Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables

The Rasch family of models considered in this paper includes models for polytomous items and multiple correlated latent traits, as well as for dichotomous items and a single latent variable. An R package is described that computes estimates of parameters and robust standard errors of a class of log-linear-by-linear association (LLLA) models, which are derived from a Rasch family of models. The LLLA models are special cases of log-linear models with bivariate interactions. Maximum likelihood estimation of LLLA models in this form is limited to relatively small problems; however, pseudo-likelihood estimation overcomes this limitation. Maximizing the pseudo-likelihood function is achieved by maximizing the likelihood of a single conditional multinomial logistic regression model. The parameter estimates are asymptotically normal and consistent. Based on our simulation studies, the pseudo-likelihood and maximum likelihood estimates of the parameters of LLLA models are nearly identical and the loss of efficiency is negligible. Recovery of parameters of Rasch models fit to simulated data is excellent.

Mondatrész-felfedezés önszervező tanulással

A cikkben egy újszer gépi tanulási módszer elméleti hátterét és az első kísérlet végrehajtását ismertetjük. A módszer lényege, hogy a nyelvmodellben nem valamilyen generatív nyelvtant, hanem pusztán mondattani mintákat feltételezünk, és a rendszert nem elemzési vagy eldöntési feladattal teszteljük, hanem mondatok hasonlóságának felismerésével

Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables

The Rasch family of models considered in this paper includes models for polytomous items and multiple correlated latent traits, as well as for dichotomous items and a single latent variable. An R package is described that computes estimates of parameters and robust standard errors of a class of log-linear-by-linear association (LLLA) models, which are derived from a Rasch family of models. The LLLA models are special cases of log-linear models with bivariate interactions. Maximum likelihood estimation of LLLA models in this form is limited to relatively small problems; however, pseudo-likelihood estimation overcomes this limitation. Maximizing the pseudo-likelihood function is achieved by maximizing the likelihood of a single conditional multinomial logistic regression model. The parameter estimates are asymptotically normal and consistent. Based on our simulation studies, the pseudo-likelihood and maximum likelihood estimates of the parameters of LLLA models are nearly identical and the loss of efficiency is negligible. Recovery of parameters of Rasch models fit to simulated data is excellent

Statistical models of syntax learning and use

This paper shows how to define probability distributions over linguistically realistic syntactic structures in a way that permits us to define language learning and language comprehension as statistical problems. We demonstrate our approach using lexical-functional grammar (LFG), but our approach generalizes to virtually any linguistic theory. Our probabilistic models are maximum entropy models. In this paper we concentrate on statistical inference procedures for learning the parameters that define these probability distributions. We point out some of the practical problems that make straightforward ways of estimating these distributions infeasible, and develop a “pseudo-likelihood” estimation procedure that overcomes some of these problems. This method raises interesting questions concerning the nature of the data available to a language learner and the modularity of language learning and processing.15 page(s