An extension of the basic local independence model to multiple observed classifications

The basic local independence model (BLIM) is appropriate in situations where populations do not differ in the probabilities of the knowledge states and the probabilities of careless errors and lucky guesses of the items. In some situations, this is not the case. This work introduces the multiple observed classification local independence model (MOCLIM), which extends the BLIM by allowing the above probabilities to vary across populations. In the MOCLIM, each individual is characterized by proficiency, careless and guessing classes, which are observed and determine the probabilities of knowledge states, careless errors and lucky guesses of a population. Given a particular class type (proficiency, careless, or guessing), the probabilities are the same for populations with the same class but may vary between populations with different classes. Algorithms for maximum likelihood estimation of the MOCLIM parameters are provided. The results of a simulation study suggest that the true parameter values are well recovered by the estimation algorithm and that the true model can be uncovered by comparing the goodness-of-fit of alternative models. The results of an empirical application to data from Raven-like matrices suggest that the MOCLIM effectively discriminates between situations where group differences are expected and those where they are not.