Effectiveness of Person Fit Indices in Item Response Models with Different Degrees of Item Local Dependence

Abstract

This study aimed to examine the effectiveness of person fit indices (Wright’s weighted index, Drasgow index and Almehrizi’s weighted index) in item response models with different degrees of item local dependence (0.0, 0.3, 0.6, and 0.9) using simulated item parameters. Item responses for 40 samples each with 10000 subjects (a total of 400000 subjects) were simulated on a test of 60 items. Item discrimination parameters ranged between 0.19 and 1.79 and item difficulty parameters ranged between -2 and +2. 20% of test items were manipulated to show local dependence for each level of local dependence degrees. Student ability was generated to follow a standard normal distribution. Assumptions of item response theory were examined in all data sets using exploratory factor analysis and residual analysis using NOHARM platform for unidimensionality and Q3 index for local independence. Results showed that there was an increase in the percentages of non-conforming persons when increasing the degree of items local dependence for the three person fit indices (Wright’s weighted index, Drasgow index and Almehrizi’s weighted index). Results showed also that the percentages of non-conforming persons were larger with Wright’s weighted index than with Drasgow index and Almehrizi’s weighted index. The distributional properties of the three indices showed relatively consistent in distributional properties. Drasgow index and Almehrizi’s weighted index were very similar distributional properties. Also, there was a larger agreement index between Wright’s weighted index and Drasgow index.