A Logistic Latent Class Model for Multiple Choice Items

The probability of latent class membership is modeled by a logistic function. The conditional probability of the observed response, the selection of an option, given the latent class membership is assumed to be constant. The model can be viewed as a generalization of Nedelsky's (1954) method to determine a pass/fail score. Apart from giving a more detailed model on the process of solving a multiple choice item an increase in the precision of latent variable estimates in comparison with binary scoring is achieved. The model is shown to possess some favorable psychometric properties.