Detecting differential item functioning using varying coefficient models

Abstrakt

Testing for Differential Item Functioning (DIF) is an important step in the analysis of multi-item measurements. Traditionally, DIF has been investigated using a categorical grouping variable, which can be either dichotomous (e.g., gender, where groups are male and female) or polytomous (e.g., education level, with multiple categories such as high school, undergraduate, and graduate). This approach works well in many situations, but there are circumstances where the variable of interest is continuous, such as age or income. In such cases, treating the variable as categorical by arbitrarily dividing it into discrete groups may lead to a significant loss of valuable information and potentially obscure complex relationships within the data. We propose the use of varying coefficient models to better handle the continuity of covariates in DIF detection. These models allow the effect of the covariate to vary smoothly, capturing more intricate patterns that simpler methods may overlook. To demonstrate their effectiveness, we compare several model forms through a comprehensive simulation study. The simplest model is a direct extension of the logistic regression model, commonly used for DIF detection with dichotomous grouping variables. We compare the models in terms of their accuracy while also considering computational challenges, interpretability, and the identifiability issues that arise in more complex models.