See attachment for ppt.
Discussion of the Paper “Measurement Bias Detection through Factor Analysis” by Barendse et. al. (2012)
1. Examples of continuous violators: age, time, English proficiency when assessing mathematic ability using test in English.
2. Why does there exist a “d” coefficient before the measurement error term “e” in equation (2)? It allows us to manipulate measurement error variance / reliability when variances of all latent variables are fixed at 1.
3. RFA/LMS and RFA/RSP are very similar (perhaps equivalent?)
4. On page 566, second paragraph in section “Analysis”, the constrained model means the model with all intercepts and factor loadings constrained to be equal across groups; while the unconstrained model means the model with all except one intercept and one factor loading constrained to be equal. The wordings they use cause ambiguousness.
5. On page 566, third paragraph in section “Analysis”, the stopping rule of iterative procedure has two alternative conditions: no more significant results or more than half are detected as biased. When the first item is truly unbiased but detected as biased, then the power of remaining tests will be reduced. For the single run, when testing each item, all other items are assumed to be unbiased, which is violated most of the time, so the Type I error rate will inflated. When using the iterative procedure, as long as the truly biased item is not the last item to be detected, then the Type I error rate will be reduced. This is why Type I error rate of iterative procedure can be better controlled than that of the single run.
6. The conclusion “non-uniform bias is more difficult to be detected than uniform bias” is not a universal conclusion. It is related to the scale of the intercept and slope parameter (factor loading). The intercepts are usually easier to be estimated and the SEs are usually smaller, so the power of testing significant intercepts will be larger than that of testing significant slope (factor loadings).
7. Can adopt purification into the iterative procedure
8. Simulation in this paper only considered about 15% DIF item (one out of six). Can try the case when more than one item are DIF item. Increasing percentage of DIF items (e.g., two out of six) will lead to more severe inflated Type I error rates.
9. Can try the case when v is polytomous (e.g., more than two groups). Then correction for multiple tests may be considered (e.g., Bonferroni correction).