Linear and Nonlinear Indices of Score Accuracy and Item Effectiveness for Measures That Contain Locally Dependent Items

Abstract

The problem of local item dependencies (LIDs) is very common in personality and attitude measures, particularly in those that measure narrow-bandwidth dimensions. At the structural level, these dependencies can be modeled by using extended factor analytic (FA) solutions that include correlated residuals. However, the effects that LIDs have on the scores based on these extended solutions have received little attention so far. Here, we propose an approach to simple sum scores, designed to assess the impact of LIDs on the accuracy and effectiveness of the scores derived from extended FA solutions with correlated residuals. The proposal is structured at three levels—(a) total score, (b) bivariate-doublet, and (c) item-by-item deletion—and considers two types of FA models: the standard linear model and the nonlinear model for ordered-categorical item responses. The current proposal is implemented in SINRELEF.LD, an R package available through CRAN. The usefulness of the proposal for item analysis is illustrated with the data of 928 participants who completed the Family Involvement Questionnaire-High School Version (FIQ-HS). The results show not only the distortion that the doublets cause in the omega reliability estimate when local independency is assumed but also the loss of information/efficiency due to the local dependencies.