An Empirical Identification Issue of the Bifactor Item Response Theory Model

Using the bifactor item response theory model to analyze data arising from educational and psychological studies has gained popularity over the years. Unfortunately, using this model in practice comes with challenges. One such challenge is an empirical identification issue that is seldom discussed in the literature, and its impact on the estimates of the bifactor model's parameters has not been demonstrated. This issue occurs when an item's discriminations on the general and specific dimensions are approximately equal (i.e., the within-item discriminations are similar in strength), leading to difficulties in obtaining unique estimates for those discriminations. We conducted three simulation studies to demonstrate that within-item discriminations being similar in strength creates problems in estimation stability. The results suggest that a large sample could alleviate but not resolve the problems, at least when considering sample sizes up to 4,000. When the discriminations within items were made clearly different, the estimates of these discriminations were more consistent across the data replicates than that observed when the discriminations within the items were similar. The results also show that the similarity of an item's discriminatory magnitudes on different dimensions has direct implications on the sample size needed in order to consistently obtain accurate parameter estimates. Although our goal was to provide evidence of the empirical identification issue, the study further reveals that the extent of similarity of within-item discriminations, the magnitude of discriminations, and how well the items are targeted to the respondents also play factors in the estimation of the bifactor model's parameters.