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A Latent-Trait Based Reliability Estimate and Upper Bound

Published online by Cambridge University Press:  01 January 2025

W. Alan Nicewander
W. Alan Nicewander*
Affiliation:
University of Oklahoma
*
Requests for reprints should be sent to W. Alan Nicewander, Department of Psychology, University of Oklahoma, 455 West Lindsay, Room 705, Norman, OK 73019.
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Abstract

An estimate and an upper-bound estimate for the reliability of a test composed of binary items is derived from the multidimensional latent trait theory proposed by Bock and Aitkin (1981). The estimate derived here is similar to internal consistency estimates (such as coefficient alpha) in that it is a function of the correlations among test items; however, it is not a lowerbound estimate as are all other similar methods.

An upper bound to reliability that is less than unity does not exist in the context of classical test theory. The richer theoretical background provided by Bock and Aitkin's latent trait model has allowed the development of an index (called δ here) that is always greater-than or equal-to the reliability coefficient for a test (and is less-than or equal-to one). The upper bound estimate of reliability has practical uses—one of which makes use of the “greatest lower bound”.

Keywords

reliabilityitem response theoryfactor analysis
Type
Original Paper
Information
Psychometrika , Volume 55 , Issue 1 , March 1990 , pp. 65 - 74
Copyright
Copyright © 1990 The Psychometric Society

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