What could be the possible reasons for significant differences in terms of standardized factor loadings and items' intercepts between males and females while running measurement invariance analysis?
Hi Witold, invariance refers to the unstandardized loadings and intercepts. When item variances differ between groups - this doesn't violate the assumption of strong invariance - standardizes loadings will also differ.
I think it implicates that the items were interpreted differently by male and female respondents. But it could be caused by the uneven sample sizes. This article may answer your question adequately.
Article Sensitivity of Goodness of Fit Indexes to Lack of Measuremen...