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	Cognitive Diagnostic Modeling	Latent Class Analysis
Field	Education	Statistics
Family	Latent structure	Latent structure
Year of origin	2010	1950s–1968
Originator	Tatsuoka; DiBello, Roussos & Stout; Junker & Sijtsma; de la Torre	Paul F. Lazarsfeld
Type	Restricted latent class models for diagnosing mastery of discrete skills	Latent variable / person-centered classification
Seminal source	Rupp, A. A., Templin, J., & Henson, R. A. (2010). Diagnostic Measurement: Theory, Methods, and Applications. Guilford Press. ISBN: 9781606235270	Goodman, L. A. (1974). Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 61(2), 215–231.
Aliases	CDM, Diagnostic Classification Models, DCM, DINA / G-DINA Models	LCA, latent class model, latent categorical analysis, finite mixture of multinomials
Related	4	6
Summary	Cognitive diagnostic models (CDMs), also called diagnostic classification models, are restricted latent class models that report not a single ability score but a profile of which discrete skills or attributes a student has mastered. Each item is linked to the attributes it requires through a Q-matrix, and the model classifies every examinee into one of the possible binary mastery patterns. CDMs answer 'which specific skills does this student lack' rather than 'how much overall ability does this student have,' making them central to fine-grained diagnostic and formative assessment.	Latent class analysis identifies unobserved subgroups — latent classes — within a population by finding patterns of responses across a set of categorical observed indicators. It is the categorical-variable counterpart of cluster analysis, but grounded in an explicit probabilistic model, and is widely used in social, health, and behavioral sciences to discover typologies in survey or diagnostic data.