In addition, the OLR method was less powerful than HOLR across almost all conditions, with maximum difference between the two methods being as small as 0.006.
Figure 2 also illustrates Type I error rates across manipulated factors for both OLR and HOLR when DIF occurs for between-cluster variable.
In contrast to the case for within-cluster variable, across almost all conditions the power for HOLR was lower compared to OLR.
Based on our findings, HOLR and OLR performed almost equivalently in terms of controlling Type I error rate at the nominal alpha level of 0.05.
However, the magnitude of Type I error rate inflation of OLR as compared to HOLR was not as large as what was found in other studies for the between-cluster variable.
Even though, in our simulation study, both OLR and HOLR approaches showed very similar results in DIF detection, in real world situations data might be influenced by other factors that were not considered in the simulation study.
The results of the HOLR DIF analysis were summarized in Table 3.