Showing papers on "Latent variable model published in 1972"

Estimating item parameters and latent ability when responses are scored in two or more nominal categories

Abstract: A multivariate logistic latent trait model for items scored in two or more nominal categories is proposed. Statistical methods based on the model provide 1) estimation of two item parameters for each response alternative of each multiple choice item and 2) recovery of information from “wrong” responses when estimating latent ability. An application to a large sample of data for twenty vocabulary items shows excellent fit of the model according to a chi-square criterion. Item and test information curves are compared for estimation of ability assuming multiple category and dichotomous scoring of these items. Multiple scoring proves substantially more precise for subjects of less than median ability, and about equally precise for subjects above the median.

Stochastic models and factor analysis

Abstract: The present paper discusses the relationship between the traditional factor analytic model and stochastic models of test behaviour for the case of dichotomous manifest variables. It is shown that the factor loadings can be interpreted as parameters of item trace lines. Furthermore, by comparing a linear and a nonlinear model of item characteristics, it is suggested that the assumption of a small number of latent dimensions or factors (small in comparison to the number of manifest variables) always requires the estimation of communalities making the explicit conceptualization of specific factors unnecessary. In addition, it is indicated that, because of the arbitrariness of criteria for the number of common factors, the general tendency among researchers to extract a small number of latent dimensions will, for a given data set, lead to quite similar results regardless of the trace line model chosen.