4), 551–560. https://doi.org/https://doi.org/10.1007/BF02293813
- Muthén, B. O. (1984). A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika, 49(1), 115–132. https://doi.org/https://doi.org/10.1007/BF02294210
- Muthén, B. O., Asparouhov, T., Muthen, B., & Asparouhov, T. (2002). Latent variable analysis with categorical outcomes: Multiple-group and growth modeling in Mplus (tech. rep. No. 4). Mplus Web Notes.
- Muthén, B., & Kaplan, D. (1985). A comparison of some methodologies for the factor analysis of non-normal likert variables. British Journal of Mathematical and Statistical Psychology, 38(2), 171–189. https://doi.org/https://doi.org/10.1111/j.2044-8317.1985.tb00832.x
- Olsson, U. (1979). Maximum likelihood estimation of the polychoric correlation coefficient. Psychometrika, 44(4), 443–460. https://doi.org/https://doi.org/10.1007/BF02296207
- Olsson, U., Drasgow, F., & Dorans, N. (1982). The polyserial correlation coefficient. Psychometrika, 47(3), 337–347. https://doi.org/https://doi.org/10.1007/BF02294164
- R Core Team. (2019). R: A language and environment for statistical computing [Computer software manual]. https://www.R-project.org/
- Revelle, W. (2019). psych: Procedures for psychological, psychometric, and personality research (R package version 1.9.12) [Computer software manual]. https://CRAN.R-project.org/package=psych
- Rhemtulla, M., Brosseau-Liard, P. É., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17(3), 354–373. https://doi.org/https://doi.org/10.1037/a0029315
- Rigdon, E. E., & Ferguson, C. E. (1991). The performance of the polychoric correlation coefficient and selected fitting functions in confirmatory factor analysis with ordinal data. Journal of Marketing Research, 28(4), 491–497. https://doi.org/https://doi.org/10.2307/3172790
- Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph Psychometrika, 34(S1), 1–97. https://doi.org/https://doi.org/10.1007/BF03372160
- Savalei, V., & Rhemtulla, M. (2013). The performance of robust test statistics with categorical data. The British Journal of Mathematical and Statistical Psychology, 66(2), 201–223. https://doi.org/https://doi.org/10.1111/j.2044-8317.2012.02049.x
- Scharf, F., & Nestler, S. (2019). Should regularization replace simple structure rotation in exploratory factor analysis? Structural Equation Modeling: A Multidisciplinary Journal, 26(4), 576–590. https://doi.org/https://doi.org/10.1080/10705511.2018.1558060
- Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464. https://doi.org/https://doi.org/10.1214/aos/1176344136
- Serang, S., & Jacobucci, R. (2020). Exploratory mediation analysis of dichotomous outcomes via regularization. Multivariate Behavioral Research, 55(1), 69–86. https://doi.org/https://doi.org/10.1080/00273171.2019.1608145
- Sun, J., Chen, Y., Liu, J., Ying, Z., & Xin, T. (2016). Latent variable selection for multidimensional item response theory models via L1 regularization. Psychometrika, 81(4), 921–939. https://doi.org/https://doi.org/10.1007/s11336-016-9529-6
- Takane, Y., & Leeuw, J. d. (1987). On the relationship between item response theory and factor analysis of discretized variables. Psychometrika, 52(3), 393–408. https://doi.org/https://doi.org/10.1007/BF02294363
- Tibshirani, R. (1996). Regression selection and shrinkage via the lasso. Journal of the Royal Statistical Society: Series B (Methodological), 58(1), 267–288. https://doi.org/https://doi.org/10.1111/j.2517-6161.1996.tb02080.x
- Tutz, G., & Schauberger, G. (2015). A penalty approach to differential item functioning in Rasch models. Psychometrika, 80(1), 21–43. https://doi.org/https://doi.org/10.1007/s11336-013-9377-6
- Varin, C., & Vidoni, P. (2005). A note on composite likelihood inference and model selection. Biometrika, 92(3), 519–528. [Database] https://doi.org/https://doi.org/10.1093/biomet/92.3.519
- Vrieze, S. I. (2012). Model selection and psychological theory: A discussion of the differences between the akaike information criterion (aic) and the bayesian information criterion (bic). Psychological Methods, 17(2), 228–243. https://doi.org/https://doi.org/10.1037/a0027127
- Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014–1045. https://doi.org/https://doi.org/10.1007/s11336-016-9506-0
- Yang-Wallentin, F., Jöreskog, K. G., & Luo, H. (2010). Confirmatory factor analysis of ordinal variables with misspecified models. Structural Equation Modeling: A Multidisciplinary Journal, 17(3), 392–423. https://doi.org/https://doi.org/10.1080/10705511.2010.489003
- Yuan, G.-X., Ho, C.-H., & Lin, C.-J. (2012). An omproved GLMNET for L1-regularized logistic regression. Journal of Machine Learning Research, 13(1), 1999–2030.
- Yuan, K. H., Hayashi, K., & Bentler, P. M. (2007). Normal theory likelihood ratio statistic for mean and covariance structure analysis under alternative hypotheses. Journal of Multivariate Analysis, 98(6), 1262–1282. https://doi.org/https://doi.org/10.1016/j.jmva.2006.08.005
- Zhang, C. H. (2010). Nearly unbiased variable selection under minimax concave penalty. The Annals of Statistics, 38(2), 894–942. https://doi.org/https://doi.org/10.1214/09-AOS729
- Zou, H., & Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(2), 301–320. https://doi.org/https://doi.org/10.1111/j.1467-9868.2005.00503.x