Generalized Mantel-Haenszel Methods for Differential Item Functioning Detection

Mantel-Haenszel methods comprise a highly flexible methodology for assessing the degree of association between two categorical variables, whether they are nominal or ordinal, while controlling for other variables. The versatility of Mantel-Haenszel analytical approaches has made them very popular in the assessment of the differential functioning of both dichotomous and polytomous items. Up to now, researchers have limited the use of Mantel-Haenszel statistics to analyzing contingency tables of dimensions 2 x 2 (by means of the Mantel-Haenszel chi-square statistic) and of dimensions of 2 x C (by means of either the generalized Mantel-Haenszel test or Mantel's test). The main objective of this article is to illustrate a unified framework for the analysis of differential item functioning using the Mantel-Haenszel methods. This is done by means of the generalized Mantel-Haenszel statistic for the analysis of the general case of Q contingency tables with dimensions R x C. Moreover, with the new formulation in consideration, this article reviews the most recent research on differential item functioning and suggests new applications and research lines in relation to the statistics proposed.