Validation of the Cognitive Structure of an Arithmetic Test with the Least Squares Distance Model (LSDM)

The aim of the present paper is to collect evidence about validity of the cognitive structure proposed to solve the items of an arithmetic test using an cognitive diagnosis model (based on the Item Response Theory) called Least Squares Distance Model (LSDM). The test was applied to a sample of 382 students of 7th grade from five public high schools in Bogota-Colombia. With this data the objective was addressed in three ways: first, the analysis of two statistical validity indices; second by a cross-validation of the LSDM results on attribute difficulties using other cognitive model (LLTM), and third, by comparing the LSDM results with the observed scores on individual attributes. The logical behavior of the probability curves for the five attributes under study provides important evidence for their overall validity. Additional specific evidences of validity are also presented in the results.