Showing papers on "Latent variable model published in 1995"
TL;DR: In this article, an alternative estimation technique for quadratic and interaction latent variables in structural equation models using LISREL, EQS, and CALIS is proposed, which specifies these vari...
Abstract: The author proposes an alternative estimation technique for quadratic and interaction latent variables in structural equation models using LISREL, EQS, and CALIS. The technique specifies these vari...
768 citations
TL;DR: Powerful procedures for diagnosing assignable causes for the occurrence of a fault by interrogating the underlying latent variable model for the contributions of the variables to the observed deviation are presented.
328 citations
TL;DR: This work generalizes the McCullagh and Nelder approach to a latent class framework and demonstrates how this approach handles many of the existing latent class regression procedures as special cases, as well as a host of other parametric specifications in the exponential family heretofore not mentioned in the latent class literature.
Abstract: A mixture model approach is developed that simultaneously estimates the posterior membership probabilities of observations to a number of unobservable groups or latent classes, and the parameters of a generalized linear model which relates the observations, distributed according to some member of the exponential family, to a set of specified covariates within each Class. We demonstrate how this approach handles many of the existing latent class regression procedures as special cases, as well as a host of other parametric specifications in the exponential family heretofore not mentioned in the latent class literature. As such we generalize the McCullagh and Nelder approach to a latent class framework. The parameters are estimated using maximum likelihood, and an EM algorithm for estimation is provided. A Monte Carlo study of the performance of the algorithm for several distributions is provided, and the model is illustrated in two empirical applications.
314 citations
310 citations
Proceedings Article•
18 Aug 1995TL;DR: In this article, the authors show that there is a general, informative and reliable procedure for discovering causal relations when, for all the investigator knows, both latent variables and selection bias may be at work.
Abstract: We show that there is a general, informative and reliable procedure for discovering causal relations when, for all the investigator knows, both latent variables and selection bias may be at work. Given information about conditional independence and dependence relations between measured variables, even when latent variables and selection bias may be present, there are sufficient conditions for reliably concluding that there is a causal path from one variable to another, and sufficient conditions for reliably concluding when no such causal path exists.
204 citations
TL;DR: In this paper, a review is given of various goodness-of-fit measures that have been proposed for the binary choice model in the last two decades and the relative behaviour of several pseudo-R2 measures is analysed in a series of misspecified binary choice models, the misspecification being omitted variables or an included irrelevant variable.
Abstract: In this paper, a review is given of various goodness-of-fit measures that have been proposed for the binary choice model in the last two decades. The relative behaviour of several pseudo-R2 measures is analysed in a series of misspecified binary choice models, the misspecification being omitted variables or an included irrelevant variable. A comparison is made with the OLS-R2 of the underlying latent variable model and with the squared sample correlation coefficient of the true and predicted probabilities. Further, it is investigated how the values of the measures change with a changing frequency rate of successes.
168 citations
TL;DR: In this article, an example application of latent growth curve methodology, analyzing the effects of gender and parental monitoring on developmental change in adolescent alcohol consumption, is presented, and analyses are conducted within a cohort-sequential design, incorporating an approach to the analysis of missing data due to attrition.
Abstract: Recent advances in statistical methodology, in particular, latent growth modeling, allow for the testing of complex models regarding developmental trends from both an inter‐ and intraindividual perspective. An example application of latent growth curve methodology, analyzing the effects of gender and parental monitoring on developmental change in adolescent alcohol consumption, is presented. Furthermore, the analyses are conducted within a cohort‐sequential design, incorporating an approach to the analysis of missing data due to attrition. Findings are discussed with particular reference to the utility of latent growth curve models for assessing developmental processes at both the inter‐and intraindividual level across a variety of behavioral domains.
146 citations
TL;DR: The data strongly suggest that schizotypy, as assessed by the PAS, is taxonic at the latent level with a low general population taxon base rate, and the taxometric analysis of the psychological trait of femininity reveals that the MAXCOV-HITMAX procedure can detect a latent dimension, when one is hypothesized to exist.
Abstract: P. E. Meehl's model (1962, 1990) of schizotypy and the development of schizophrenia implies that the structure of liability for schizophrenia is dichotomous, hypothesizing that a «schizogene» determines one's membership in a latent class (or taxon; P. E. Meehl & R. R. Golden, 1982). The present study sought to replicate earlier findings concerning the taxonic latent structure and general population base rate of schizotypy (M. F. Lenzenweger & L. Korfine, 1992). P. E. Meehl's (1973; P. E. Meehl & R. R. Golden, 1982) MAXCOV-HITMAX taxometric analytic procedures were applied to a subset of items from the Perceptual Aberration Scale (PAS; L. J. Chapman, J. P. Chapman, & M. L. Raulin, 1978), a prominent psychometric index of schizotypy, derived from a new randomly ascertained nonclinical university sample (N = 1,646). Consistent with the authors'previous results as well as Meehl's conjectures, the data strongly suggest that schizotypy, as assessed by the PAS, is taxonic at the latent level with a low general population taxon base rate (i.e., <. 10). Moreover, individuals falling within the putative schizo-taxon underlying the PAS present greater levels of schizotypic phenomenology than nontaxon members. The taxometric analysis of the psychological trait of femininity also reveals that the MAXCOV-HITMAX procedure can detect a latent dimension, when one is hypothesized to exist, and the procedure does not appear to generate «spurious» evidence for taxonicity as a function of the psychometric format (e.g., true-false) of the data under analysis. The statistical implication of a taxonic entity occurring at a low base is discussed with respect to results obtained using the MAXCOV-HITMAX technique
135 citations
Posted Content•
01 Jan 1995
TL;DR: In this article, a flexible logit regression approach was proposed to regress the latent states occupied at various points in time on both time-constant and time-varying covariates.
Abstract: Discrete-time discrete-state Markov chain models can be used to describe individual change in categorical variables. But when the observed states are subject to measurement error, the observed transitions between two points in time will be partially spurious. Latent Markov models make it possible to separate true change from measurement error. The standard latent Markov model is, however, rather limited when the aim is to explain individual differences in the probability of occupying a particular state at a particular point in time. This paper presents a flexible logit regression approach which allows to regress the latent states occupied at the various points in time on both timeconstant and time-varying covariates. The regression approach combines features of causal log-linear models and latent class models with explanatory variables. In an application pupils' interest in physics at different points in time is explained by the time-constant covariate sex and the time-varying covariate physics grade. Results of both the complete and partially observed data are presented.
TL;DR: In this article, a framework for analyzing structural equation models (SEMs) that include nonlinear functions of latent or a mix of latent and observed variables in their equations is presented. But their methods are limited by the required distributional assumptions, by their complexity in implementation, and by the unknown distributions of the estimators.
Abstract: Busemeyer and Jones (1983) and Kenny and Judd (1984) proposed methods to include interactions of latent variables in structural equation models (SEMs). Despite the value of these works, their methods are limited by the required distributional assumptions, by their complexity in implementation, and by the unknown distributions of the estimators. This paper provides a framework for analyzing SEMs ("LISREL" models) that include nonlinear functions of latent or a mix of latent and observed variables in their equations. It permits such nonlinear functions in equations that are part of latent variable models or measurement models. I estimate the coefficient parameters with a two-stage least squares estimator that is consistent and asymptotically normal with a known asymptotic covariance matrix. The observed random variables can come from nonnormal distributions. Several hypothetical cases and an empirical example illustrate the method.
TL;DR: LTMs for clustered ordinal data are proposed which are derived as natural extensions of latent variable models for clustered binary data which can be applied to repeated measures data, familial data, longitudinal data, and data with both cluster specific and occasion specific covariates.
Abstract: Existing methods for the analysis of clustered, ordinal data are inappropriate for certain applications. We propose latent variable models for clustered ordinal data which are derived as natural extensions of latent variable models for clustered binary data (Qu, Williams, Beck, and Medendorp, 1992. Biometrics 48, 1095-1102). These models can be applied to repeated measures data, familial data, longitudinal data, and data with both cluster specific and occasion specific covariates with a wide range of correlation structures.
Journal Article•
TL;DR: Two latent variables : drivers' attitudes toward route diversion and their perceptions of the reliability of information provided by radio traffic reports (RTRs) or changeable message signs (CMSs) were determined to be significant explanatory variables of route diversion intentions.
Abstract: One of the benefits of advanced traveler information systems (ATISs) is their ability to divert travelers to alternative routes during traffic incidents to alleviate congestion. ATISs may effectively convince travelers to divert to alternative routes by providing information that is considered useful. Therefore, it is important to identify the factors that explain drivers' route diversion behaviors to properly assist in the design and implementation of ATISs. An application of latent variable models to determine the factors that affect drivers' stated intentions to divert from their usual routes when faced with traffic congestion is described. Two latent variables were identified : drivers' attitudes toward route diversion and their perceptions of the reliability of information provided by radio traffic reports (RTRs) or changeable message signs (CMSs). These two latent variables were determined to be significant explanatory variables of route diversion intentions. Some drivers' travel and socioeconomic characteristics and the type of information provided by RTRs and CMSs were also found to be important explanatory variables.
TL;DR: It is suggested that latent class models can be usefully applied to the evaluation of other psychiatric disorders as well and represent an important new tool in evaluating diagnostic criteria by providing a way of dealing with data lacking an observable gold standard.
Abstract: Objective To illustrate the use of latent class models for comparing alternative diagnostic criteria for autism. The models are based on the notion that the “true” classification of an individual is unknown but does exist at some unobserved, or “latent,” level. Estimates of sensitivity and specificity are obtained for each set of diagnostic criteria through maximum likelihood techniques in relation to the latent standard. Method In this paper, latent class models are used to compare DSM-III, DSM-III-R, and ICD-10 criteria for autism in a sample of 342 individuals with autism or other developmental disabilities. The diagnoses were made by one or more child psychiatrists who evaluated each patient and assigned a diagnosis of autism based on their own expert clinical judgment. In addition, the raters also determined whether criteria were met for the various diagnostic systems. Results The results indicate that the ICD-10 criteria agree best with the latent standard and a diagnosis based on expert opinion. Conclusion It is suggested that latent class models can be usefully applied to the evaluation of other psychiatric disorders as well and represent an important new tool in evaluating diagnostic criteria by providing a way of dealing with data lacking an observable gold standard.
TL;DR: In this article, the effect of unmeasured variables and their interactions on structural models was investigated in the context of Latent Variable Models and their application in Causal Modeling with Latent Variables.
Abstract: PART ONE: THEORETICAL ISSUES: CONCEPTS IN LATENT VARIABLES ANALYSIS Causal Inference in Latent Variable Models - Michael E Sobel The Theory of Confounding and its Application in Causal Modeling with Latent Variables - Rolf Steyer and Thomas Schmitt The Specification of Equivalent Models before the Collection of Data - Scott L Hershberger PART TWO: ANALYSIS OF LATENT VARIABLES IN DEVELOPMENTAL RESEARCH: CONTINUOUS VARIABLES APPROACHES The Effect of Unmeasured Variables and their Interactions on Structural Models - Phillip K Wood Exploratory Factor Analysis with Latent Variables and the Study of Processes of Development and Change - John R Nesselroade Dynamic Latent Variable Models in Developmental Psychology - Peter C M Molenaar Latent Variables Models and Missing Data Analysis - Michael J Rovine On the Arbitrary Nature of Latent Variables - Peter C M Molenaar and Alexander von Eye PART THREE: ANALYSIS OF LATENT VARIABLES IN DEVELOPMENTAL RESEARCH: CATEGORICAL VARIABLES APPROACHES Latent Class Models for Longitudinal Assessment of Trait Acquisition - George B Macready and C Mitchell Dayton Latent Trait Models for Measuring Change - Christiane Spiel Measuring Change Using Latent Class Analysis - Anton K Formann Mixture Decomposition when the Components are of Unknown Form - Hoben Thomas Latent Variables in Log-Linear Models of Repeated Observations - Jacques A Hagenaars Latent Logit Models with Polytomous Effects Variables - Allan L McCutcheon Latent Variables Markov Models - Rolf Langeheine PART FOUR: TESTING IN THE ANALYSIS OF LATENT VARIABLES Corrections to Test Statistics and Standard Errors in Covariance Structure Analysis - Albert Satorra and Peter M Bentler Testing in Latent Class Models Using a Posterior Predictive Check Distribution - Donald B Rubin and Hal S Stern
TL;DR: It is argued that deciding between a dimensional and a mixed- measurement representation of item response heterogeneity should not rest solely on statistical criteria and suggested some research contexts in which the mixed- Measurement model may be conceptually more appropriate than the traditional factor model.
Abstract: The mixed-measurement IRT model and the traditional factor analytic model are two fundamentally different ways of representing the structure underlying an item response matrix. To contrast these approaches, the parameters of full-information item factor models of varying dimensionality and mixed-measurement models of varying numbers of latent classes were estimated in a sample of 1,000 responses to a 14-item measure of Positive Interpersonal Engagement. Findings indicated that either a two latent factor or a two latent class mixed-model provided the most appropriate representation of the data. We also found that the factor models were, in general, more parsimonious than the mixed-measurement models. Nevertheless, we argue that deciding between a dimensional and a mixed- measurement representation of item response heterogeneity should not rest solely on statistical criteria. In the discussion, we suggest some research contexts in which the mixed- measurement model may be conceptually more appropriate than the traditional factor model.
01 Jan 1995
TL;DR: The paper introduces the latent class/Rasch model (LC/RM), a model that perfectly fits the raw score distribution in most cases and results in the same item parameter estimates as obtained under the conditional maximum likelihood method in the RM.
Abstract: As a special case of linear logistic latent class analysis, the paper introduces the latent class/Rasch model (LC/RM). While its item latent probabilities axe restricted according to the RM, its unconstrained class sizes describe an unknown discrete ability distribution. It is shown that when the number of classes is (at least) half the number of items plus one, the LC/RM perfectly fits the raw score distribution in most cases and thus results in the same item parameter estimates as obtained under the conditional maximum likelihood method in the RM. Two reasons account for this equivalence. Firstly, the maximum likelihood (ML) method for the LC/RM can be seen to be a version of the Kiefer-Wolfowitz approach, so that the structural item parameters as well as the unknown ability distribution are estimated consistently. Secondly, through its moment structure the observed raw score distribution constrains the ability distribution. Irrespective of whether the ability distribution is assumed to be continuous or discrete, it has to be replaced by a step function with the number of steps (=classes) being half the number of items plus one. An empirical example (Stouffer-Toby data on role conflict) illustrates these findings. Finally, conclusions are drawn concerning the properties of the ML item parameter estimates in the LC/RM, and some relations to other methods of parameter estimation in the RM are mentioned.
TL;DR: In this article, the 1-parameter logistic latent trait model was used to compare subjects with ordinal independence models and even within the 2-parameters logistic model.
Abstract: Comparisons of subjects are specifically objective if they do not depend on the items involved. Such comparisons are not restricted to the 1-parameter logistic latent trait model, but may also be defined within ordinal independence models and even within the 2-parameter logistic model.
TL;DR: The authors use Structural Equation Models (SEM) to estimate error variance and produce highly accurate coefficients for formulation of selection gradients, which is particularly appropriate when the selection is viewed as happening at the level of the latent variables.
Abstract: Selection studies involving multiple intercorrelated independent variables have employed multiple regression analysis as a means to estimate and partition natural and sexual selection's direct and indirect effects. These statistical models assume that independent variables are measured without error. Most would conclude that such is not the case in the field studies for which these methods are employed. We demonstrate that the distortion of estimates resulting from error variance is not trivial. When independent variables -are intercorrelated, extreme distortions may occur. We propose to use Structural Equation Models (SEM), to estimate error variance and produce highly accurate coefficients for formulation of selection gradients. This method is particularly appropriate when the selection is viewed as happening at the level of the latent variables
TL;DR: In this article, the application of unidimensional Rasch models to longitudinal data assumes homogeneity of change over persons, using latent class models, several classes with qualitatively distinct patterns of de...
Abstract: The application of unidimensional Rasch models to longitudinal data assumes homogeneity of change over persons. Using latent class models, several classes with qualitatively distinct patterns of de...
Posted Content•
01 Jan 1995
TL;DR: It is shown that when the loadings of two (or more) observed variables that load on different latent variables are constrained to be equal, then different choices for setting the metric define distinct models.
Abstract: Researchers using structural equation models with latent variables know that they must set the metric of each latent variable in the model. Whether the metric is set by fixing the variance of the latent variable or by fixing a loading of one of its indicators to a nonzero constant is viewed by most researchers as a necessary but unimportant decision. We show, however, that when the loadings of two (or more) observed variables that load on different latent variables are constrained to be equal, then different choices for setting the metric define distinct models. These models can differ in important ways: (a) their fit to the same observed covariance matrix, (b) the estimated values of their unstandard‐ized and standardized parameters, and (c) their identification statuses.
TL;DR: This chapter describes the building of causal graphs from statistical data in the presence of latent variables, and discusses the spurious causal dependencies, inducing paths and graphs, and partially oriented inducing path graphs.
Abstract: Publisher Summary This chapter describes the building of causal graphs from statistical data in the presence of latent variables. The problem of inferring causal relations from statistical data in the absence of experiments arises repeatedly in many scientific disciplines, including sociology, economics, epidemiology, and psychology. In addition, the building of expert systems could be expedited if background knowledge elicited from experts could be supplemented with automated techniques using relevant statistics. The efficient algorithms for determining causal relationships between random variables from appropriate statistical data when there are no unmeasured or “latent” variables are discovered. Inferring causal relations when unmeasured variables are also acting is a much more difficult problem. In many cases, it is impossible to infer the structure among the latent variables from statistical relations among the measured variables. But the presence of latent variables can also make it difficult to infer the causal relations among the measured variables themselves. The chapter discusses the spurious causal dependencies, inducing paths and graphs, and partially oriented inducing path graphs.
Posted Content•
TL;DR: In this article, a partial least squares (PLS) approach to dynamic modeling with latent variables is proposed. And the procedure is being programmed in ISP, where the model can be used for forecasting purposes.
Abstract: In this paper a partial least squares (PLS) approach to dynamic modelling with latent variables is proposed. Let Y be a matrix of manifest variables and H the matrix of the corresponding latent variables. And let H = BH+e be a structural PLS model with a coefficient matrix B. Then this model can be made a dynamic one by substituting for B a matrix F = B + CL containing the lag operator L. Then the structural dynamic model H = FH+e is formally estimated like an ordinary PLS model. In an exploratory way the model can be used for forecasting purposes. The procedure is being programmed in ISP.
TL;DR: A psychometric investigation using a factor analytic approach and latent trait analysis was made on the Charles F Kettering Ltd (CFK) School Climate Profile, a popular measure in the organizational climate literature as mentioned in this paper.
Abstract: A psychometric investigation using a factor analytic approach and latent trait analysis was made on the Charles F Kettering Ltd (CFK) School Climate Profile, a popular measure in the organizational climate literature The results of the study suggest major revisions for the instrument The factor analytic and latent trait analyses demonstrate that the subscales group in a different manner than was proposed by the scale's developers The findings suggest that a school climate scale needs to separate affective-experiential features of the setting from the cognitive-managerial components Furthermore, it may not be possible to develop a single scale appropriate for all members of a school setting
Journal Article•
TL;DR: A review is given of various goodness-of-fit measures that have been proposed for the binary choice model in the last two decades and how the values of the measures change with a changing frequency rate of successes is investigated.
Abstract: In this paper, a review is given of various goodness-of-fit measures that have been proposed for the binary choice model in the last two decades. The relative behaviour of several pseudo-R 2 measures is analysed in a series of misspecified binary choice models, the misspecification being omitted variables or an included irrelevant variable. A comparison is made with the OLS-R 2 of the underlying latent variable model and with the squared sample correlation coefficient of the true and predicted probabilities. Further, it is investigated how the values of the measures change with a changing frequency rate of successes
TL;DR: In this article, a dynamic discrete choice model with latent market segments using panel data is developed, which consists of two models: a latent segmentation model and a choice model, which is applied to panel data of shopping place choice.
Abstract: This study is aimed to develop a dynamic discrete choice model with latent market segments using panel data. The model system consists of two models: a latent segmentation model and a choice model with serial correlation. This model system is applied to panel data of shopping place choice. The estimation results shows that the latent segmentation model significantly improved goodness of fit and the choice model yielded more efficient parameter estimates by taking into account of serial correlation.