Showing papers on "Latent variable model published in 1983"

Application of Unidimensional Item Response Theory Models to Multidimensional Data

Abstract: A simulation model was developed for generating item responses from a multidimensional latent trait space The model permits the prepotency of a general latent trait underlying responses to all simu...

Characterizing the manifest probabilities of latent trait models

Abstract: The problem of characterizing the manifest probabilities of a latent trait model is considered. The item characteristic curve is transformed to the item passing-odds curve and a corresponding transformation is made on the distribution of ability. This results in a useful expression for the manifest probabilities of any latent trait model. The result is then applied to give a characterization of the Rasch model as a log-linear model for a 2 J -contingency table. Partial results are also obtained for other models. The question of the identifiability of “guessing” parameters is also discussed.

Parameter Estimation in Latent Trait Models.

Abstract: Latent trait models for binary responses to a set of test items are considered from the point of view of estimating latent trait parametersθ=(θ 1, …,θ n ) and item parametersβ=(β 1, …,β k ), whereβ j may be vector valued. Withθ considered a random sample from a prior distribution with parameterφ, the estimation of (θ, β) is studied under the theory of the EM algorithm. An example and computational details are presented for the Rasch model.

Maximum likelihood estimation in a latent variable problem

Abstract: Publisher Summary This chapter discusses the maximum likelihood estimation in a latent variable problem. Latent variates are random variables, which cannot be measured directly, but play essential roles in the description of observable quantities. They occur in a broad range of statistical problems. In the case that the dependent variate y is discrete, latent structure models play an important role, arising in connection with ability tests. Computing uniform residuals is an effective general means to proceed in latent variable problems. In some cases, the subject's ability can be eliminated by conditioning on an appropriate statistic. Maximum likelihood estimation is a viable approach to a broad class of latent variable problems. Generalized linear interactive modeling (GLIM) is an effective tool for carrying out the needed computations. GLIM also contains a high-level syntax for handling variables with factorial structure, vectors, and nonfull rank models. Its powerful directives shorten the length of the program considerably and allow simple simulation of the whole situation for checking programs and logic.

An Extension of the Two-Parameter Logistic Model to the Multidimensional Latent Space.

Abstract: : A multidimensional extension of the two-parameter logistics latent trait model is presented and some of its characteristics are discussed. In addition, sufficient statistics for the parameters of the model are derived, as is the information function. Finally, the estimation of the parameters of the model using the maximum likelihood estimation technique is also discussed. (Author)

Expanding the rasch model to a general model having more than one dimension

Abstract: The well-known Rasch model is generalized to a multicomponent model, so that observations of component events are not needed to apply the model. It is shown that the generalized model has retained the property of the specific objectivity of the Rasch model. For a restricted variant of the model, maximum likelihood estimates of its parameters and a statistical test of the model are given. The results of an application to a mathematics test involving six components are described.

Two Kinds of Factor Analysis For Ordered Categorical Variables

Abstract: In factor analysis of variables with ordered categories, latent response variables are assumed. These latent response variables may be either discrete or continuous. Different assumptions regarding the latent response variables lead to different kinds of factor models. A convenient assumption is to postulate that the latent response variables are continuous and normally distributed. In this paper the relationship between two kinds of factor analysis is discussed. It is shown, mathematically, that factor analysis of data with integer values only (the category numbers) is very sensitive to the skewness of the manifest variables and the size of the factor loadings. This was also shown by Olsson (1979b) by a simulation study with "perfect" data. Further, in the paper we propose a simple estimation procedure for the factor model of categorical variables, in which it is assumed that the latent response variables are normally distributed.

A general framework for using latent class analysis to test hierarchical and nonhierarchical learning models

Abstract: Several articles in the past fifteen years have suggested various models for analyzing dichotomous test or questionnaire items which were constructed to reflect an assumed underlying structure. This paper shows that many models are special cases of latent class analysis. A currently available computer program for latent class analysis allows parameter estimates and goodness-of-fit tests not only for the models suggested by previous authors, but also for many models which they could not test with the more specialized computer programs they developed. Several examples are given of the variety of models which may be generated and tested. In addition, a general framework for conceptualizing all such models is given. This framework should be useful for generating models and for comparing various models.

Scaling Models for Categorical Variables: An Application of Latent Structure Models

Abstract: We demonstrate how latent structure analysis can be used to model rating scale data that have ordered categories, and propose a modification of the basic latent structure approach to analyze response errors in the context of a traditional multitrait-multimethod matrix. The extended approach provides the researcher with the ability to (1) use formal test statistics to select a response error model, (2) assess the effects due to traits versus methods, and (3) examine and test a wide array of plausible measurement error hypotheses.

Some Latent Trait Models for Measuring Change in Qualitative Observations

Abstract: Publisher Summary This chapter presents some latent trait models for measuring change in qualitative observations. It discusses a variation of the general latent trait model as described by Fischer. Unlike the other latent trait models, Fischer's is based on qualitative variables. Also unlike the others, which are designed to measure status variables at one point in time, Fischer's model—based on the one-parameter logistic (Rasch) model—is explicitly designed to measure change. The model assigns one effect parameter to each discrete type of social environment, thus explaining observed ability differences between twins brought up in separation in terms of environmental effects and allowing predictions about the effects of environmental changes. The results of empirical applications of this model are, in principle, sample free. A further advantageous property of the model is that intelligence need not be represented by a unidimensional scale but is considered a multidimensional construct represented by the chosen sample of items; technically, one latent ability dimension corresponds to each item. The chapter discusses only two of the many possible variations of latent trait models for general measurement problems, both within and outside the field of psychological testing. These models and their applications emphasize the general power of this class of models for innovative solutions to a wide range of psychological measurement problems.

Measuring Mental Abilities with Latent State Models

Abstract: SYNOPTIC ABSTRACTThe three goals of this paper are (1) to review the latent state models which have been proposed for measuring aptitude and achievement, (2) to outline the measurement problems that can now be solved with latent state models, and (3) to discuss how latent state and latent trait models are related. It is pointed out that latent state and latent trait models measure different things that are related to one another in a complicated fashion.

Ordinal data, ordered scale points, and order statistics

Abstract: This paper concerns ordinal responses. An ordered Dirichlet distribution describes prior and posterior beliefs about the cumulative probabilities of response categories. Associating the response categories with intervals of a latent random variable then induces a distribution on the order statistics of that variable. The psychometrician can use the asymptotic theory of order statistics to learn how distributional assumptions about the latent variable effect inference. An example relates the skewness of a latent variable to the proportional odds and proportional hazards models of McCullagh [1980].