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The dimensionality of tests and items
Author(s) -
McDonald Roderick P.
Publication year - 1981
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 - 10.1111/j.2044-8317.1981.tb00621.x
Subject(s) - generalizability theory , mathematics , curse of dimensionality , statistics , explication , trait , item response theory , factor analysis , latent variable model , consistency (knowledge bases) , latent variable , econometrics , computer science , psychometrics , discrete mathematics , philosophy , epistemology , programming language
An explication is offered for the notion of dimensionality both for tests and items. A set of n tests or of n binary items is unidimensional if and only if the tests or the items fit a common factor model, generally non‐linear, with one common factor, that is, one latent trait. Both test scores and item responses in general contain stable specific factors as well as errors of retest measurement. The two‐parameter normal ogive model can be obtained from a joint space which in general is of n + 1 dimensions. One of these is the latent trait continuum while the remaining n are dimensions of unique (specific and error) variation. If and only if the items fit the perfect scale the n + 1 dimensions collapse into one dimension. Proposals to regard coefficient alpha as a coefficient measuring homogeneity, internal consistency, or generalizability, do not appear to be well founded.