Local Dependence Indexes for Item Pairs Using Item Response Theory

Abstract

Four statistics are proposed for the detection of local dependence (LD) among items analyzed using item response theory. Among them, the X² and G² LD indexes are of special interest. Simulated data are used to study the distribution and sensitivity of these statistics under the null condition, as well as under conditions in which LD is introduced. The results show that under the null condition of local independence, both the X² and G² LD indexes have distributions very similar to the X² distribution with 1 degree of freedom. Under the locally dependent conditions, both indexes appear to be sensitive in detecting LD or multidimensionality among items. When compared to Q₃, another statistic often used to detect LD, these new statistics are somewhat less powerful for underlying LD, equally powerful for surface LD, and better behaved in the null case.