Showing papers on "Latent variable model published in 1981"
TL;DR: It is argued here that, if all variables in the model are random, then Bayes' theorem provides the logical link between the data and the unobserved latent variables.
Abstract: The term posterior analysis is used in this paper to refer to methods of drawing inferences about the latent variables in factor analysis after the model has been fitted. In particular with the problem of locating each individual in the latent space on the basis of the values of the observed variables. This problem has been traditionally treated by determining factor scores. It is argued here that, if all variables in the model are random, then Bayes' theorem provides the logical link between the data and the unobserved latent variables. Viewed in this perspective the indeterminacy of factor scores is simply an expression of the fact that the latent variables are still random variables after the manifest variables have been observed. The name, factor scores, can then reasonably be given to the location parameters of the posterior distributions. The paper is primarily expository and it contains no new mathematics. Its concern is with the logical framework within which the analysis should be carried out and interpreted.
83 citations
TL;DR: In this paper, both likelihood and Bayesian estimation procedures for a model with multiple indicators and multiple causes of a single unobservable latent variable were considered, where the model is complicated by its reduced form, which displays a mixture of econometric and psychometric themes.
Abstract: This article considers both likelihood and Bayesian estimation procedures for a model with multiple indicators and multiple causes of a single unobservable latent variable. The model is complicated by its reduced form, which displays a mixture of econometric and psychometric themes. We avoid this complexity via the estimation of the unobservable latent variable through direct use of the original structural form. This approach not only provides maximum likelihood estimates that are equivalent to those derived from the reduced form, but it also permits a feasible Bayesian approach, which would be technically complex to execute otherwise.
42 citations
TL;DR: In this paper, a method for estimating the unknown parameters of an interdependent simultaneous equations model with latent variables is described. But the method involves only repeated application of ordinary least squares and no distributional assumptions are needed.
Abstract: This paper describes a method for estimating the unknown parameters of an interdependent simultaneous equations model with latent variables. For each latent variable there may be single or multiple indicators. Estimation proceeds in three stages: first, estimates of the latent variables are constructed from the associated manifest indicators; second, treating the estimates as directly observed, fix-point estimates of the structural form parameters are obtained; third, the location parameters are estimated. The method involves only repeated application of ordinary least squares and no distributional assumptions are needed. The paper concludes with an empirical application of the method.
38 citations
TL;DR: The theory of estimation and inference in a very general class of latent variable models for time series is developed by showing that the distribution theory for the finite Fourier transform of the observable variables in LDA models is isomorphic to that for the observable variable themselves in classical latent variables themselves as mentioned in this paper.
30 citations
TL;DR: In this paper, the authors present a procedure based on the well-known likelihood ratio criterion (Wilks, 1962), which can be described as follows: one estimates the full set of r parameters of a model and calculates a likelihood ratio X2(r) goodness-of-fit statistic.
Abstract: Interest has developed recently in making comparisons among the three logistic latent trait models (Dinero & Haertel, 1977; Hutton, 1979; Reckase, 1978). While issues such as type of item and possible use of the item pool are fundamental when selecting a model, it would be useful to have a technique available to aid in making the choice of model. This paper presents such a procedure based on the well-known likelihood ratio criterion (Wilks, 1962). Briefly, the general likelihood ratio procedure may be described as follows: One estimates the full set of r parameters of a model and calculates a likelihood ratio X2(r) goodness-of-fit statistic. One then estimates only a subset of these parameters of size s using assumed values for the remaining p = r s parameters, and calculates a likelihood ratio x2(s). Finally, one calculates the difference between the two, x2(p) = [X2(r) x2(s)]. This statistic , x2(p), can then be used to test the importance of estimating the p remaining parameters.
17 citations
TL;DR: In this paper, a general method is suggested which proposes to make comparative analyses of factors possible without the assumption of equal variances across populations, which is an assumption that is probably only rarely found in comparative research.
7 citations
TL;DR: In this paper, a model of urban immigration for the thirty-three largest Dutch cities is estimated using a linear structural equation approach, where the lagged variables are compressed to latent variables in a measurement model.
Abstract: Lagged variables play an important role in cross-sectional models in geography and regional sciences. This paper starts with an overview of the situations in which they may be required. Lagged variables also pose serious problems from a statistical point of view: multicollinearity and the determination of the length of the lag. Some common approaches to these two problems are discussed and evaluated. As an alternative a linear structural equation approach is presented, where the lagged variables are compressed to latent variables in a measurement model. The relationship between the lagged variables, thus compressed, and the dependent variable is expressed in the structural model. Both the measurement model and the structural model are estimated simultaneously. The paper ends with an application. A model of urban immigration for the thirty-three largest Dutch cities is estimated.
6 citations
01 Jan 1981
TL;DR: Hutten et al. as mentioned in this paper explored the fit of data to the Rasch and three-parameter logistic latent trait models with 25 empirical datasets and found that deviations in data from latent trait model assumptions were the primary variables of interest.
Abstract: The Fit of Empirical Data to Two Latent Trait Models September 1981 Leah R. Hutten, B.A., University of Wisconsin-Madison Ed.D., University of Massachusetts Directed by: Ronald K. Hambleton Fit of data to the Rasch and three-parameter logistic latent trait models was explored with 25 empirical datasets. Deviations in data from latent trait model assumptions were the primary variables of interest. The study also investigated estimation precision for small samples and short test lengths and evaluated costs for latent trait parameter estimation by the two latent trait models. Ability and item parameters were estimated under the assumptions of the Rasch and three-parameter models for tests with 40 items and 1000 examinees. Estimated parameters were substituted for true parameters to make predictions about number-correct score distributions. When ability is known, a theorem by Lord (1980) equates ability with the conditional distribution of number-correct scores. Predicted score distributions were compared to observed score distributions with statistical and graphical techniques. Both Kolmogorov-Smirnov and Chi-square test statistics were obtained. The importance of three latent trait model assumptions,
3 citations
TL;DR: A class of statistical models is derived for the problem of differential diagnosis between several types of disease and the performance of models for differential diagnosis among three and four types is assessed on clinical data.
Abstract: SUMMARY A class of statistical models is derived for the problem of differential diagnosis between several types of disease. The performance of models for differential diagnosis between three and four types is assessed on clinical data.
2 citations
01 Apr 1981
2 citations