Estimation of a Rasch model including subdimensions
This paper proposed the subdimension model to solve the problem of local item dependence (LID) which would arise when test analyst directly use unidimensional model and multidimensional model. Also, the proposed model considers correlation between subdimensions which is an extend model of the Rasch testlet model but is a special case of the multidimensional random coefficients multinomial logit model (MRCMLM). The author used the subdimension model to fit the TIMSS 2003 data by CONQUEST along with the unidimensional model, the multidimensional model, and the Rasch testlet model. Results illustrates that the proposed model has the best fit of -2 Log Likelihood.
Sharing, Question and Future study:
1) According to the TIMSS 2003 data, I’m a bit suspicious of the data format is a number of testlets due to the fact that the subdimensions the author depicted here seems to be different contents only. Even if the test format is testlet, how do we decide to choose which model (of the Rasch testlet model and the subdimension model) to analysis the data? Why I’m asking the question is because that -2 Log Likelihood of these two models in table 1 are quite close. Since the two models are all fit the data, it’s reasonable to choose the simpler one.
2) The structure of the subdimension model is similar to the Rasch testlet model, except it also takes correlation between subdimensions into account. As I know, most information from the responses is mainly used to estimate main ability and the rest information is used to estimate subdimensional latent traits. Thus, estimates of subdimensional latent traits usually are not accurate enough. Therefore, I guess that estimates of correlation for subdimension with one another are basically not precise, too.