Designing a theory-based assessment with sound psychometric qualities to measure a higher-order cognitive construct is a highly desired yet challenging task for many practitioners. This paper proposes a framework for designing a theory-based assessment to measure a higher-order cognitive construct. This framework results in a modularized yet…

Three plausible assumptions of conditional independence in a hierarchical model for responses and response times on test items are identified. For each of the assumptions, a Lagrange multiplier test of the null hypothesis of conditional independence against a parametric alternative is derived. The tests have closed-form statistics that are easy to…

Coefficient alpha, the most commonly used estimate of internal consistency, is often considered a lower bound estimate of reliability, though the extent of its underestimation is not typically known. Many researchers are unaware that coefficient alpha is based on the essentially tau-equivalent measurement model. It is the violation of the…

Four discussions of test construction based on item response theory (IRT) are presented. The first discussion, "Test Design as Model Building in Mathematical Programming" (T. J. J. M. Theunissen), presents test design as a decision process under certainty. A natural way of modeling this process leads to mathematical programming. General…

A method is proposed to equate different sets of items administered to different groups of individuals using the Rasch model. A Rasch equating model was formulated to describe one common Rasch scale in different groups with different but overlapping sets of items. The item parameters can then be estimated simultaneously, avoiding different…

Extends dynamic model of cognitive growth proposed by van Geert in three directions: (1) added a term to consider exposure to material to be learned; (2) developed method to apply model to cross-sectional studies; and (3) developed procedure to scale cognitive abilities tests with items of varying difficulty. Tests model with 2- to 15-year-olds'…