This paper proposed a subdimension Rasch model by accounting the local item dependence which often violated in a testlet format test using in larger-scale assessment (like PISA & TIMMS). Comparing to the nonrestrict multidimensional Rasch model, the proposed model modeled a “main dimension” and multiple subsimensions which related to group-specific or method-specific factors. Besides of the model identification constrain (Restriction 1 and 3), a covariance of the overall ability parameter and specific ability parameter is also restricted. Then, an outstanding brief guide of using conquest for estimation is given. At last, an empirical data from TIMSS 2003 was analysis using four models: unidimensional Rasch model, Rasch testlet model, multidimensional Rasch model and the proposed model. The results show that the proposed model has more satisfied measurement precisions. The author also proposed some topics for further investigation, such as subdimensional Rasch model for vertical scaling and simulation studies, as well as modeling by revised the covariance of overall ability parameter and specific ability parameter.
I am interested in comparing models on the topic of measurement precisions and this paper presents a brief logic of doing so by comparing the variance, reliability, and model fit. This might worth a systematic literature reading on this topic. But for this paper, since the analysis just based on empirical data, I have no idea to trust the explanation of its discussion.
This paper also discusses booklet effect under the viewing of subdimensions. When I read the technical report of PISA, I have no idea of how they handing this effect and this paper give me a clue.
Questions:
1. The author said that this model is a special case of MRCMLM, but how is the transformation process?
2. The data from TIMSS 2003 for empirical data analysis, how do the author handle the mix format of items (dichotomous and polytomous)?