Differential Item Functioning - Procedures For Detecting DIF - Logistic Regression

Logistic Regression

Logistic regression approaches to DIF detection involve running a separate analysis for each item. The independent variables included in the analysis are group membership, an ability matching variable typically a total score, and an interaction term between the two. The dependent variable of interest is the probability or likelihood of getting a correct response or endorsing an item. Because the outcome of interest is expressed in terms of probabilities, maximum likelihood estimation is the appropriate procedure. This set of variables can then be expressed by the following regression equation:

where β₀ corresponds to the intercept or the probability of a response when M and G are equal to 0 with remaining β_s corresponding to weight coefficients for each independent variable. The first independent variable, M, is the matching variable used to link individuals on ability, in this case a total test score, similar to that employed by the Mantel-Haenszel procedure. The group membership variable is denoted G and in the case of regression is represented through dummy coded variables. The final term MG corresponds to the interaction between the two above mentioned variables.

For this procedure, variables are entered hierarchically. Following the structure of the regression equation provided above, variables are entered by the following sequence: matching variable M, grouping variable G, and the interaction variable MG. Determination of DIF is made by evaluating the obtained chi-square statistic with 2 degrees of freedom. Additionally, parameter estimate significance is tested.

From the results of the logistic regression, DIF would be indicated if individuals matched on ability have significantly different probabilities of responding to an item and thus differing logistic regression curves. Conversely, if the curves for both groups are the same, then the item is unbiased and therefore DIF is not present. In terms of uniform and nonuniform DIF, if the intercepts and matching variable parameters for both groups are not equal, then there is evidence of uniform DIF. However, if there is a nonzero interaction parameter, this is an indication of nonuniform DIF.