Abstract
Results of a comprehensive simulation study are reported investigating the effects of sample size, test length, number of attributes and base rate of mastery on item parameter recovery and classification accuracy of four DCMs (i.e., C-RUM, DINA, DINO, and LCDMREDUCED). Effects were evaluated using bias and RMSE computed between true (i.e., generating) parameters and estimated parameters. Effects of simulated factors on attribute assignment were also evaluated using the percentage of classification accuracy. More precise estimates of item parameters were obtained with larger sample size and longer test length. Recovery of item parameters decreased as the number of attributes increased from three to five but base rate of mastery had a varying effect on the item recovery. Item parameter and classification accuracy were higher for DINA and DINO models.
Highlights
Diagnostic classification models (DCMs), known as cognitive diagnostic models (CDMs), can be viewed as restricted versions of general latent class models (Rupp and Templin, 2008).These models provide one way of classifying respondents into different diagnostic states
The present simulation study was designed to investigate the effects of sample size on item parameter recovery and classification accuracy of four DCMs, the compensatory reparameterized unified model (C-RUM), DINA, DINO, and LCDMREDUCED
Previous simulations on DCMs showed that classification accuracy and item recovery can be poor with small sample sizes, they tended to focus on a limited number of sample size conditions, making results somewhat difficult to generalize to other practical testing conditions
Summary
Diagnostic classification models (DCMs), known as cognitive diagnostic models (CDMs), can be viewed as restricted versions of general latent class models (Rupp and Templin, 2008). + exp λ1,0 + λA where λi,0 represents the intercept, that is the logit of a correct response for an examinee who has not mastered any of the attributes required by item i. The C-RUM can be considered an LCDM without an interaction effect as it includes only intercept and main effects as shown below: The qi represents the ith row vector of the Q-matrix (Tatsuoka, 1983) that consists of 0 and 1 to indicate an item i gives information about the presence of an attribute a The DINO model, on the other hand, functions differently than the DINA, as it requires the mastery of at least one attribute exp(λ1,0 + λ1,1(3) αc3 + λ1,1(4) αc4 )
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