Linear Logistic Test Modeling with R.

Abstract

The present paper gives a general introduction to the linear logistic test model (Fischer, 1973), an extension of the Rasch model with linear constraints on item parameters, along with eRm (an R package to estimate different types of Rasch models; Mair, Hatzinger, & Mair, 2014) functions to estimate the model and interpret its parameters. The applications of the model in test validation, hypothesis testing, cross-cultural studies of test bias, rule-based item generation, and investigating construct irrelevant factors which contribute to item difficulty are explained. The model is applied to an English as a foreign language reading comprehension test and the results are discussed. An important aspect of validity theory is ‘explaining’ the mental processes that are triggered when test items are solved. This is in contrast to ‘prediction’ which is based on the correlation of tests with external criteria (Messick, 1989, Embretson, 1998). cognitive