Mixture Rasch Model with Main and Interaction Effects of Covariates on Latent Class Membership

Year 2019, Volume: 6 Issue: 3, 362 - 377, 15.10.2019

Tugba Karadavut , Allan S. Cohen Seock-ho Kim

https://doi.org/10.21449/ijate.592789

Cited By: 2

Abstract

Covariates have been used in mixture IRT models to help explain why examinees are classed into different latent classes. Previous research has considered manifest variables as covariates in a mixture Rasch analysis for prediction of group membership. Latent covariates, however, are more likely to have higher correlations with the latent class variable. This study investigated effects of including latent variables as covariates in a mixture Rasch model, in presence of and in absence of interactions between the covariates. Results indicated the latent and manifest covariates influenced latent class membership but did not have much influence on class ability means or class proportions. The influence was relatively higher for latent covariates compared to manifest covariates. The effects of the covariates on class membership and on item parameters were class specific. Substantial effects of covariates on item parameters yielded smaller standard errors for item parameter estimates. A significant interaction term also had an effect on the coefficients for predicting and explaining latent class membership.

Keywords

Covariates, Item response theory, Latent class membership, Latent covariates, Mixture Rasch model

Mixture Rasch Model with Main and Interaction Effects of Covariates on Latent Class Membership

Abstract

Covariates
have been used in mixture IRT models to help explain why examinees are classed
into different latent classes. Previous research has considered manifest
variables as covariates in a mixture Rasch analysis for prediction of group
membership. Latent covariates, however, are more likely to have higher
correlations with the latent class variable. This study investigated effects of
including latent variables as covariates in a mixture Rasch model, in presence
of and in absence of interactions between the covariates. Results indicated the
latent and manifest covariates influenced latent class membership but did not
have much influence on class ability means or class proportions. The influence
was relatively higher for latent covariates compared to manifest covariates.
The effects of the covariates on class membership and on item parameters were
class specific. Substantial effects of covariates on item parameters yielded
smaller standard errors for item parameter estimates. A significant interaction
term also had an effect on the coefficients for predicting and explaining
latent class membership.

Keywords

Covariates, Item response theory, Latent class membership, Latent covariates, Mixture Rasch model

References

• Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716-723.
• Bilir, M. K. (2009). Mixture item response theory-MIMIC Model: Simultaneous estimation of differential item functioning for manifest groups and latent classes. Unpublished doctoral dissertation. Florida State University.
• Bolt, D. M., Cohen, A. S., & Wollack, J. A. (2002). Item parameter estimation under conditions of test speededness: Application of a mixture Rasch model with ordinal constraints. Journal of Educational Measurement, 39, 331-348.
• Bonnet, G. (2002). Reflections in a Critical Eye: On the pitfalls of international assessment. Assessment in Education: Principles, Policy & Practice, 9, 387-399.
• Cho, S. J., Cohen, A. S., & Kim, S.-H. (2013). Markov chain Monte Carlo estimation of a mixture item response theory model. Journal of Statistical Computation and Simulation, 83, 278-306.
• Choi, Y. J. (2014). Metric identification in mixture IRT models. Unpublished doctoral dissertation. University of Georgia.
• Choi, Y. J., Alexeev, N., & Cohen, A. S. (2015). Differential item functioning analysis using a mixture 3-parameter logistic model with a covariate on the TIMSS 2007 mathematics test. International Journal of Testing, 15, 239-253.
• Cohen, A. S., & Bolt, D. M. (2005). A mixture model analysis of differential item functioning. Journal of Educational Measurement, 42, 133-148.
• Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hills-dale, NJ: Erlbaum.
• Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). New York, NY: Routledge.
• Dai, Y. (2013). A mixture Rasch model with a covariate: A simulation study via Bayesian Markov chain Monte Carlo estimation. Applied Psychological Measurement, 37, 375-396.
• Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to calculating posterior moments. In J. M. Bernardo, J. O. Berger, A. P. Dawid, & F. M. Smith (Eds.), Bayesian statistics 4 (pp.169-193). New York, NY: Oxford Press.
• Graham, M. H. (2003). Confronting multicollinearity in ecological multiple regression. Ecology, 84, 2809-2815.
• Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31, 1109-1144.
• Lunn, D., Spiegelhalter, D., Thomas, A., & Best, N. (2009). The BUGS project: Evolution, critique and future directions. Statistics in Medicine, 28, 3049-3082.
• Marco, G. L. (1977). Item characteristic curve solutions to three intractable testing problems. Journal of Educational Measurement 14, 139-160.
• Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149-174.
• OECD. (2013), PISA 2012 assessment and analytical framework: Mathematics, reading, science, problem solving and financial literacy. Paris, France: OECD Publishing. Retrieved from http://dx.doi.org/10.1787/9789264190511-en
• OECD. (2014). PISA 2012 technical report. Paris, France: OECD Publishing. Retrieved from www.oecd.org/pisa/pisaproducts/PISA-2012-technical-report-final.pdf
• Pajares, F., & Schunk, D. H. (2001). Self-beliefs and school success: Self-efficacy, self-concept, and and school achievement. In R. Riding & S. Rayner (Eds.), Perception (pp. 239-266). London, England: Ablex.
• Rost, J. (1990). Rasch models in latent classes: An integration of two approaches to item analysis. Applied Psychological Measurement, 14, 271-282.
• Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461-464.
• Smit, A., Kelderman, H., & van der Flier, H. (1999). Collateral information and mixed Rasch models. Methods of Psychological Research Online, 4, 1-13.
• Venables, W. N., & Ripley, B. D. (2002). Modern applied statistics with S (4th ed.). New York, NY: Springer.