Showing papers on "Latent variable model published in 1992"

Latent Class Models for Stage-Sequential Dynamic Latent Variables

Abstract: Stage-sequential dynamic latent variables are of interest in many longitudinal studies. Measurement theory for these latent variables, called Latent Transition Analysis (LTA), can be found in recent generalizations of latent class theory. LTA expands the latent Markov model to allow applications to more complex latent variables and the use of multiple indicators. Because complex latent class models result in sparse contingency tables, that may lead to poor parameter estimation, a simulation study was conducted in order to determine whether model parameters are recovered adequately by LTA, and whether additional indicators result in better measurement or in impossibly sparse tables. The results indicated that parameter recovery was satisfactory overall, although as expected the standard errors were large in some conditions with few subjects. The simulation also indicated that at least within the conditions examined here, the benefits of adding indicators outweigh the costs. Additional indicators improved s...

Bivariate Latent Variable Models for Clustered Discrete and Continuous Outcomes

Abstract: We use the concept of a latent variable to derive the joint distribution of a continuous and a discrete outcome, and then extend the model to allow for clustered data. The model can be parameterized in a way that allows one to write the joint distribution as a product of a standard random effects model for the continuous variable and a correlated probit model for the discrete variable. This factorization suggests a convenient approach to parameter estimation using quasi-likelihood techniques. Our approach is motivated by the analysis of developmental toxicity experiments for which a number of discrete and continuous outcomes are measured on offspring clustered within litters. Fetal weight and malformation data illustrate the results.

A Latent Class Poisson Regression Model for heterogeneous Count Data with an Application to Direct Mail

Abstract: In this paper an approach is developed that accommodates heterogeneity in Poisson regression models for count data. The model developed assumes that heterogeneity arises from a distribution of both the intercept and the coefficients of the explanatory variables. We assume that the mixing distribution is discrete, resulting in a finite mixture model formulation. An EM algorithm for estimation is described, and the algorithm is applied to data on customer purchases of books offered through direct mail. Our model is compared empirically to a number of other approaches that deal with heterogeneity in Poisson regression models.

Assumptions of the Two-Step Approach to Latent Variable Modeling

Abstract: Although methods for latent variable modeling that allow a joint analysis of measurement and theory have become popular, they are not without difficulties. As these difficulties have become more apparent, several researchers have recently called for a “two-step approach” to latent variable modeling in which measurement is evaluated separately from theory. This implies that programs for covariance structure analysis are not needed because factor analysis and regressions would suffice for analysis. Before a return to earlier practice using seemingly simpler analysis tools can be recommended, it seems prudent to consider the assumptions underlying a two-step approach. At least four implicit assumptions can be identified: (a) theory and measurement are independent, (b) results of factor analysis specifications can be generalized to other specifications, (c) the estimators have desirable statistical properties, and (d) the statistical test in one step is independent of the test in the other. The authors show t...

Linear Logistic Latent Class Analysis for Polytomous Data

Abstract: For latent class analysis, a widely known statistical method for the unmixing of an observed frequency table into several unobservable ones, a flexible model is presented in order to restrain the unknown class sizes (mixing weights) and the unknown latent response probabilities. Two systems of basic equations are stated such that they simultaneously allow parameter fixations, the equality of certain parameters as well as linear logistic constraints of each of the original parameters. The maximum likelihood equations for the parameters of this “linear logistic latent class analysis” are given, and their estimation by means of the EM algorithm is described. Further, the criteria for their local identifiability and statistical tests (Pearson- and likelihood-ratio-χ 2) for goodness of fit are outlined. The practical applicability of linear logistic latent class analysis is demonstrated by three examples: mixed logistic regression, a mixed Bradley-Terry model for paired comparisons with ties, and a lo...

Assumptions about unmeasured variables with studies of reciprocal relationships : the case of employee attitudes

Abstract: Recent applications of latent variable modeling (LVM) of reciprocal relationships involving employee attitudes were examined with regard to assumptions made about unmeasured variables and correlations among residuals of structural equations. Data from two published studies from the job satisfaction and organizational commitment literature were reanalyzed with LVM. The consequence of specifying residual correlations were examined for models containing nonlagged and lagged reciprocal effects. The results of model comparison tests in both samples supported the importance of specifying correlations among the residuals, and many of the residual correlations estimated were statistically significant

Multiple regression analysis of twin data: a model-fitting approach.

Abstract: The multiple regression methodology proposed by DeFries and Fulker (DF; 1985, 1988) for the analysis of twin data is compared with maximum-likelihood estimation of genetic and environmental parameters from covariance structure. Expectations for the regression coefficients from submodels omitting theh2 andc2 terms are derived. Model comparisons similar to those conducted using maximum-likelihood estimation procedures are illustrated using multiple regression. Submodels of the augmented DF model are shown to yield parameter estimates highly similar to those obtained from the traditional latent variable model. While maximum-likelihood estimation of covariance structure may be the optimal statistical method of estimating genetic and environmental parameters, the model-fitting approach we propose is a useful extension to the highly flexible and conceptually simple DF methodology.

Latent Variable Models for Clustered Dichotomous Data with Multiple Subclusters

Abstract: SUMMARY Regression models for clustered binary data are derived from nonlinear mixed models in terms of latent normal variables. The marginal response probabilities are functions of covariates through generalized linear models. Within a cluster, the pairwise tetrachoric correlations are all equal and are not restricted by marginal probabilities. This approach accommodates hierarchically nested binary data. An algorithm for estimation using generalized estimating equations is proposed. An example illustrates the application of this approach.

Likelihood Evaluation for Dynamic Latent Variables Models

Abstract: We propose a general Monte Carlo simulation technique for evaluating the likelihood function of dynamic latent variables models, based on artificial factorizations of the sequential joint density of the observables and latent variables. The feasibility of the proposed technique is demonstrated by means of a pilot application to a one-parameter disequilibrium model. Extensions to models with weakly exogenous variables and the use of acceleration methods are discussed.

The problem of indicator-latent relationship in metric models. Part 1

Abstract: Metric models, i.e. formalisms describing relationships between indicators and latent variables, are discussed. In modern metric models, a latent is regarded as independent of the measuring person. It is suggested that this defect of metric models be avoided if the latent is assignment a priori by fixing a form of latent distribution.

The problem of indicator-latent relationship in metric models. part 2 metric models with a priori latent assignment

Abstract: Metric models in which indicator distribution and a priori assigned latent distributions coincide in form are developed

Il problema dell'indeterminatezza nei modelli con variabili latenti

Abstract: This paper deals with a crucial problem of models with latent variables, the indeterminacy of the latent variables. Indeterminacy of the latent variables has the consequence that it is in most cases impossible to attach a real meaning to this variables. Particularly the common factor analysis model, models with error in the variables and the Lisrel model are analysed. An alternative method which resolves the indeterminacy of the latent variables is presented.

Estimation and application of latent variable models in categorical data analysis

Abstract: Bartholomew (1980, 1984a) has laid down a foundation for factor analysis based on latent variable models. Shea (1984, 1985) has provided computer programs for estimating one-factor latent variable models when responses are binary or polytomous variables. However, the programs have limitations on number of variables and the sample size, which limits their applicability, especially when variables are polytomous. However, the more important limitation is that it is not possible to use two-factor models when one-factor models are not adequate. Here, we have gone further and successfully obtained maximum likelihood estimates for both the one-factor and two-factor latent variable models for binary and polytomous variables. The new algorithm is much faster because of careful and efficient programming. More importantly, generalization to high latent domensions is straightforward. Formal hypothesis testing is very difficult when variables are very large in number. However, we have shown in our examples that some interesting graphical interpretations can be made.

Latent Traits or Latent States? The Role of Discrete Models for Ability and Performance.

Abstract: Classical test theory, item response theory, and generalizability theory all treat the abilities to be measured as continuous variables, and the items of a test as independent probes of underlying continua. These models are well-suited to measuring the broad, diffuse traits of traditional differential psychology, but not for measuring the outcomes of school learning. Discrete latent structure models offer a powerful and promising alternative. Abilities can be modeled as partially ordered sets of discrete states (at a minimum, "nonmastery" and "mastery") and may be linked according to an asymmetric "prerequisite" relation. Narrower, simpler abilities may be combined into broader, more complex abilities. The various possible outcomes of performing a task can be modeled as a partially ordered set of task performance states. Abilities and task performances are clearly distinguished from one another, and more than one ability pattern may permit successful performance of a given task. Subtasks need not be modeled as conditionally independent given ability. The mapping from ability states to task performance states shows clearly what a given test can and cannot measure, and what may be inferred from a given pattern of test performance. These models for ability and task performance, together with the mapping between them, may be augmented with a suitable model for measurement error (misclassification) to complete an alternative framework for scoring, analyzing, and interpreting test performance. This framework has the potential to solve significant measurement problems inherent in performance testing and other applications. (Contains 12 figures.) (Author/SLD) *********************************************************************** Reproductions supplied by EDRS are the best that can be made *' from the original document. ***********************************************************************

A hierarchical assessment of latent traits by using latent guttman scaling

Abstract: The aim of the present paper is to discuss a hierarchical assessment of continuous latent traits by use of latent Guttman’s scales. The latent space under consideration is expressed as a compact space $$\mathop \Pi \limits_{i = 1}^K \left[ {0,1} \right]$$ , and is partitioned into several domains which imply the levels of K latent traits. The amount of information about the latent space, which the present latent class analysis includes, is considered, and the latent class analysis is evaluated through the amount of information about the latent space. Concerning the correlation of latent traits, an indicator of the correlation is derived, and in addition a method for testing the correlation of latent traits is proposed. A numerical example is also presented to demonstrate the present analysis.

A comparison of three response models incorporated in the latent class models for the analysis of pick any/n' data

Abstract: This paper presents two new response models for the analysis of preference or dominance date called «pick any/n» data. The one assumes that in Stage 1 a subject determines the number of stimuli to be chosen as most preferred, and in Stage 2 he involuntarily ranks m (=the number determined) stimuli out of all n stimuli, giving that partial ranking as a «pick any/n» response, and the other assumes that in Stage 2 the subject finds a set of m stimuli every member of which is more preferred to all the remaining n-m stimuli, providing this set as a response. These response models besides the conventional threshold model are implemented in the latent class models

PARELLA: Measurement of Latent Attitude via the Statistical Modelling of Response Processes

Abstract: A model for the measurement of latent traits by proximity items (the PARELLA model) will be introduced. This model assumes that the responses of persons to items result from proximity relations: the smaller the (psychological) distance between person and item, the larger the probability that the person will respond positively to the item. The model is unidimensional and estimates the locations of items and persons on the latent trait. This paper will introduce the model, discuss the EM-algorithm based estimation procedure and provide an example of an application.