tmt: Estimation of the Rasch Model for Multistage Tests

Source: R/tmt.r

Provides conditional maximum likelihood (CML) item parameter estimation of both sequential and cumulative deterministic multistage designs (Zwitser & Maris, 2015, doi:10.1007/s11336-013-9369-6 ) and probabilistic sequential and cumulative multistage designs (Steinfeld & Robitzsch, 2021, doi:10.31234/osf.io/ew27f ). Supports CML item parameter estimation of conventional linear designs and additional functions for the likelihood ratio test (Andersen, 1973, doi:10.1007/BF02291180 ) as well as functions for simulating various types of multistage designs.

Details

In multistage tests different groups of items (modules) are presented to persons depending on their response behavior to previous item groups. Multistage testing is thus a simple form of adaptive testing. If data is collected on the basis of such a multistage design and the items are estimated using the Conditional Maximum Likelihood (CML) method, Glas (1989) <doi:10.3102/10769986013001045> has shown, that the item parameters are biased. Zwitser and Maris (2015) <doi:10.1007/s11336-013-9369-6> showed in their work, that taking the applied multistage design in consideration and including it in the estimation of the item parameters, the estimation of item parameters is not biased using the CML method. Their proposed solution is implemented in our package. MST designs with a probabilistic instead of a deterministic routing rule (see, e.g. Chen, Yamamoto, & von Davier, 2014 <doi:10.1201/b16858>) are not estimated with this method, therefore the proposed solouting is again modified by Steinfeld and Robitzsch (2021) <doi:10.31234/osf.io/ew27f> which is also integrated into this package.

An application example can be found in the vignette by using the following command in the R console vignette("introduction_to_tmt")

References

  • Andersen, E. B. (1973). A goodness of fit test for the Rasch model. Psychometrika, 38(1), 123-140.

  • Baker, F. B., & Harwell, M. R. (1996). Computing elementary symmetric functions and their derivatives: A didactic. Applied Psychological Measurement, 20(2), 169-192. Chicago

  • Baker, F. B., & Kim, S. H. (2004). Item response theory: Parameter estimation techniques. CRC Press.

  • Chen, H., Yamamoto, K., & von Davier, M. (2014). Controlling multistage testing exposure rates in international large-scale assessments. In A. Yan, A. A. von Davier, & C. Lewis (Eds.), Computerized Multistage Testing: Theory and Applications (pp. 391-409). New York: CRC Press. https://doi.org/10.1201/b16858

  • Fischer, G. H., & Molenaar, I. W. (Eds.). (2012). Rasch models: Foundations, recent developments, and applications. Springer Science & Business Media.

  • Formann, A. K. (1986). A note on the computation of the second-order derivatives of the elementary symmetric functions in the Rasch model. Psychometrika, 51(2), 335-339.

  • Glas, C.A.W. (1988). The Rasch model and multistage testing. Journal of Educational Statistics, 13(1), 45-52.

  • Glas, C.A.W. (2016). Maximum-Likelihood Estimation. In van der Linden, W.J. (Ed.), Handbook of Item Response Theory: Volume two: Statistical tools. (pp. 197 - 236). New York: CRC Press.

  • Rasch, G. (1960). Probabalistic models for some intelligence and attainment tests. Danmarks paedagogiske institut.

  • Steinfeld, J., & Robitzsch, A. (accepted). Conditional maximum likelihood estimation in probability-based multistage designs. Behaviormetrika, xx(x), xxx-xxx.

  • Steinfeld, J., Robitzsch, A. (2023). Estimating item parameters in multistage designs with the tmt package in R. Quantitative and Computational Methods in Behavioral Science, 3, e10087. https://doi.org/10.5964/qcmb.10087

  • Steinfeld, J., & Robitzsch, A. (2021). Item parameter estimation in multistage designs: A comparison of different estimation approaches for the Rasch model. Psych, 3(3), 279-307. https://doi.org/10.3390/psych3030022

  • Verhelst, N.D., Glas, C.A.W. und van der Sluis, A. (1984). Estimation Problems in the Rasch-Model: The Basic Symmetric Functions. Computational Statistics Quatarly, 1(3), 245-262.

  • Zwitser, R. J., & Maris, G. (2015). Conditional statistical inference with multistage testing designs. Psychometrika, 80(1), 65-84.

Author

Maintainer: Jan Steinfeld jan.d.steinfeld@gmail.com (ORCID)

Authors:

Examples

tmt:::tmt_ascii()
#>  _             _   
#> | |_ _ __ ___ | |_ 
#> | __| '_ ` _ \| __|
#> | |_| | | | | | |_ 
#>  \__|_| |_| |_|\__|
#> 
##  _             _   
## | |_ _ __ ___ | |_ 
## | __| '_ ` _ \| __|
## | |_| | | | | | |_ 
##  \__|_| |_| |_|\__|