Showing papers on "Latent variable model published in 1982"

A Rasch Model for Partial Credit Scoring.

Abstract: A unidimensional latent trait model for responses scored in two or more ordered categories is developed. This “Partial Credit” model is a member of the family of latent trait models which share the property of parameter separability and so permit “specifically objective” comparisons of persons and items. The model can be viewed as an extension of Andrich's Rating Scale model to situations in which ordered response alternatives are free to vary in number and structure from item to item. The difference between the parameters in this model and the “category boundaries” in Samejima's Graded Response model is demonstrated. An unconditional maximum likelihood procedure for estimating the model parameters is developed.

An Extension of the Rasch Model for Ratings Providing Both Location and Dispersion Parameters.

Abstract: An elaboration of a psychometric model for rated data, which belongs to the class of Rasch models, is shown to provide a model with two parameters, one characterising location and one characterising dispersion The later parameter, derived from the idea of a unit of scale, is also shown to reflect the shape of rating distributions, ranging from unimodal, through uniform, and then to U-shaped distributions A brief case is made that when a rating distribution is treated as a random error distribution, then the distribution should be unimodal

On the usefulness of latent variable causal modeling in testing theories of naturally occurring events (including adolescent drug use): A rejoinder to Martin.

Abstract: This paper considers the arguments raised by Martin (1982) against the methodologies used by Huba, Wingard, and Bentler (1981) and their subsequent conclusions. Several of Martin's criticisms are the result of a misreading of our paper and selective citations, whereas other criticisms were discussed in the original paper and resolved through alternate forms of data analysis. Further analyses are presented to address issues raised by Martin. Martin's arguments against latent variable models are refuted.

Linear Logistic Latent Class Analysis

Abstract: In the present paper the linear logistic extension of latent class analysis is described. Thereby it is assumed that the item latent probabilities as well as the class sizes can be attributed to some explanatory variables. The basic equations of the model state the decomposition of the log-odds of the item latent probabilities and of the class sizes into weighted sums of basic parameters representing the effects of the predictor variables. Further, the maximum likelihood equations for these effect parameters and statistical tests for goodness-of-fit are given. Finally, an example illustrates the practical application of the model and the interpretation of the model parameters.

Some Latent Trait Theory in a Multidimensional Latent Space.

Abstract: ABSTRACT This paper reviews the existing multidimensional item response theory (IRT) models and demonstrates how one of the models can be applied to estimation of abilities from a test measuring more than one dimension. The purposes of this paper were threefold. First, the fundamental concepts required when considering multidimensional models for the interaction of a person and a test item were defined. These concepts incluAed the multidimensional latent space, the item difficulty function, and the item discrimination function. These definitions were conceived as multidimensional generalizations of similar concepts in unidimensional IRT models. Second, six existing multidimensional models were reviewed and, on the basis of their similarities, were classified into three general categories. The characteristics of these categories were described, and the general Rasch model was selected for further study on the basis of ease of parameter estimation. Third, estimation procedures for the parameters of the general Rasch model were described and applied to a set of simulation data that had been generated according to a two-dimensional special case of the model. The results indicated that a very close correspondence had been obtained between the estimated item parameters and those used to generate the simulation data. (PN)

Causal Analysis and Latent Class Models: An Application to a Communication Hierarchy of Effects Model:

Abstract: The authors illustrate the use of latent structure analysis to test, in a confirmatory sense, causal hypotheses in an experimental design setting. Two latent factors conceptualized as arousal and y...

34 Multivariate analysis with latent variables

Abstract: Publisher Summary This chapter focuses on models in which both manifest and latent variables are continuous. This restriction still generates a large class of models when they are considered simultaneously in several populations and when certain variables are considered fixed rather than random. The field of multivariate analysis with continuous latent and measured random variables has made substantial progress in recent years, particularly, from mathematical and statistical points of view. Mathematically, clarity has been achieved in understanding representation systems for structured linear random variable models. Statistically, large sample theory has been developed for a variety of competing estimators, and the associated hypothesis testing procedures have been developed. The applied statistician, who is concerned with utilizing the above theory in empirical applications, will quickly find that causal modeling is a very finicky methodology having many pitfalls.

Estimating Latent Variable Systems When Specification is Uncertain: Generalized Component Analysis and the Eliminant Method

Abstract: This article argues that, to relieve the specification difficulties that frequently accompany latent variable models, a first application should in most cases employ an estimator that makes no assumption about the nature of the unobservables. The two possibilities are generalized component analysis, with the unobservables treated as incidental parameters; and the eliminant method, where they are removed by transformation of the model before estimation. It is shown that these are equivalent, whichever transformation is used, but that the latter has substantial practical advantages.

The Metric of the Latent Variables in a LISREL-IV Analysis

Abstract: A potential source of confusion in the interpretation of a LISREL-IV analysis is the metric of the latent variables. This paper demonstrates that fixing the pattern coefficient of one of the indicators of each latent variable to 1.0 results in an arbitrary and meaningless metric which is usually different for each latent variable. Since many of the parameter estimates such as the pattern coefficients, the factor loadings, and the variance-covariance matrix of the latent variables are a function of the metric of the latent variables, much of the LISREL-IV output may be uninterpretable. This paper demonstrates how to specify a priori the variances of the latent variables in a LISREL-IV analysis.

Latent trait models and ability parameter estimation

Abstract: In recent years several authors have viewed latent trait models for binary data as special models for contingency tables. This connection to contingency table analysis is used as the basis for a survey of various latent trait models. This article discusses estimation of item parameters by conditional, direct, and marginal maximum likelihood methods, and estimation of individual latent parameters as opposed to an estimation of the parameters of a latent population density. Various methods for testing the goodness of fit of the model are also described. Several of the estimators and tests are applied to a data set concerning consumer complaint behavior.

The use of latent class models for assessing prerequisite relations and transference among traits

Abstract: This paper presents a strategy for pairwise assessment which may be used to evaluate the nature of both “prerequisite” and “transference” relations existing among a set of traits This strategy is appropriate for use both within a confirmatory context, in which an attempt is made to establish the validity of some specified set of relations among traits, as well as within an exploratory context, in which a search is made for unconjectured prerequisite and transference relations existing between pairs of traits Both uses of this strategy are based on a variety of latent class models which are representative of various possible relational states existing between pairs of traits Thus, the nature of trait relations may be investigated through the use of statistical assessments of both absolute and relative fit attained by these models An application is presented to exemplify how this strategy may be used within the exploratory context