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| Bayesian explorative Faktoranalyse (BEFA)× | Item Response Theory (IRT)× | |
|---|---|---|
| Fachgebiet | Psychometrie | Psychometrie |
| Familie | Latent structure | Latent structure |
| Entstehungsjahr≠ | 2004 (Bayesian formulation); factor analysis roots: 1904 | 1952–1968 |
| Urheber≠ | Lopes & West (seminal Bayesian treatment); roots in classical factor analysis (Spearman, 1904) | Frederic M. Lord (and Allan Birnbaum for the 2PL/3PL models) |
| Typ≠ | Probabilistic latent variable model | Probabilistic measurement model |
| Wegweisende Quelle≠ | Lopes, H. F. & West, M. (2004). Bayesian model assessment in factor analysis. Statistica Sinica, 14(1), 41–67. link ↗ | Lord, F. M. & Novick, M. R. (1968). Statistical Theories of Mental Test Scores. Addison-Wesley. link ↗ |
| Aliasnamen | Bayesian factor analysis, BEFA, Bayesian common factor model, probabilistic factor analysis | IRT, latent trait theory, item characteristic curve theory, modern test theory |
| Verwandt≠ | 4 | 5 |
| Zusammenfassung≠ | Bayesian exploratory factor analysis applies a full probabilistic framework to the common factor model. By placing prior distributions over factor loadings and unique variances, it yields posterior distributions rather than point estimates, quantifies uncertainty around every loading, and can treat the number of factors as an unknown to be inferred from data. | Item response theory models the probability that a respondent answers an item correctly (or endorses it) as a function of the respondent's latent trait level and the item's own statistical properties — difficulty, discrimination, and guessing. Unlike classical test theory, IRT places persons and items on the same scale, yielding measurement that is sample-independent for items and test-independent for persons. |
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