Attribute continuity in cognitive diagnosis models: impact on parameter estimation and its detection

Most cognitive diagnosis models assume that skills or attributes are binary latent variables, which greatly simplifies the interpretation of model parameters. However, the assumption may be violated in practice, especially when some attributes are coarser-grained. This study investigates the impact of the violation of this assumption on parameter estimation and whether the violation can be detected empirically. Simulation study showed that when the binary attribute assumption was violated, item parameter estimates were biased but person classification may still be useful unless the conditions were very unfavorable. In addition, the univariate attribute mastery probability plot and a newly proposed uncertainty index may be used for detecting the violation of the binary attribute assumption when items were of moderate or high quality.