Some Uses of Structural Equation Modeling in Validity Studies: Extending IRT to External Variables Using SIMS Results

This paper proposes the use of a new extension of standard Item Response Theory (IRT) modeling of dichotomous variables to include external variables. The extension requires the formulation of a model for the relationships between both categorical and continuous external variables and response items. Four important issues in item analysis are addressed simultaneously:

1. Estimation of IRT type item measurement parameters.
2. Assessment of the strengths of hypothesized antecedents to the student’s latent trait level
3. Detection of item bias (differential item performance)
4. Testing and relaxation of the IRT requirements of unidimensionality and conditional independence

The model and its underlying methodology are illustrated with data from the eighth grade US sample from the Second International Mathematics study.