I am using mirt (an R-package) for the IRT( Item Response Theory) analysis. Current data, I am dealing with is sparse (contains missing value). Responses are missing because the test is adaptive. ( In the adaptive test not all the questions in the item bank are presented to the test taker hence the responses to the questions he was not presented and the ones he could not solve are missing ). Now the "mirt " function in mirt package takes care that you can calibrate the data with missing values (i.e. fitting the IRT models (Rasch, 2PL, 3PL). However when it comes to the item fit analysis (using "itemfit" function to carry out the item fit analysis) you can not put the sparse data. In this package for the sparse data if you need to go for item fit analysis, you must use imputation. I have two questions here:
1. Are there any more methods available besides imputation for item fit analysis when you have the sparse data?
2. What is the maximum percentage of sparseness in the response data matrix, where you can use imputation method to get reliable results?
Irshad, have you considered using different software? Missing data is no problem for Rasch methodology. Imputation is not necessary. In fact, counter-productive. 99%+ missing data is acceptable. See, for instance, "Rasch Lessons from the Netflix® Prize Challenge Competition" at the link.
http://www.rasch.org/rmt/rmt233d.htm
John, many thanks for your reply. No, I haven't considered using different software yet. I know that imputation is not required for estimating the ability and item parameters (in mirt package) . But what about the item fit? The article in your link does not say anything about item fit statistics such as X2, S-X2, and Zh (specially when data is missing).
Any suggestions regarding that?
Irshad, imputed data always biases fit statistics. Please choose fit statistics that are estimable for incomplete data and suitable for CAT tests. For instance, parameter-estimate-based DIF analysis and CUSUM.
http://jeb.sagepub.com/content/26/2/199.abstract
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