3.1 MIRT vs CDMs
3.1.1 Multidimensional item response theory (IRT) models
Attributes are assumed to be continuous
Examples include multidimensional 2- and 3PL models, the multicomponent latent trait model, and the multidimensional random coefficients multinomial logit model
Challenges in using multidimensional IRT models
handling a large number of attributes
structuring the latent space
accommodating diverse item-trait interactions
3.1.2 Cognitive Diagnosis models
Attributes are assumed to be categorical
Also called Diagnostic classification models, Cognitive psychometric models, Multiple classification (latent class) models, Latent response models, Restricted latent class models, Structured located latent class models, Structured IRT models
Defining characteristics of CDMs (Rupp et al., 2010)
Multidimensional nature
Confirmatory nature
Complexity of their loading structure
Types of observed response variables
Types of latent predictor variables
Interactions of the latent predictor variables
Criterion-referenced interpretations
Diagnostic nature of the interpretations
Types of heterogeneity they can model