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49
MIXED MNL MODELS FOR DISCRETE RESPONSE
 JOURNAL OF APPLIED ECONOMETRICS J. APPL. ECON. 15: 447470 (2000)
, 2000
"... This paper considers mixed, or random coefficients, multinomial logit (MMNL) models for discrete response, and establishes the following results. Under mild regularity conditions, any discrete choice model derived from random utility maximization has choice probabilities that can be approximated as ..."
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Cited by 469 (15 self)
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This paper considers mixed, or random coefficients, multinomial logit (MMNL) models for discrete response, and establishes the following results. Under mild regularity conditions, any discrete choice model derived from random utility maximization has choice probabilities that can be approximated as closely as one pleases by a MMNL model. Practical estimation of a parametric mixing family can be carried out by Maximum Simulated Likelihood Estimation or Method of Simulated Moments, and easily computed instruments are provided that make the latter procedure fairly efficient. The adequacy of a mixing specification can be tested simply as an omitted variable test with appropriately defined artificial variables. An application to a problem of demand for alternative vehicles shows that MMNL provides a flexible and computationally practical approach to discrete response analysis.
Beyond SEM: General latent variable modeling
 Behaviormetrika
, 2002
"... This article gives an overview of statistical analysis with latent variables. Using traditional structural equation modeling as a starting point, it shows how the idea of latent variables captures a wide variety of statistical concepts, including random e&ects, missing data, sources of variatio ..."
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Cited by 113 (9 self)
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This article gives an overview of statistical analysis with latent variables. Using traditional structural equation modeling as a starting point, it shows how the idea of latent variables captures a wide variety of statistical concepts, including random e&ects, missing data, sources of variation in hierarchical data, hnite mixtures, latent classes, and clusters. These latent variable applications go beyond the traditional latent variable useage in psychometrics with its focus on measurement error and hypothetical constructs measured by multiple indicators. The article argues for the value of integrating statistical and psychometric modeling ideas. Di&erent applications are discussed in a unifying framework that brings together in one general model such di&erent analysis types as factor models, growth curve models, multilevel models, latent class models and discretetime survival models. Several possible combinations and extensions of these models are made clear due to the unifying framework. 1.
Latent class factor and cluster models, biplots, and related graphical displays
 Sociological Methodology
"... Heijden for helpful comments. We propose an alternative method of conducting exploratory latent class analysis that utilizes latent class factor models, and compare it to the more traditional approach based on latent class cluster models. We show that when formulated in terms of R mutually independe ..."
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Cited by 42 (14 self)
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Heijden for helpful comments. We propose an alternative method of conducting exploratory latent class analysis that utilizes latent class factor models, and compare it to the more traditional approach based on latent class cluster models. We show that when formulated in terms of R mutually independent, dichotomous latent factors, the LC factor model has the same number of distinct parameters as an LC cluster model with R+1 clusters. Analyses over several data sets suggest that LC factor models typically fit data better and provide results that are easier to interpret than the corresponding LC cluster models. We also introduce a new graphical “biplot ” display for LC factor models and compare it to similar plots used in correspondence analysis and to a barycentric coordinate display for LC cluster models. We conclude by describing various model extensions and an approach for eliminating boundary solutions that we have implemented in a new computer program called Latent GOLD®.
Social stratification and cultural consumption: music in England
 European Sociological Review
, 2005
"... In this article we use recent survey data to test three arguments on the relationship between social stratification and cultural consumption: i.e. what we label as the homology, individualization and omnivore–univore arguments. We note various conceptual and methodological problems in the ways these ..."
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Cited by 17 (5 self)
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In this article we use recent survey data to test three arguments on the relationship between social stratification and cultural consumption: i.e. what we label as the homology, individualization and omnivore–univore arguments. We note various conceptual and methodological problems in the ways these arguments have been advanced, and stress in particular the importance of maintaining the Weberian distinction between class and status. We concentrate on musical consumption and apply latent class models to identify types of musical consumer. We then examine the social character of these types through a regression analysis that includes a range of demographic and stratification variables. As would be anticipated from a Weberian standpoint, type of musical consumption proves to be more closely associated with status, and also with education, than with class. In general, our results provide little support for the homology or individualisation arguments. They are more consonant with the omnivore–univore argument, although a number of qualifications to this are also suggested. Introduction—The Three
Building an identifiable latent class model with covariate effects on underlying and measured variables. Psychometrika 69
, 2004
"... In recent years, latent class models have proven useful for analyzing relationships between measured multiple indicators and covariates of interest. Such models summarize shared features of the multiple indicators as an underlying categorical variable, and the indicators’ substantive associations w ..."
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Cited by 17 (0 self)
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In recent years, latent class models have proven useful for analyzing relationships between measured multiple indicators and covariates of interest. Such models summarize shared features of the multiple indicators as an underlying categorical variable, and the indicators’ substantive associations with predictors are built directly and indirectly in unique model parameters. In this paper, we provide a detailed study on the theory and application of building models that allow mediated relationships between primary predictors and latent class membership, but also allow direct effects of secondary covariates on the indicators themselves. Theory for model identification is developed. We detail an ExpectationMaximization algorithm for parameter estimation, standard error calculation and convergent properties. Comparison of the proposed model with models underlying existing latent class modeling software is provided. A detailed analysis of how visual impairments affect older persons’ functioning requiring distance vision is used for illustration.
Bayesian inference with probability matrix decomposition models
 Journal of Educational and Behavioral Statistics
, 2001
"... check, psychometrics Probability Mcatrix Decompositioni models mtay bve uised to model observed binary associations between two sets of elements. More specifically, to explain observed associations betweeni two elements, it is assumed that B laitent Bernoulli variables are realized for each element ..."
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Cited by 10 (7 self)
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check, psychometrics Probability Mcatrix Decompositioni models mtay bve uised to model observed binary associations between two sets of elements. More specifically, to explain observed associations betweeni two elements, it is assumed that B laitent Bernoulli variables are realized for each element and that these variables are subsequently mapped into an observed data point accordingg to a prespecijied dererministic rule. In this papet; we present a fully Bayesian analysis for the PMD model makintg use of the Gibbs sampler. 7his approach is shown to yield three dislinct advantages: (a) in addition to posterior mean1 estim'lates it yields ( / 1 o<) % posterior intervals for the parameters. (b) it allows for an investigation of kypothesi7ed indeterminacies in the model's parameters and for thle visualization of the best possible reduction oJ ' the posterior distribution in a lowdimnensional space, and (c) it allows Jfr a broad range of goodnessof fit tests, making use of the technique of posterior predictive checks. To illustrate the approach, we applied the PMI) model to opinions of respondents of diferent countries concerning the possibility of contracting AID)S in a specific sitizationi.
Lectures on SimulationAssisted Statistical Inference
, 1996
"... this paper of writing moment conditions as a sequence of conditional moments was motivated by the work of Michael Keane on discrete panel data. The step of utilizing increasing sequences of conditional moments was suggested by work of Paul Ruud on adaptive search algorithms. Key elements in the proo ..."
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Cited by 9 (1 self)
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this paper of writing moment conditions as a sequence of conditional moments was motivated by the work of Michael Keane on discrete panel data. The step of utilizing increasing sequences of conditional moments was suggested by work of Paul Ruud on adaptive search algorithms. Key elements in the proof of the asymptotic efficiency of the partitioning algorithm were provided by Peter Bickel, Whitney Newey, and Keunkwan Ryu. A number of the results collected here were first presented at the Rotterdam Conference on Simulation Estimators, June 1991
A taxonomy of latent structure assumptions for probability matrix decomposition models
 Psychometrika
, 2003
"... A taxonomy of latent structure assumptions (LSAs) for probability matrix decomposition (PMD) models is proposed which includes the original PMD model (Maxis, De Boeck, & Van Mechelen, 1996) as well as a threeway extension of the multiple classification latent class model (Marls, 1999). It is s ..."
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Cited by 8 (6 self)
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A taxonomy of latent structure assumptions (LSAs) for probability matrix decomposition (PMD) models is proposed which includes the original PMD model (Maxis, De Boeck, & Van Mechelen, 1996) as well as a threeway extension of the multiple classification latent class model (Marls, 1999). It is shown that PMD models involving different LSAs axe actually restricted latent class models with latent variables that depend on some external variables. For parameter stimation a combined approach is proposed that uses both a modefinding algorithm (EM) and a samplingbased approach (Gibbs sampling). A simulation study is conducted to investigate the extent o which information criteria, specific model checks, and checks for global goodness of fit may help to specify the basic assumptions of the different PMD models. Finally, an application is described with models involving different latent structure assumptions for data on hostile behavior in frustrating situations. Key words: discrete data, matrix decomposition, Bayesian analysis, data augmentation, posterior predictive check, psychometrics. PMD models were introduced by Maris, De Boeck, and Van Mechelen (1996) to analyze threeway threemode binary data. The data typically represent associations between two types of elements that are repeatedly observed, for instance, persons who judge whether or not they
Latent variable modelling: A survey
 Scandinavian Journal of Statistics
"... ABSTRACT. Latent variable modelling has gradually become an integral part of mainstream statistics and is currently used for a multitude of applications in different subject areas. Examples of ‘traditional ’ latent variable models include latent class models, item–response models, common factor mode ..."
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Cited by 7 (1 self)
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ABSTRACT. Latent variable modelling has gradually become an integral part of mainstream statistics and is currently used for a multitude of applications in different subject areas. Examples of ‘traditional ’ latent variable models include latent class models, item–response models, common factor models, structural equation models, mixed or random effects models and covariate measurement error models. Although latent variables have widely different interpretations in different settings, the models have a very similar mathematical structure. This has been the impetus for the formulation of general modelling frameworks which accommodate a wide range of models. Recent developments include multilevel structural equation models with both continuous and discrete latent variables, multiprocess models and nonlinear latent variable models.
Addendum to the Latent GOLD User’s Guide: Upgrade Manual for Version 3.0
 Statistical Innovations Inc
, 2003
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