Showing papers on "Latent variable model published in 1974"

Exploratory latent structure analysis using both identifiable and unidentifiable models

Abstract: SUMMARY This paper considers a wide class of latent structure models. These models can serve as possible explanations of the observed relationships among a set of m manifest polytomous variables. The class of models considered here includes both models in which the parameters are identifiable and also models in which the parameters are not. For each of the models considered here, a relatively simple method is presented for calculating the maximum likeli- hood estimate of the frequencies in the m-way contingency table expected under the model, and for determining whether the parameters in the estimated model are identifiable. In addition, methods are presented for testing whether the model fits the observed data, and for replacing unidentifiable models that fit by identifiable models that fit. Some illus- trative applications to data are also included. This paper deals with the relationships among m polytomous variables, i.e. with the analysis of an m-way contingency table. These m variables are manifest variables in that, for each observed individual in a sample, his class with respect to each of the m variables is observed. We also consider here polytomous variables that are latent in that an individ- ual's class with respect to these variables is not observed. The classes of a latent variable will be called latent classes. Consider first a 4-way contingency table which cross-classifies a sample of n individuals with respect to four manifest polytomous variables A, B, C and D. If there is, say, some latent dichotomous variable X, so that each of the n individuals is in one of the two latent classes with respect to this variable, and within the tth latent class the manifest variables (A, B, C, D) are mutually independent, then this two-class latent structure would serve as a simple explanation of the observed relationships among the variables in the 4-way con- tingency table for the n individuals. There is a direct generalization when the latent variable has T classes. We shall present some relatively simple methods for determining whether the observed relationships among the variables in the m-way contingency table can be explained by a T-class structure, or by various modifications and extensions of this latent structure. To illustrate the methods we analyze Table 1, a 24 contingency table presented earlier by Stouffer & Toby (1951, 1962, 1963), which cross-classifies 216 respondents with respect to whether they tend towards universalistic values ( + ) or particularistic values (-) when confronted by each of four different situations of role conflict. The letters A, B, C and D in

The Analysis of Systems of Qualitative Variables When Some of the Variables Are Unobservable. Part I-A Modified Latent Structure Approach

Abstract: This article presents methods for analyzing the relationships among a set of qualitative variables when some of these variables are specified manifest (i.e., observed) variables and others are latent (i.e., unobserved or unobservable) variables. We shall show how to estimate the magnitude of the various effects represented in pathdiagram models that include both the manifestand latent variables, and also how to test whether this kind of path-diagram model is congruent with the observed data. These methods can be applied in order to analyze data obtained in various kinds of surveys (including panel studies), and also in order to construct tests and indices for purposes of measurement and prediction. To illustrate their wide applicability and flexibility, we shall use these methods to reanalyze several different sets of data which were analyzed earlier by Coleman (1964), Lazarsfeld (1948, 1970), Goodman (1973a), and others. Except for some related conclusions in Goodman (1973a), the methods introduced herei...

Normal ogive model on the continuous response level in the multidimensional latent space

Abstract: The homogeneous case of the continuous response model is expanded to the multi-dimensional latent space, and the normal ogive model is presented. The operating density characteristic of the continuous item response and the vector of basic functions are developed. It is found out that there is a vector of sufficient statistics for estimating the subject's vector of latent traits, given the item parameter vectors. The relationship between the model and the linear factor analysis is observed. The matrix of item response information functions is introduced. Some additional observations are also made.

Removing the Effects of Random Guessing from Latent Trait Ability Estimates. Research Bulletin No. 74-32.

Abstract: In latent trait models the standard procedure for handling the problem caused by guessing on multiple choice tests is to estimate a parameter which is intended to measure the “guessingness” inherent in an item. Birnbaum's three parameter model, which handles guessing in this manner, ignores individual differences in guessing tendency. This paper presents a model or procedure which uses the information contained in the interaction between a person and an item to remove the effects of random guessing from estimates of ability, difficulty, and discrimination. Simulated and real data are presented which support the model in terms of fit and information.