1981/05/01 by Roderick P. McDonald · 2 citations
Computer Science · #Advanced Statistical Modeling Techniques
paper · doi:10.1111/j.2044-8317.1981.tb00621.x
openalex publication_date 1981/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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.