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Original Articles

Bayesian Estimation for Item Factor Analysis Models with Sparse Categorical Indicators

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References

  • Albert, J. H., & Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association, 88(422), 669–679. doi:10.1080/01621459.1993.10476321
  • Beck, A., Kovacs, M., Weissman, A., & Garfield, Sol L. (1979). Assessment of suicidal intention: The scale for suicide ideation. Journal of Consulting and Clinical Psychology, 47(2), 343–352. doi:10.1037/0022-006X.47.2.343
  • Béguin, A., & Glas, C. (2001). MCMC estimation and some model-fit analysis of multidimensional IRT models. Psychometrika, 66(4), 541–561. doi:10.1007/bf02296195
  • Bentler, P. M., & Chou, C. (1987). Practical issues in structural modeling. Sociological Methods & Research, 16(1), 78–117. doi:10.1177/0049124187016001004
  • Berger, J. O., & Bernardo, J. M. (1992). Ordered group reference priors with application to the multinomial problem. Biometrika, 79(1), 25. doi:10.1093/biomet/79.1.25
  • Bollen, K. A., & Bauldry, S. (2010). Model identification and computer algebra. Sociological Methods & Research, 39(2), 127–156. doi:10.1177/0049124110366238
  • Bollen, K. A., & Maydeu-Olivares, A. (2007). A polychoric instrumental variable (PIV) estimator for structural equation models with categorical variables. Psychometrika, 72(3), 309–326. doi:10.1007/s11336-007-9006-3
  • Cai, L. (2010a). A two-tier full-information item factor analysis model with applications. Psychometrika, 75(4), 581–612. doi:10.1007/s11336-010-9178-0
  • Cai, L. (2010b). High-dimensional exploratory item factor analysis by a Metropolis-Hastings Robbins-Monro algorithm. Psychometrika, 75, 33–57. doi:10.1007/s11336-009-9136-x
  • Carpenter, B., Gelman, A., Hoffman, M., Lee, D., Goodrich, B., Betancourt, M., Brubaker, M., Guo, J., Li, P., & Riddell, A. (2017). Stan: A probabilistic programming language. Journal of Statistical Software, 76(1), 1–32. doi:10.18637/jss.v076.i01
  • Chassin, L., Presson, C., Il-Cho, Y., Lee, M., & Macy, J. (2013). Developmental factors in addiction: Methodological considerations. In J. MacKillop, & H. de Wit (Eds.), The Wiley-Blackwell handbook of addiction psychopharmacology. Oxford, UK: Wiley-Blackwell. doi:10.1002/9781118384404.ch1
  • Collins, L., Schafer, J., & Kam, C. (2001). A comparison of inclusive and restrictive strategies in modern missing data procedures. Psychological Methods, 6(4), 330–351. doi:10.1037//1082-989x.6.4.330
  • Depaoli, S. (2014). The impact of inaccurate “informative” priors for growth parameters in bayesian growth mixture modeling. Structural Equation Modeling, 21(2), 239–252. doi:10.1080/10705511.2014.882686
  • Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987). Hybrid monte carlo. Physics Letters B, 195(2), 216–222. doi:10.1016/0370-2693(87)91197-x
  • Dunson, D. B., & Dinse, G. E. (2001). Bayesian incidence analysis of animal tumorigenicity data. Journal of the Royal Statistical Society.Series C (Applied Statistics), 50(2), 125–141. doi:10.1111/1467-9876.00224
  • Edwards, M. C. (2010). A Markov chain Monte Carlo approach to confirmatory item factor analysis. Psychometrika, 75, 474–497. doi:10.1007/s11336-010-9161-9
  • Forero, C. G., & Maydeu-Olivares, Alberto. (2009). Estimation of IRT graded response models: Limited versus full information methods. Psychological Methods, 14(3), 275–299. doi:10.1037/a0015825
  • Gagné, P. E., & Hancock, G. R. (2006). Measurement model quality, sample size, and solution propriety in confirmatory factor models. Multivariate Behavioral Research, 41, 65–83. doi:10.1207/s15327906mbr4101_5
  • Gelfand, A. E., & Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85(409), 398. doi:10.1080/01621459.1990.10476213
  • Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A, & Rubin, D. B. (2013). Bayesian data analysis. Boca Raton, FL: Chapman & Hall.
  • Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical Science, 7(4), 457–472. doi:10.1214/ss/1177011136
  • Ghosh, J., & Dunson, D. B. (2009). Default prior distributions and efficient posterior computation in bayesian factor analysis. Journal of Computational and Graphical Statistics, 18(2), 306–320. doi:10.1198/jcgs.2009.07145
  • Hallquist, M., & Wiley, J. (2014). MplusAutomation: Automating mplus model estimation and interpretation. R package version 0.6-3. https://CRAN.R-project.org/package=MplusAutomation
  • Hoffman, M., & Gelman, A. (2014). The no-U-turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Resaerch, 15, 1593–1623.
  • Huber, P. J., & Ronchetti, E. M. (2009). Robust Statistics, 2nd Edition. Chichester, UK: Wiley. doi:10.1002/9780470434697
  • Hussong, A. M., Flora, D. B., Curran, P. J., Chassin, L. A., & Zucker, R. A. (2008). Defining risk heterogeneity for internalizing symptoms among children of alcoholic parents. Development and Psychopathology, 20(1), 165–193. doi:10.1017/s0954579408000084
  • Jacobucci, R., Grimm, K., & Mcardle, J. (2016). Regularized structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 23(4), 555–566. doi:10.1080/10705511.2016.1154793
  • Kass, R. E., & Wasserman, L. (1996). The selection of prior distributions by formal rules. Journal of the American Statistical Association, 91(435), 1343–1370. doi:10.1080/01621459.1996.10477003
  • Kline, P. (1994). An easy guide to factor analysis. London, UK: Routledge.
  • Lee, S., & Song, X. (2012). Basic and advanced Bayesian structural equation modeling: With applications in the medical and behavioral sciences. GB: Wiley. doi:10.1002/9781118358887
  • Lee, S. Y., & Tang, N. S. (2006). Bayesian analysis of structural equation models with mixed exponential family and ordered categorical data. British Journal of Mathematical and Statistical Psychology, 59, 151–172. doi:10.1348/000711005x81403
  • Loken, E. (2005). Identification constraints and inference in factor models. Structural Equation Modeling, 12, 232–244. doi:10.1207/s15328007sem1202_3
  • Marsh, H. W., Hau, K., Balla, J. R., & Grayson, D. (1998). Is more ever too much? The number of indicators per factor in confirmatory factor analysis. Multivariate Behavioral Research, 33(2), 181–220. doi:10.1207/s15327906mbr3302_1
  • Maxwell, S. E. (2004). The persistence of underpowered studies in psychological research: Causes, consequences, and remedies. Psychological Methods, 9(2), 147–163. doi:10.1037/1082-989x.9.2.147
  • McCall, W., & Black, V. (2013). The link between suicide and insomnia: Theoretical mechanisms. Current Psychiatry Reports, 15(9), 1–9. doi:10.1007/s11920-013-0389-9
  • Mislevy, R. J. (1986). Bayes modal estimation in item response models. Psychometrika, 51(2), 177–195. doi:10.1007/bf02293979
  • Morin, C. M. (1993) Insomnia: Psychological assessment and management. New York, NY: Guilford Press.
  • Moshagen, M., & Musch, J. (2014). Sample size requirements of the robust weighted least squares estimator. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 10(2), 60–70. doi:10.1027/1614-2241/a000068
  • Muthén, B., du Toit, S. H. C., & Spisic, D. (1997). Robust inference using weighted least squares and quadratic estimating equations in latent variable modeling with categorical and continuous outcomes. Los Angeles, CA: Muthén & Muthén.
  • Muthén, L. K., & Muthén, B. O. (2015). Mplus user's guide (7th ed.). Los Angeles, CA: Muthén & Muthén.
  • Neal, R. (2011). MCMC using Hamiltonian dynamics. In S. Brooks, A. Gelman, G. L. Jones, & X. Meng (Eds.), Handbook of Markov Chain Monte Carlo. Boca Raton, FL: CRC Press. doi:10.1201/b10905
  • Olsson, U. (1979). Maximum likelihood estimation of the polychoric correlation coefficient. Psychometrika, 44, 443–460. doi:10.1007/bf02296207
  • Park, T., & Casella, G. (2008). The bayesian lasso. Journal of the American Statistical Association, 103(482), 681–686. doi:10.1198/016214508000000337
  • Patz, R. J., & Junker, B. W. (1999). A straightforward approach to Markov chain Monte Carlo methods for item response models. Journal of Educational and Behavioral Statistics, 24(2), 146–178. doi:10.2307/1165199
  • Peddada, S. D., Dinse, G. E., & Kissling, G. E. (2007). Incorporating historical control data when comparing tumor incidence rates. Journal of the American Statistical Association, 102(480), 1212–1220. doi:10.1198/016214506000001356
  • 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, 354–373. doi:10.1037/a0029315
  • Rindskopf, D. (1984). Structural equation models: Empirical identification, Heywood cases, and related problems. Sociological Methods & Research, 13(1), 109–119. doi:10.1177/0049124184013001004
  • R Core Team. (2015). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. URL http://www.R-project.org/
  • Savalei, V. (2011). What to do about zero frequency cells when estimating polychoric correlations. Structural Equation Modeling: A Multidisciplinary Journal, 18(2), 253–273. doi:10.1080/10705511.2011.557339
  • Song, X. Y., & Lee, S. Y. (2002). Analysis of structural equation model with ignorable missing continuous and polytomous data. Psychometrika, 67(2), 261–288. doi:10.1007/bf02294846
  • Stan Development Team. (2015). Stan modeling language users guide and reference manual, version 2.7.0. Retrieved from http://mc-stan.org/users/documentation/
  • Takane, Y., & de Leeuw, J. (1987). On the relationship between item response theory and factor analysis of discretized variables. Psychometrika, 52, 393–408. doi:10.1007/bf02294363
  • Tanner, M. A., & Wong, W. H. (1987). The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association, 82(398), 528–540. doi:10.1080/01621459.1987.10478458
  • Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological), 58(1), 267–288. doi:10.1214/10-aoas375supp
  • Timpano, K. R., Keough, M. E., Traeger, L., & Schmidt, N. B. (2011). General life stress and hoarding: Examining the role of emotional tolerance. International Journal of Cognitive Therapy, 4(3), 263–279. doi:10.1521/ijct.2011.4.3.263
  • Wasserman, L. (2005). All of statistics. New York, NY: Springer Science + Business Media, Inc. doi:10.1007/978-0-387-21736-9
  • Winsper, C., & Tang, N. (2014). Linkages between insomnia and suicidality: Prospective associations, high-risk subgroups and possible psychological mechanisms. International Review of Psychiatry, 26(2), 189–204. doi:10.3109/09540261.2014.881330
  • Wirth, R. J., & Edwards, M. C. (2007). Item factor analysis: Current approaches and future directions. Psychological Methods, 12, 58–79. doi:10.1037/1082-989x.12.1.58
  • Yuan, K., Wu, R., & Bentler, P. (2011). Ridge structural equation modelling with correlation matrices for ordinal and continuous data. British Journal of Mathematical & Statistical Psychology, 64(1), 107. doi:10.1348/000711010x497442
  • Zhu, M., & Lu, A. Y. (2004). The counter-intuitive non-informative prior for the Bernoulli family. Journal of Statistics Education, 12(2), 1–10.

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