Applying Logistic Regression to Detect Differential Item Functioning in Multidimensional Data

Hui-Fang Chen, Kuan-Yu Jin

Conventional differential item functioning (DIF) approaches such as logistic regression (LR) often assume unidimensionality of a scale and match participants in the reference and focal groups based on total scores. However, many educational and psychological assessments are multidimensional by design, and a matching variable using total scores that does not reflect the test structure may not be good practice in multidimensional items for DIF detection. We propose the use of all subscores of a scale in LR and compare its performance with alternative matching methods, including the use of total score and individual subscores. We focused on uniform DIF situation in which 250, 500, or 1,000 participants in each group answered 21 items reflecting two dimensions, and the 21st item was the studied item. Five factors were manipulated in the study: (a) the test structure, (b) numbers of cross-loaded items, (c) group differences in latent abilities, (d) the magnitude of DIF, and (e) group sample size. The results showed that, when the studied item measured a single domain, the conventional LR incorporating total scores as a matching variable yielded inflated false positive rates (FPRs) when two groups differed in one latent ability. The situation worsened when one group had a higher ability in one domain and lower ability in another. The LR using a single subscore as the matching variable performed well in terms of FPRs and true positive rates (TPRs) when two groups did not differ in either one latent ability or differed in one latent ability. However, this approach yielded inflated FPRs when two groups differed in two latent abilities. The proposed LR using two subscores yielded well-controlled FPRs across all conditions and yielded the highest TPRs. When the studied item measured two domains, the use of either the total score or two subscores worked well in the control of FPRs and yielded similar TPRs across conditions, whereas the use of a single subscore resulted in inflated FPRs when two groups differed in one or two latent abilities. In conclusion, we recommend the use of multiple subscores to match subjects in DIF detection for multidimensional data.