Project Activities
To reach its goal, the project team carried out the following steps. First, the team derived theoretical properties of the proposed model with a focus on identification and substantive interpretability of the parameters. The modeling framework was implemented in the C++ programming language. Second, they extended the MH-RM algorithm and optimize it for use with the nonlinear multilevel latent variable model. The algorithm was implemented in C++. Third, the project team conducted simulation studies to test the performance of the algorithm and define the conditions under which the model can be applied. Fourth, the team developed new model checking diagnostic procedures targeted at model-data fit. Fifth, the developed software and methods were used to analyze large-scale educational data sets (e.g., ECLS-K, LSAY, and PISA) to empirically illustrate them and to contrast the results with those from analyses using observed predictors. In addition, the efficiency of the MH-RM based program was compared with other available programs (e.g., WinBUGS, Mplus, or Gllamm).
People and institutions involved
IES program contact(s)
Project contributors
Products and publications
ERIC Citations: Find available citations in ERIC for this award here.
Book chapter
Cai, L. (2013). Factor Analysis of Tests and Items. In K.F. Geisinger, B.A. Bracken, J.F. Carlson, J.C. Hansen, N.R. Kuncel, S.P. Reise, and M.C. Rodriguez (Eds.), APA Handbook of Testing and Assessment in Psychology, Volume 1: Test Theory and Testing and Assessment in Industrial and Organizational Psychology (pp. 85-100). Washington, DC: American Psychological Association.
Cai, L. (2018). Two-Tier Item Factor Analysis Modeling. In W.J. van der Linden (Ed.), Handbook of Modern Item Response Theory (2nd ed.). New York: Chapman and Hall.
Gibbons, R., and Cai, L. (2018). Dimensionality Assessment. In W.J. van der Linden (Ed.), Handbook of Modern Item Response Theory (2nd ed.). New York: Chapman and Hall.
Thissen, D., and Cai, L. (2018). Nominal Categories Models. In W. J. van der Linden (Ed.), Handbook of Modern Item Response Theory. New York: Chapman and Hall.
Journal article, monograph, or newsletter
Cai, L. (2010). A Two-Tier Full-Information Item Factor Analysis Model With Applications. Psychometrika, 75(4): 581-612.
Cai, L. (2015). Lord-Wingersky Algorithm Version 2.0 for Hierarchical Item Factor Models with Applications in Test Scoring, Scale Alignment, and Model Fit Testing. Psychometrika, 80(2): 535-559.
Cai, L., and Hansen, M. (2013). Limited-Information Goodness-of-Fit Testing of Hierarchical Item Factor Models. British Journal of Mathematical and Statistical Psychology, 66(2): 245-276.
Cai, L., Yang, J., and Hansen, M. (2011). Generalized Full-Information Item Bifactor Analysis. Psychological Methods, 16(3): 221-248.
Cole, D.A., Cai, L., Martin, N.C., Findling, R.L., Youngstrom, E.A., Garber, J., Curry, J.F., Hyde, J.S., Essex, M.J., Compas, B.E., Goodyer, I.M., Rohde, P., Stark, K.D., Slattery, M.J., and Forehand, R. (2011). Structure and Measurement of Depression in Youths: Applying Item Response Theory to Clinical Data. Psychological Assessment, 23(4): 819-833.
Falk, C. F., and Cai, L. (2016). Maximum Marginal Likelihood Estimation of a Monotonic Polynomial Generalized Partial Credit Model with Applications to Multiple Group Analysis. Psychometrika, 81(2): 434-460.
Lee, T., and Cai, L. (2012). Alternative Multiple Imputation Inference for Mean and Covariance Structure Modeling. Journal of Educational and Behavioral Statistics, 37(6): 675-702.
Preston, K., Reise, S., Cai, L., and Hays, R.D. (2011). Using the Nominal Response Model to Evaluate Response Category Discrimination in the PROMIS Emotional Distress Item Pools. Educational and Psychological Measurement, 71(3): 523-550.
Tian, W., Cai, L., and Thissen, D. (2013). Numerical Differentiation Methods for Computing Error Covariance Matrices in Item Response Theory Modeling: An Evaluation and a new Proposal. Educational and Psychological Measurement, 73(3): 412-439.
Woods, C.M., Cai, L., and Wang, M. (2013). The Langer-Improved Wald Test for DIF Testing With Multiple Groups: Evaluation and Comparison to Two-Group IRT. Educational and Psychological Measurement, 73(3): 532-547.
Yang, J., Hansen, M., and Cai, L. (2012). Characterizing Sources of Uncertainty in Item Response Theory Scale Scores. Educational and Psychological Measurement, 72(2): 264-290.
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