Adjusting the Adjusted chi(2)/df Ratio Statistic for Dichotomous Item Response Theory Analyses: Does the Model Fit?

作者：Tay Louis^*; Drasgow Fritz

来源：Educational and Psychological Measurement, 2012, 72(3): 510-527.

DOI：10.1177/0013164411416976

• adjusted chi(2)df
• bootstrap
• fit statistic
• item response theory

Two Monte Carlo simulation studies investigated the effectiveness of the mean adjusted chi(2)/df statistic proposed by Drasgow and colleagues and, because of problems with the method, a new approach for assessing the goodness of fit of an item response theory model was developed. It has been previously recommended that mean adjusted chi(2)/df values greater than 3 using a cross-validation data set indicate substantial misfit. The authors used simulations to examine this critical value across different test lengths (15, 30, 45) and sample sizes (500, 1,000, 1,500, 5,000). The one-, two- and three-parameter logistic models were fitted to data simulated from different logistic models, including unidimensional and multidimensional models. In general, a fixed cutoff value was insufficient to ascertain item response theory model-data fit. Consequently, the authors propose the use of the parametric bootstrap to investigate misfit and evaluated its performance. This new approach produced appropriate Type I error rates and had substantial power to detect misfit across simulated conditions. In a third study, the authors applied the parametric bootstrap approach to LSAT data to determine which dichomotous item response theory model produced the best fit. Future applications of the mean adjusted chi(2)/df statistic are discussed.

• 出版日期2012-6