Hello Drs. Muthen. I am running a multiple group 2-parameter logistic IRT model and found evidence of differential item functioning for 2 of the 15 binary variables. I am using the syntax below which forces the loadings and thresholds to be the same for the remaining variables. The item difficulty and discrimination parameters for these variables are not equal across groups though, which I thought should be the case. Can you tell me how to get the difficulty/discrimination parameters to be consistent across groups for the variables without DIF?
I assume that your loadings and thresholds are group-invariant but when translated to IRT parameters those are not invariant. This is due to group differences in factor means and variances. See Section 3 of the IRT document
Thank you, Dr. Muthen! After fixing the factor mean to 0 and variance to 1 in each group as well as the residual variances to 1 for each item, I was able to get the invariant discrimination and difficulty IRT parameters.