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Common factor models of validity and reliability for use with ordinal data in k × k tables
Author(s) -
Grayson D. A.
Publication year - 2001
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711001159492
Subject(s) - polychoric correlation , ordinal data , deviance (statistics) , statistics , mathematics , reliability (semiconductor) , goodness of fit , econometrics , contingency table , correlation , power (physics) , physics , geometry , quantum mechanics
Three common factor models are proposed for the analysis of k × k ordinal data arising from test validity or reliability situations. These models represent an extension of the polychoric correlation model and item response theory. Identification is complete in the most usual reliability situation, where data from only two indicators (raters) are available. Full maximum likelihood estimation is available together with associated informative deviance tests and goodness‐of‐fit tests, examples of which are provided.