A General Linear Framework for Modeling Continuous Responses With Error in Persons and Items

Abstract

This study develops a general linear model intended for personality and attitude items with (approximately) continuous responses that is based on a double source of measurement error: items and persons. Two restricted sub-models are then obtained from the general model by placing restrictions on the item and person parameters. And it follows that the standard unidimensional factor-analytic model is one of these sub-models. Procedures for (a) calibrating the items, (b) obtaining individual estimates of location and fluctuation, (c) assessing model-data fit, and (d) assessing measurement precision are discussed for all the models considered, and illustrated with two empirical examples in the personality domain.