Abstract
Multilevel item response theory (MLIRT) models are used widely in educational and psychological research. This type of modeling has two or more levels, including an item response theory model as the measurement part and a linear-regression model as the structural part, the aim being to investigate the relation between explanatory variables and latent variables. However, the linear-regression structural model focuses on the relation between explanatory variables and latent variables, which is only from the perspective of the average tendency. When we need to explore the relationship between variables at various locations along the response distribution, quantile regression is more appropriate. To this end, a quantile-regression-type structural model named as the quantile MLIRT (Q-MLIRT) model is introduced under the MLIRT framework. The parameters of the proposed model are estimated using the Gibbs sampling algorithm, and comparison with the original (i.e., linear-regression-type) MLIRT model is conducted via a simulation study. The results show that the parameters of the Q-MLIRT model could be recovered well under different quantiles. Finally, a subset of data from PISA 2018 is analyzed to illustrate the application of the proposed model.
Highlights
Multilevel or hierarchical linear models are used widely in educational and psychological researches (e.g., Raudenbush, 1988; Goldstein, 1995; Snijders and Bosker, 1999)
Estimates of the item parameters of the Q-Multilevel item response theory (MLIRT) model under different quantiles are close to the true parameter values, reflected mainly in the facts that (i) the cosine similarities between the true-parameter vector and the estimated-parameter vectors under different quantiles are all very close to 1 and (ii) the root-mean-square error (RMSE) are all small
For case 3, the bias of the difficulty parameters for the mean regression multilevel IRT (M-MLIRT) model are always larger than the quantile MLIRT (Q-MLIRT) model, but from the cosine similarity and RMSE points of view, the estimates of the difficulty parameters for the M-MLIRT model and Q-MLIRT model are close
Summary
Multilevel or hierarchical linear models are used widely in educational and psychological researches (e.g., Raudenbush, 1988; Goldstein, 1995; Snijders and Bosker, 1999). These models allow data to be collected at different levels; for example, test data are obtained from students, students are nested within schools, and so on. Adams et al (1997) noted that a two-level IRT model could be seen as a multilevel perspective on item response modeling. When jointly modeling the responses and response times, the ability and speed parameters can be considered as outcome variables of a multivariate multilevel model for various analyses (e.g., Entink et al, 2009; Fox, 2010)
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