Item Response Models for Multiple Ratings

Implements some item response models for multiple ratings, including the hierarchical rater model, conditional maximum likelihood estimation of linear logistic partial credit model and a wrapper function to the commercial FACETS program. See Robitzsch and Steinfeld (2018) for a description of the functionality of the package. See Wang, Su and Qiu (2014; <doi:10.1111/jedm.12045>) for an overview of modeling alternatives.

Author

Alexander Robitzsch [aut, cre], Jan Steinfeld [aut]

Maintainer: Alexander Robitzsch <robitzsch@ipn.uni-kiel.de>

Details

The immer package has following features:

• Estimation of the hierarchical rater model (Patz et al., 2002) with immer_hrm and simulation of it with immer_hrm_simulate.

• The linear logistic partial credit model as an extension to the linear logistic test model (LLTM) for dichotomous data can be estimated with conditional maximum likelihood (Andersen, 1995) using immer_cml.

• The linear logistic partial credit model can be estimated with composite conditional maximum likelihood (Varin, Reid & Firth, 2011) using the immer_ccml function.

• The linear logistic partial credit model can be estimated with a bias-corrected joint maximum likelihood method (Bertoli-Barsotti, Lando & Punzo, 2014) using the immer_jml function.

• Wrapper function immer_FACETS to the commercial program FACETS (Linacre, 1999) for analyzing multi-faceted Rasch models.

• ...

References

Andersen, E. B. (1995). Polytomous Rasch models and their estimation. In G. H. Fischer & I. W. Molenaar (Eds.). Rasch Models (pp. 39-52). New York: Springer.

Bertoli-Barsotti, L., Lando, T., & Punzo, A. (2014). Estimating a Rasch Model via fuzzy empirical probability functions. In D. Vicari, A. Okada, G. Ragozini & C. Weihs (Eds.). Analysis and Modeling of Complex Data in Behavioral and Social Sciences, Springer.

Linacre, J. M. (1999). FACETS (Version 3.17)[Computer software]. Chicago: MESA.

Patz, R. J., Junker, B. W., Johnson, M. S., & Mariano, L. T. (2002). The hierarchical rater model for rated test items and its application to large-scale educational assessment data. Journal of Educational and Behavioral Statistics, 27(4), 341-384.

Robitzsch, A., & Steinfeld, J. (2018). Item response models for human ratings: Overview, estimation methods, and implementation in R. Psychological Test and Assessment Modeling, 60(1), 101-139.

Varin, C., Reid, N., & Firth, D. (2011). An overview of composite likelihood methods. Statistica Sinica, 21, 5-42.

Wang, W. C., Su, C. M., & Qiu, X. L. (2014). Item response models for local dependence among multiple ratings. Journal of Educational Measurement, 51(3), 260-280.

See also

For estimating the Rasch multi-facets model with marginal maximum likelihood see also the TAM::tam.mml.mfr and sirt::rm.facets functions.

For estimating the hierarchical rater model based on signal detection theory see sirt::rm.sdt.

For conditional maximum likelihood estimation of linear logistic partial credit models see the eRm (e.g. eRm::LPCM) and the psychotools (e.g. psychotools::pcmodel) packages.

Examples

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