Item Response Modeling of Forced-Choice Questionnaires
Model：A multidimensional IRT model based on Thurstone’s framework for comparative data is introduced
Proper Data：Any forced-choice questionnaire composed of items fitting the dominance response model, with any number of measured traits, and any block sizes.
Program：Mplus
The first thought occurred in my mind is that the model is very useful for social investigation which usually adopts multidimensional forced-choice format questionnaire. Typically for this kind of data, researchers will only use frequency to describe the nature of the data.
The steps are summarized as follows:
Firstly, the response of the item should be transformed into binary data.
Secondly, the Thurstonian IRT Model reparameterized by the Thurstonian factor model is used for model construction. The identification of the model is that imposing a constraint among the uniquenesses within each block. (The model is identified simply by imposing a constraint among the uniquenesses within each block. This general identification rule is valid in all but two special cases: (a) when n = 2 and d > 2 (i.e., items presented in pairs measuring more than 2 traits) and (b) when d = n =2 (only two traits are measured using pairs of items).
Thirdly, Mplus using the DWLS estimator is used for estimating the parameters of the model.
Two simulation studies and one empirical study were used to demonstrate the performance of the model.
The feeling about this paper is a bit complicated. It seems no place that you can’t understand. However to understand it thoroughly, the mathematic foundation is needed, for example, the source of the formulations and its deduction. The most difficult process may be the simulation of the data and conditions. How to simulate this kind of data and analyze the data?