The cognitive structure of an algebra test was
defined and validated using the linear logistic test
model (LLTM) and quadratic assignment (QA),
respectively. The LLTM is an extension of the Rasch
model with a linear constraint that describes the
difficulty of a test item in terms of the cognitive
operations required to solve it. The cognitive structure
of a test is specified using the weight matrix W.
The cognitive structure defined here was based on
a set of eight production rules that represented the
mathematical procedures employed in solving linear
equations with one variable. A 29-item test was
constructed and administered to 235 ninth-graders.
Item response data were analyzed using Fischer &
Formann’s (1972) LLTM computer program. A QA
confirmatory approach was used to validate the
cognitive structure of the test. The structure was
validated-examinees solved the items using the set
of rules specified in the W matrix. The parameters
estimated using the LLTM are quantitative indexes
of the difficulties of each of the cognitive rules
included in the W matrix. Index terms: componential
models, confirmatory analysis, content validity,
linear logistic test model, quadratic assignment, cognitive
Medina-Diaz, Maria. (1993). Analysis of cognitive structure using the linear logistic test model and quadratic assignment. Applied Psychological Measurement, 17, 117-130. doi:10.1177/014662169301700202
Analysis of cognitive structure using the linear logistic test model and quadratic assignment.
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