Latent Conditional Independence Test Using Bayesian Network Item Response Theory

Abstract

Item response theory (IRT) is widely used for test analyses. Most models of IRT assume that a subject's responses to different items in a test are statistically independent. However, actual situations often violate this assumption. Thus, conditional independence (CI) tests among items given a latent ability variable are needed, but traditional CI tests suffer from biases. This study investigated a latent conditional independence (LCI) test given a latent variable. Results show that the LCI test can detect CI given a latent variable correctly, whereas traditional CI tests often fail to detect CI. Application of the LCI test to mathematics test data revealed that items that share common alternatives might be conditionally dependent.