Estimation of a Rasch model including subdimensions
Steffen Brandt
Main ideas:
Combined with actual situation that many test, especially the large scale assessments composed of other more specific abilities, the common approach that analyze the same data-set once using a unidimensional model and once using a multidimensional model has two downsides. It not only poses a theoretical contradiction but also means neglecting the assumed local dependencies between the items of the same “specific” ability within the unidimensional model.
The author suggested that we can use a Rasch subdimension model that explicitly considers local item dependence (LID) due to specific abilities and thereby yields more adequate estimates
The paper accordingly uses an empirical example to show how results using the subdimension model differ from results arising out of the unidimensional model, the multidimensional model, and the Rasch testlet model (as an alternative model that models LID).
Key concepts:
Rasch subdimensional model
The model uses an additional set of parameters for subdimensions, which based on the assumption that each person has a general ability in the measured dimension as well as strengths and weaknesses in the subdimensions that measure specific abilities within the measured main dimension.
The equations stated for dichotomous items can be extended to polytomous items, which is present in the paper with the constrains of the model
Three restrictions were as follows:
The first one is assuring q is the average of persons’ absolute abilities in the subdimensions; The second is constraining all subdimension-specific factors to have the same covariance with the main dimension (namely zero).Then the subdimensions are defined to be equally weighted for the composition of the main dimension; Restriction 3 is one of the common restrictions that ensure correct identification of the model.
The software ConQuest (Wu et al., 1998) was used to estimate the model.
The empirical study:
The analyzed test used data obtained from the United States sub-sample of students who participated in TIMSS 2003. The sub-sample consisted of 8,912 students in total, and the test included 194 mathematics items.
The other three models (the unidimensional model, the testlet model, and the (unrestricted) multidimensional model) were used for comparison.
The results show that the application of the subdimension model allows for an increase in measurement precision for the students’ unidimensional parameter estimates despite the very unfavorable conditions. For the analyses conducted above, the parameter estimates from the multidimensional model yield higher measurement precision for researchers endeavoring to interpret a person’s abilities relative to the subtests.
Comments:
The model is appealing, especially for the large scale test. The code of the model is easier to overwrite for our own research. The biggest selling point of the model is that it allows for correlations between the subtest-specific factors which make the account for the differences in the subtests possible. However its strength is just its limitations.
Only when the variances of the measured subdimensions are approximately equal, the model can be used. The condition limits its extensive applications.