Showing papers on "Latent class model published in 1993"

Bayesian analysis of binary and polychotomous response data

Abstract: A vast literature in statistics, biometrics, and econometrics is concerned with the analysis of binary and polychotomous response data. The classical approach fits a categorical response regression model using maximum likelihood, and inferences about the model are based on the associated asymptotic theory. The accuracy of classical confidence statements is questionable for small sample sizes. In this article, exact Bayesian methods for modeling categorical response data are developed using the idea of data augmentation. The general approach can be summarized as follows. The probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data. Values of the latent data can be simulated from suitable truncated normal distributions. If the latent data are known, then the posterior distribution of the parameters can be computed using standard results for normal linear models. Draws from this posterior are used to sample new latent data, and t...

Loglinear Models with Latent Variables

Abstract: Introduction The Loglinear Model The Latent Class Model Loglinear Modeling with Latent Variables Internalizing External Variables Causal Models with Latent Variables A Modified LISREL Approach Latent Variable Models for Longitudinal Data Problems and New Developments

Accelerated gaussian importance sampler with application to dynamic latent variable models

Abstract: SUMMARY We propose a new generic and highly efficient Accelerated Gaussian Importance Sampler (AGIS) for the numerical evaluation of (very) high-dimensional density functions. A specific case of interest to us is the evaluation of likelihood functions for a broad class of dynamic latent variable models. The feasibility of our method is strikingly illustrated by means of an application to a first-order dynamic stochastic volatility model for daily stock returns, whose likelihood for an actual sample of size 2022 (!) is evaluated with high numerical accuracy by means of 10,000 Monte Carlo replications. The estimated model parsimoniously dominates ARCH and GARCH alternatives, one of which includes twelve lags.

Structured latent curve models

Abstract: Latent curve models are equivalent to factor analysis models in which common factor means are not assumed to be zero. The data model therefore generates a structure for the manifest variable mean vector as well as for the manifest variable covariance matrix. As in unrestricted factor analysis, there is a rotation problem in latent curve analysis. This problem may be avoided if a structure is imposed on the factor matrix. A method for doing this was employed in Browne and Du Toit (1991). The present paper presents theoretical details of this method for obtaining structured latent curve models for learning data. It is shown that use of a first order Taylor expansion about a monotonic target function generates a restricted factor matrix that has properties that allow meaningful interpretation of its columns as latent curves. Possible monotonic mean curves are discussed and details are given of associated factor matrices whose elements are functions of a small number of parameters. Models for the error covariance matrix are also considered. Joint latent curve and factor analysis models are suggested. These models are suitable for situations where both learning scores and scores on concomitant variables are available. A practical example is presented. Theory derived in Browne (1990) concerning the robustness of asymptotic properties of normal theory minimum discrepancy methods is applied to investigate the asymptotic robustness of maximum multivariate normal likelihood methods for the present models.

Analyzing twin resemblance in multisymptom data: Genetic applications of a latent class model for symptoms of conduct disorder in juvenile boys

Abstract: A model based on the latent class model is developed for the effects of genes and environment on multivariate categorical data in twins. The model captures many essential features of dimensional and categorical conceptions of complex behavioral phenotypes and can include, as special cases, a variety of major locus models including those that allow for etiological heterogeneity, differential sensitivity of latent classes to measured covariates, and genotype × environment interaction (G×E). Many features of the model are illustrated by an application to ratings on eight items relating to conduct disorder selected from the Rutter Parent Questionnaire (RPQ). Mothers rated their 8-to 16-year-old male twin offspring [174 monozygotic (MZ) and 164 dizygotic (DZ) pairs]. The impact of age on the frequency of reported symptoms was relatively slight. Preliminary latent class analysis suggests that four classes are required to explain the reported behavioral profiles of the individual twins. A more detailed analysis of the pairwise response profiles reveals a significant association between twins for membership of latent classes and that the association is greater in MZ than DZ twins, suggesting that genetic factors played a significant role in class membership. Further analysis shows that the frequencies of MZ pairs discordant for membership of some latent classes are close to zero, while others are definitely not zero. One possible explanation of this finding is that the items reflect underlying etiological heterogeneity, with some response profiles reflecting genetic categories and others revealing a latent environmental risk factor. We explore two “four-class” models for etiological heterogeneity which make different assumptions about the way in which genes and environment interact to produce complex disease phenotypes. The first model allows for genetic heterogeneity that is expressed only in individuals exposed to a high-risk (“predisposing”) environment. The second model allows the environment to differentiate two forms of the disorder in individuals of high genetic risk. The first model fits better than the second, but neither fits as well as the general model for four latent classes associated in twins. The results suggest that a single-locus/two-allele model cannot fit the data on these eight items even when we allow for etiological heterogeneity. The pattern of endorsement probabilities associated with each of the four classes precludes a simple “unidimensional” model for the latent process underlying variation in symptom profile in this population. The extension of the approach to larger pedigrees and to linkage analysis is briefly considered.

Statistical Modeling of Expert Ratings on Medical Treatment Appropriateness

Abstract: This article uses latent structure analysis to model ordered category ratings by multiple experts on the appropriateness of indications for the medical procedure carotid endarterectomy. The statistical method used is a form of located latent class analysis, which combines elements of latent class and latent trait analysis. It assumes that treatment indications fall into distinct latent classes, with each latent class corresponding to a different level of appropriateness. The appropriateness rating of a treatment indication by a rater is assumed determined by the latent class membership of the indication, rating category thresholds of the rater, and random measurement error. The located latent class model has two alternative forms: a normal ogive form, which derives from the assumption of normally distributed measurement error, and a logistic approximation to the normal form. The approach has the following advantages for the analysis of ordered category ratings by multiple experts: (1) it assesses...

A Latent Class Approach to Fitting the Weighted Euclidean Model, CLASCAL.

Abstract: A weighted Euclidean distance model for analyzing three-way proximity data is proposed that incorporates a latent class approach. In this latent class weighted Euclidean model, the contribution to the distance function between two stimuli is per dimension weighted identically by all subjects in the same latent class. This model removes the rotational invariance of the classical multidimensional scaling model retaining psychologically meaningful dimensions, and drastically reduces the number of parameters in the traditional INDSCAL model. The probability density function for the data of a subject is posited to be a finite mixture of spherical multivariate normal densities. The maximum likelihood function is optimized by means of an EM algorithm; a modified Fisher scoring method is used to update the parameters in the M-step. A model selection strategy is proposed and illustrated on both real and artificial data.

A maximum likelihood method for latent class regression involving a censored dependent variable

Abstract: The standard tobit or censored regression model is typically utilized for regression analysis when the dependent variable is censored. This model is generalized by developing a conditional mixture, maximum likelihood method for latent class censored regression. The proposed method simultaneously estimates separate regression functions and subject membership in K latent classes or groups given a censored dependent variable for a cross-section of subjects. Maximum likelihood estimates are obtained using an EM algorithm. The proposed method is illustrated via a consumer psychology application.

Simultaneous Microeconometric Models with Censored or Qualitative Dependent Variables

Abstract: Publisher Summary This chapter defines two classes of simultaneous limited dependent variable regression models. The distinction between these two classes depends on whether the structural economic model is simultaneous in the latent or observed dependent variables. This distinction corresponds closely to whether or not the censoring mechanism itself acts as a constraint on individual agents' behavior. Type I models, which form the first class, are defined to be simultaneous in the underlying latent dependent variables. As a result, there exists an explicit and unique reduced form in the latent dependent variables under the usual identification conditions. In Type I models, individual behavior is completely described by the latent variable model and the censoring process simply acts as a constraint on the information available to the econometrician. Type II models form a general class in which the nonlinearity implicit in the censoring or discrete grouping process prevents an explicit solution for the reduced form. In Type II models, the observability rule also constrains the agent's choice set. For this second class of discrete or censored models a further coherency condition is required, this condition imposes restrictions that guarantee the existence of a unique but implicit reduced form for the observable endogenous variables. The chapter focuses on conditional maximum likelihood estimation. Estimation procedures may be applied across a wide variety of popular models and provide a useful basis for comparison and inference in such models.

Simulation‐based estimation of models with lagged latent variables

Abstract: We extend here our earlier work (Laroque-Salanie, 1989) and propose a dynamic simulated pseudo-maximum likelihood method to deal with a very general class of dynamic non-linear models, including models with lagged latent variables. We test this method on Monte Carlo-generated data for a canonical disequilibrium model. It appears to provide very satisfactory estimates at little computational cost. However, accurate estimation of the standard errors of the estimates may require some care in non-differentiable models.

Quasi-symmetric latent class models, with application to rater agreement

Abstract: Suppose we observe responses on several categorical variables having the same scale. We consider latent class models for the joint classification that satisfy quasi-symmetry. The models apply when subject-specific response distributions are such that (i) for a given subject, responses on different variables are independent, and (ii) odds ratios comparing marginal distributions of the variables are identical for each subject. These assumptions are often reasonable in modeling multirater agreement, when a sample of subjects is rated independently by different observers. In this application, the model parameters describe two components of agreement--strength of association between classifications by pairs of observers and degree of heterogeneity among the observers' marginal distributions. We illustrate the models by analyzing a data set in which seven pathologists classified 118 subjects in terms of presence or absence of carcinoma, yielding seven categorical classifications with the same binary scale. A good-fitting model has a latent classification that differentiates between subjects on whom there is agreement and subjects on whom there is disagreement.

Local homogeneity in latent trait models. A characterization of the homogeneous monotone IRT model

Abstract: The stochastic subject formulation of latent trait models contends that, within a given subject, the event of obtaining a certain response pattern may be probabilistic. Ordinary latent trait models do not imply that these within-subject probabilities are identical to the conditional probabilities specified by the model. The latter condition is called local homogeneity. It is shown that local homgeneity is equivalent to subpopulation invariance of the model. In case of the monotone IRT model, local homogeneity implies absence of item bias, absence of item specific traits, and the possibility to join overlapping subtests. The following characterization theorem is proved: the homogeneous monotone IRT model holds for a finite or countable item pool if and only if the pool is experimentally independent and pairwise nonnegative association holds in every positive subpopulation.

A latent class binomial logit methodology for the analysis of paired-comparison choice data - an application reinvestigating the determinants of perceived risk

Abstract: A latent class model for identifying classes of subjects in paired comparison choice experiments is developed. The model simultaneously estimates a probabilistic classification of subjects and the logit models' coefficients relating characteristics of objects to choices for each respective group among two alternatives in paired comparison experiments. A modest Monte Carlo analysis of algorithm performance is presented. The proposed model is illustrated with empirical data from a consumer psychology experiment that examines the determinants of perceived consumer risk. The predictive validity of the method is assessed and compared to that of several other procedures. The sensitivity of the method to (randomly) eliminate comparisons, which is important in view of reducing respondent fatigue in the task, is investigated.

A latent class unfolding model for analyzing single stimulus preference ratings

Abstract: A multidimensional unfolding model is developed that assumes that the subjects can be clustered into a small number of homogeneous groups or classes. The subjects that belong to the same group are represented by a single ideal point. Since it is not known in advance to which group of class a subject belongs, a mixture distribution model is formulated that can be considered as a latent class model for continuous single stimulus preference ratings. A GEM algorithm is described for estimating the parameters in the model. The M-step of the algorithm is based on a majorization procedure for updating the estimates of the spatial model parameters. A strategy for selecting the appropriate number of classes and the appropriate number of dimensions is proposed and fully illustrated on some artificial data. The latent class unfolding model is applied to political science data concerning party preferences from members of the Dutch Parliament. Finally, some possible extensions of the model are discussed.

Latent variable modeling of growth with missing data and multilevel data

Abstract: Latent variable modeling in psychometrics is connected with mainstream statistical theory in the areas of random coefficients, missing data, and clustered data. An educational achievement example points to the need for integrating these developments in a single analysis framework. It is shown that existing methods and software for latent variable modeling accomplish this.

A latent class vector model for preference ratings

Abstract: A latent class formulation of the well-known vector model for preference data is presented. Assuming preference ratings as input data, the model simultaneously clusters the subjects into a small number of homogeneous groups (or latent classes) and constructs a joint geometric representation of the choice objects and the latent classes according to a vector model. The distributional assumptions on which the latent class approach is based are analogous to the distributional assumptions that are consistent with the common practice of fitting the vector model to preference data by least squares methods. An EM algorithm for fitting the latent class vector model is described as well as a procedure for selecting the appropriate number of classes and the appropriate number of dimensions. Some illustrative applications of the latent class vector model are presented and some possible extensions are discussed.

Latent Variables in Log-Linear Models of Repeated Observations

Abstract: .After a very brief introduction into log-linear modeling and an explanation of the latent class model as a log-linear model with latent variables, it is shown that even a small amount of unreliability may lead to quite misleading conclusions about the underlying processes of change .' Next, measurement models for indicators measured at several points in time are discussed . The main purpose of this discussion is to show how to disentangle 'true', latent changes and observed changes caused by unreliability of measure ments A main topic is the causal analysis of panel data . Extending Goodman's loglinear 'modified path analysis approach' to include latent variables, it is shown how to set up 'modified LISREL models' for the analyses of cross-sectional and longitudinal data . Finally, some other possible applications of the (categorical) latent variable approach are pointed out, along with some important new developments

Statistical modelling and latent variables

Abstract: Criminometrics, Latent Variables, and Panel Data (J. Aasness, E. Eide, T. Skjerpen). Scale Construction by Maximizing Reliability (D.J. Bartholomew, M. Knott). Finite Sample Properties of Limited Information Estimation: An Algebraic Approach (P.A. Bekker). Structural Equation Models as Nonlinear Regression Models (P.M. Bentler). Stochastic Frontier and Switching Regression Models with Latent Variables (R. Colombi). Latent Class Models with Ordered Latent Classes: An Approach to Nonparametric Latent Trait Modelling (M.A. Croon). System Identification and Errors in the Variables (M. Deistler, W. Scherrer). Principal Components and Proportionality in Patterned Covariance Matrices (B.D. Flury, B. Neuenschwander). Errors-in-Variables Identification and Model Uniqueness (R.P. Guidorzi). Measurement Error Models with Unequal Error Variances (N.A. Hasabelnaby, W.A. Fuller). Latent Variable Modelling with Ordinal Variables (K.G. Joereskog). Asymptotic Properties of Statistical Inference Based on Fisher Consistent Estimators in the Analysis of Covariance Structures (Y. Kano). Imposed Quasi-Normality in Covariance Structure Analysis (R. Koning, H. Neudecker, T. Wansbeek). Structural Equation Models with Hierarchical Data (S.-Y. Lee, W.-Y. Poon). Global Optimization Criteria of the PLS-Algorithm in Recursive Path Models with Latent Variables (H. Mathes). Structural Equation Models with Transformed Variables (A. Mooijaart). Individual Unit Models versus Structural Equations: Growth Curve Examples (D. Rogosa). Multi-Sample Analysis of Moment-Structures: Asymptotic Validity of Inferences Based on Second-Order Moments (A. Satorra). Consistency at Large in Models with Latent Variables (H. Schneeweiss). A DYMIMIC Model of Employment: Another Look at Some Issues of Formulation, Identification and Estimation (U. Trivellato, S. Bordignon, C. Gaetan). General Least Squares Regression in Linear Errors-in-Variables Models with Correlated Errors (L. Wang).

A latent class procedure for the structural analysis of two-way compositional data

Abstract: This paper develops a new procedure for simultaneously performing multidimensional scaling and cluster analysis on two-way compositional data of proportions. The objective of the proposed procedure is to delineate patterns of variability in compositions across subjects by simultaneously clustering subjects into latent classes or groups and estimating a joint space of stimulus coordinates and class-specific vectors in a multidimensional space. We use a conditional mixture, maximum likelihood framework with an E-M algorithm for parameter estimation. The proposed procedure is illustrated using a compositional data set reflecting proportions of viewing time across television networks for an area sample of households.

Latent Structure Models for Ranking Data

Abstract: In this paper several latent structure models for analyzing data that consist of complete or incomplete rankings are discussed. First, attention is given to some latent class extensions of the Bradley-Terry-Luce model for ranking data. Next, various latent class models based on log-linear modeling of ranking data are described. Within this latter family of latent class models, a main distinction is made between models based on the assumption of quasi-independence within the latent classes, and models in which some form of association between the ranking positions is allowed to exist within the classes. All models are applied to a real data set from a large scale cross-national survey on political values.

Discrete choice models with latent explanatory variables using subjective data

Abstract: 非集計交通行動モデルの説明変数には, 計測が容易な変数のみ通常用いられるが, 人間の選択行動には定量化されにくい主観的要因や個人の知覚の相違などの潜在要因が大きく影響している. 本論文は, 潜在要因を考慮した既存研究のレビューとともに, このような潜在要因を含んだより精緻な意思決定機構を内包した非集計離散型選択分析の方法論を提案するものである.

A new item response model with parameters reflecting state of knowledge

Abstract: The authors developed a new latent trait model for polytomous data. A unique feature of this model is that it explains the psychological process through which a subject reaches correct or wrong responses. This model is an integration of two parts. One part discriminates states of knowledge, namely, it classifies them into three categories, i.e., a) complete knowledge, b) partial knowledge, and c) complete ignorance. Another feature of the model is that we have two different kinds of manifest data, i.e. confidence data and correct/wrong responses. The subject is required to choose whether he is confident of his answer or not. In this paper, we make use of confidence data as auxiliary information in making effective estimation of parameters. Then the new model was applied to mathematics test data of high school students.