In this article, the Type I error rate and the power of a number of existing and new tests of fit to the 3-parameter logistic model (3PLM) are investigated. The first test is a generalization of a test for the evaluation of the fit to the 2-parameter logistic model (2PLM) based on the Lagrange multiplier (LM) test or the equivalent efficient score test. This technique is applied to two model violations: deviation from the 3PLM item characteristic curve and violation of local stochastic independence. The LM test for the first violation is compared with the Q ₁ – G² _j and S – G² _j tests, respectively. The LM test for the second violation is compared with the Q ₃ test and a new test, the S ₃ test, which can be viewed as a generalization of the approach of the S – G² _j test to the evaluation of violation of local independence. The results of simulation studies indicate that all tests, except the Q ₁ – G² _j test, have a Type I error rate that is acceptably close to the nominal significance level, and good power to detect the model violations they are targeted at. When, however, misfitting items are present in a test, the proportion of items that are flagged incorrectly as misfitting can become undesirably high, especially for short tests.

The Cognitive Fusion Questionnaire (CFQ) is a recently published measure of cognitive fusion – a key construct in the model of psychopathology of acceptance and commitment therapy (ACT). This study presents the psychometric properties and factor structure data of a Spanish translation of the CFQ in Colombia. Three samples with a total of 1,763 participants were analyzed. The Spanish CFQ showed psychometric properties very similar to the ones obtained in the original version. Internal consistency across the different samples was good (Cronbach's alpha between .89 and .93). The one-factor model found in the original scale showed a good fit to the data. Measurement invariance was also found across sample and gender. The mean score of the clinical sample on the CFQ was significantly higher than the scores of the nonclinical samples. CFQ scores were significantly related to experiential avoidance, emotional symptoms, mindfulness, and life satisfaction. The CFQ was sensitive to the effects of a 1-session ACT intervention. This Spanish version of the CFQ shows good psychometric properties in Colombia