Abstract
The aim of cognitive diagnosis is to classify respondents' mastery status of latent attributes from their responses on multiple items. Since respondents may answer some but not all items, item-level missing data often occur. Even if the primary interest is to provide diagnostic classification of respondents, misspecification of missing data mechanism may lead to biased conclusions. This paper proposes a joint cognitive diagnosis modeling of item responses and item-level missing data mechanism. A Bayesian Markov chain Monte Carlo (MCMC) method is developed for model parameter estimation. Our simulation studies examine the parameter recovery under different missing data mechanisms. The parameters could be recovered well with correct use of missing data mechanism for model fit, and missing that is not at random is less sensitive to incorrect use. The Program for International Student Assessment (PISA) 2015 computer-based mathematics data are applied to demonstrate the practical value of the proposed method.
Highlights
Cognitive diagnosis has recently received increasing concern in psychological and educational assessment, which can provide fine-grained classifications and diagnostic feedback for respondents from their performance on test items (Leighton and Gierl, 2007; Rupp et al, 2010)
The missing completely at random (MCAR) holds if the missing response pattern is independent of the individual’s knowledge state and of the observed responses; the missing at random (MAR) holds if the missing response pattern is conditionally independent of the knowledge state given the observed responses; and the missing not at random (MNAR) holds if the missing response pattern depends on the knowledge state
We propose a joint cognitive diagnosis modeling including a higher-order latent trait model for item responses and a missingness propensity model for item-level missing data mechanism
Summary
Cognitive diagnosis has recently received increasing concern in psychological and educational assessment, which can provide fine-grained classifications and diagnostic feedback for respondents from their performance on test items (Leighton and Gierl, 2007; Rupp et al, 2010). More general CDMs, such as the log-linear cognitive diagnosis model (LCDM; Henson et al, 2009) and the generalized DINA model (de la Torre, 2011), assume a more flexible relationship between the item responses and latent attributes. The MCAR holds if the missing response pattern is independent of the individual’s knowledge state (i.e., the collection of all items that an individual is capable of solving in a certain disciplinary domain) and of the observed responses; the MAR holds if the missing response pattern is conditionally independent of the knowledge state given the observed responses; and the MNAR holds if the missing response pattern depends on the knowledge state. We propose a joint cognitive diagnosis modeling including a higher-order latent trait model for item responses and a missingness propensity model for item-level missing data mechanism.
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