The regDIF R Package: Evaluating Complex Sources of Measurement Bias Using Regularized Differential Item Functioning

Abstract

Measurement bias (MB), or differences in the measurement properties of a latent variable, is often evaluated for a single categorical background variable (e.g., gender). However, recent statistical advances now allow MB to be simultaneously evaluated across multiple continuous and categorical background variables (e.g., gender, age, culture). Regularization has also shown promising results for selecting true differential item functioning (DIF) effects in high-dimensional measurement models. Despite this progress, current software tools make it difficult for applied researchers to implement regularized DIF (Reg-DIF). The regDIF R package is thus introduced and shown to be a relatively fast and flexible implementation of the Reg-DIF method. Namely, regDIF allows for simultaneous modeling of multiple background variables, a variety of different item response functions, and multiple types of penalty methods, among other possibilities. This article demonstrates these features using simulated and real data and provides example code for researchers to use in their own work.

Keywords:

• Differential item functioning
• measurement bias
• R statistical software
• regularization

Notes

1 In theory, DIF does not depend on statistical significance, but rather on whether the conditional item response distribution varies as a function of a background characteristic, controlling for the latent variable.

2 Technically, simple MB has two predictors that affect the item responses: θ (latent variable) and x (exogenous variable). Simple MB refers to a single observed variable that is evaluated for bias.

3 A linear predictor is a linear combination of coefficients and covariates used to predict an outcome variable. Linear predictors are integral to the generalized linear modeling framework, where a variety of outcome types (e.g., continuous, binary, categorical, etc.) can all be specified using a linear predictor, a link function, and a distribution for the outcome.

4 By combining the baseline intercept with each threshold, we obtain C − 1 location parameters; the first location parameter is ${\nu }_{0j};$ the second is ${\nu }_{0j}-{\tau }_1;$ the third is ${\nu }_{0j}-{\tau }_2;$ and so on.

5 The multivariate extension applies the MCP penalty to each DIF effect simultaneously.

6 The likelihood function with MCP is not concave in some regions of the regularization path.

7 Reg-DIF refers to the method of using regularization to identify DIF across one or more sources of bias. regDIF refers to the R package that implements Reg-DIF. regDIF() refers to the main function in the regDIF R package.