Analysis of an arithmetic test by means of a logistic linear trait model

This paper presents an illustration of the integration of cognitive psychology and psychometric models to determine sources of item difficulty in an Arithmetic Test (AT), constructed by the authors, by means of its analysis with the LLTM. In order to reach this aim, a group of operations required to solve the items of the test were proposed, the dimensionality was evaluated, and the goodness of fit of items to both the Rasch and the LLTM models was studied. Results obtained were used to illustrate the advantages and limitations of the LLTM for the componential measurement; the main techniques used in the analysis were also introduced.