I am using the mirt package for sparse data from adaptive testing. I found that the residuals() function with type = 'LDG2' and type = 'LDX2' works well for my bifactor model on 30 reading passages with 6 items each. However, I couldn't find an explicit explanation of what those residuals reflect. Am I right to conclude that low values in the residual summaries suggest that the items are not locally dependent after controlling for the dependencies due to the general factor AND the dependencies due to specific factors (i.e., the testlets effect)? Based on the concepts of X2 and G2 residuals of local dependency, can we infer the following?
1) If the LDX2 or LDG2 residuals are high for items within a testlet, it may suggest that the model is not fully capturing the testlet effect. Conversely, if these residuals are low, it indicates that the correlation due to the testlet effect is adequately accounted for by the model.
2) If the LDX2 or LDG2 residuals are high for items from different testlets, it may suggest an excessive covariance between those items after accounting for their covariance due to a general factor. Conversely, if these residuals are low, it suggests that the model meets the IRT assumption of local independence for the items from different testlets.
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