Latent variable model

About: Latent variable model is a research topic. Over the lifetime, 3589 publications have been published within this topic receiving 235061 citations.

Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities.

Abstract: The purpose of this paper is to introduce a new method for fitting item response theory models with the latent population distribution estimated from the data using splines. A spline-based density estimation system provides a flexible alternative to existing procedures that use a normal distribution, or a different functional form, for the population distribution. A simulation study shows that the new procedure is feasible in practice, and that when the latent distribution is not well approximated as normal, two-parameter logistic (2PL) item parameter estimates and expected a posteriori scores (EAPs) can be improved over what they would be with the normal model. An example with real data compares the new method and the extant empirical histogram approach.

Latent-Variable Modeling of String Transductions with Finite-State Methods

Abstract: String-to-string transduction is a central problem in computational linguistics and natural language processing. It occurs in tasks as diverse as name transliteration, spelling correction, pronunciation modeling and inflectional morphology. We present a conditional loglinear model for string-to-string transduction, which employs overlapping features over latent alignment sequences, and which learns latent classes and latent string pair regions from incomplete training data. We evaluate our approach on morphological tasks and demonstrate that latent variables can dramatically improve results, even when trained on small data sets. On the task of generating morphological forms, we outperform a baseline method reducing the error rate by up to 48%. On a lemmatization task, we reduce the error rates in Wicentowski (2002) by 38--92%.

The Asymptotic Posterior Normality of the Latent Trait in an IRT Model.

Abstract: It has long been part of the item response theory (IRT) folklore that under the usual empirical Bayes unidimensional IRT modeling approach, the posterior distribution of examinee ability given test response is approximately normal for a long test. Under very general and nonrestrictive nonparametric assumptions, we make this claim rigorous for a broad class of latent models.

Structured latent curve models

Abstract: Latent curve models are equivalent to factor analysis models in which common factor means are not assumed to be zero. The data model therefore generates a structure for the manifest variable mean vector as well as for the manifest variable covariance matrix. As in unrestricted factor analysis, there is a rotation problem in latent curve analysis. This problem may be avoided if a structure is imposed on the factor matrix. A method for doing this was employed in Browne and Du Toit (1991). The present paper presents theoretical details of this method for obtaining structured latent curve models for learning data. It is shown that use of a first order Taylor expansion about a monotonic target function generates a restricted factor matrix that has properties that allow meaningful interpretation of its columns as latent curves. Possible monotonic mean curves are discussed and details are given of associated factor matrices whose elements are functions of a small number of parameters. Models for the error covariance matrix are also considered. Joint latent curve and factor analysis models are suggested. These models are suitable for situations where both learning scores and scores on concomitant variables are available. A practical example is presented. Theory derived in Browne (1990) concerning the robustness of asymptotic properties of normal theory minimum discrepancy methods is applied to investigate the asymptotic robustness of maximum multivariate normal likelihood methods for the present models.