Probability spaces, hilbert spaces, and the axioms of test theory

Zimmerman, Donald W.

doi:10.1007/bf02291765

Cited by 104 publications

(105 citation statements)

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“…The paper is organized as follows: In the next section, a brief overview of the CFA approach to MTMM data and its problems is given. Then, a new model is introduced that was developed in the tradition of Zimmerman's (1975Zimmerman's ( , 1976) and Steyer's (1989) work on classical psychometric test theory (CTT). It is shown that the trait and method factors can be defined as functions of the true-score variables.…”

Section: Introductionmentioning

confidence: 99%

A multitrait-multimethod model with minimal assumptions

2000

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Section: Introductionmentioning

confidence: 99%

A multitrait-multimethod model with minimal assumptions

2000

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“…With the expected value definition of true score in (5), the parallelism of the forms and the assumption of linear experimental independence lbr different measurements, the CTT model can be obtained by "construction" rather than assumption (see Lord and Novick, 1968;Zimmerman, 1975Zimmerman, , 1976 to give:…”

Section: Es) = 0 (8)mentioning

confidence: 99%

Reliability as a function of the number of item options derived from the “knowledge or random guessing” model

MacCann¹

2004

Psychometrika

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“…They may have possibly different variances, say ψ 11 , ψ 22 , · · · , ψ pp . Thus, τ and the components of X and e are all regarded as random variables for a populations of examinees (Zimmerman, 1975). The p-component vector µ is treated as the mean score vector of X.…”

Section: Introductionmentioning

confidence: 99%

Tau-Proportionate Form of Congeneric Covariance Structure

Maiti¹

2016

IJSP

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From the view point of constructing a composite possessing the largest possible common covariability with all of its constituent tests, the concept of the best equi-covariable composite (BEC) has been introduced. When the covariance matrix of the constituent tests are so structured that its row (column) totals are all equal, the corresponding BEC is shown to be reducible to simple aggregated (or averaged) test. Under the purview of congeneric tests, it is shown that there exists a special form termed tau-proportionate congeneric form in which case the simple aggregated (or averaged) test is not only the BEC but also the most reliable composite. Statistical techniques of the estimation of parameters, testing and goodness-of-fit of the such structure are considered with the aid of an illustrative example.

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Probability spaces, hilbert spaces, and the axioms of test theory

Cited by 104 publications

References 2 publications

A multitrait-multimethod model with minimal assumptions

A multitrait-multimethod model with minimal assumptions

Reliability as a function of the number of item options derived from the “knowledge or random guessing” model

Tau-Proportionate Form of Congeneric Covariance Structure

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