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15
Bayesian Model Assessment In Factor Analysis
, 2004
"... Factor analysis has been one of the most powerful and flexible tools for assessment of multivariate dependence and codependence. Loosely speaking, it could be argued that the origin of its success rests in its very exploratory nature, where various kinds of datarelationships amongst the variable ..."
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Cited by 103 (10 self)
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Factor analysis has been one of the most powerful and flexible tools for assessment of multivariate dependence and codependence. Loosely speaking, it could be argued that the origin of its success rests in its very exploratory nature, where various kinds of datarelationships amongst the variables at study can be iteratively verified and/or refuted. Bayesian inference in factor analytic models has received renewed attention in recent years, partly due to computational advances but also partly to applied focuses generating factor structures as exemplified by recent work in financial time series modeling. The focus of our current work is on exploring questions of uncertainty about the number of latent factors in a multivariate factor model, combined with methodological and computational issues of model specification and model fitting. We explore reversible jump MCMC methods that build on sets of parallel Gibbs samplingbased analyses to generate suitable empirical proposal distributions and that address the challenging problem of finding e#cient proposals in highdimensional models. Alternative MCMC methods based on bridge sampling are discussed, and these fully Bayesian MCMC approaches are compared with a collection of popular model selection methods in empirical studies.
Fullinformation item factor analysis
 Applied Psychological Measurement
, 1988
"... 1EEEEEc7EE m11hEEEhEhE mEEMEEEEE I."'.MEMME 1.1.1 1112 2. ..."
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Cited by 89 (5 self)
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Recent developments in the factor analysis of categorical variables
 Journal of Educational Statistics
, 1986
"... ABSTRACT. Despite known shortcomings of the procedure, exploratory factor analysis of dichotomous test items has been limited, until recently, to unweighted analyses of matrices of tetrachoric correlations. Superior methods have begun to appear in the literature, in professional symposia, and in com ..."
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Cited by 55 (0 self)
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ABSTRACT. Despite known shortcomings of the procedure, exploratory factor analysis of dichotomous test items has been limited, until recently, to unweighted analyses of matrices of tetrachoric correlations. Superior methods have begun to appear in the literature, in professional symposia, and in computer programs. This paper places these developments in a unified framework, from a review of the classical common factor model for measured variables through generalized least squares and marginal maximum likelihood solutions for dichotomous data. Further extensions of the model are also reported as work in progress. Under classical Thurstonian factor analysis (Thurstone, 1947), values of p measured variables are modeled as linear functions of some smaller number of m continuous latent variables, the "factors " that account for the correlations among the observed variables. The usual objectives in factor analysis are (a) to determine the number of factors that provide a satisfactory fit to the observed correlation matrix and (b) to estimate the regression coefficients of the observed variables on the factors—all this, it is hoped, leading to a more
Bayesian Estimation and Testing of Structural Equation Models
 Psychometrika
, 1999
"... The Gibbs sampler can be used to obtain samples of arbitrary size from the posterior distribution over the parameters of a structural equation model (SEM) given covariance data and a prior distribution over the parameters. Point estimates, standard deviations and interval estimates for the parameter ..."
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Cited by 43 (10 self)
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The Gibbs sampler can be used to obtain samples of arbitrary size from the posterior distribution over the parameters of a structural equation model (SEM) given covariance data and a prior distribution over the parameters. Point estimates, standard deviations and interval estimates for the parameters can be computed from these samples. If the prior distribution over the parameters is uninformative, the posterior is proportional to the likelihood, and asymptotically the inferences based on the Gibbs sample are the same as those based on the maximum likelihood solution, e.g., output from LISREL or EQS. In small samples, however, the likelihood surface is not Gaussian and in some cases contains local maxima. Nevertheless, the Gibbs sample comes from the correct posterior distribution over the parameters regardless of the sample size and the shape of the likelihood surface. With an informative prior distribution over the parameters, the posterior can be used to make inferences about the parameters of underidentified models, as we illustrate on a simple errorsinvariables model.
Bayesian Inference in Factor Analysis  Revised
, 1997
"... We propose a new method for analyzing factor analysis models using a Bayesian approach. Normal theory is used for the sampling distribution, and we adopt a model with a full disturbance covariance matrix. Using vague and natural conjugate priors for the parameters, we find that the marginal posterio ..."
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Cited by 3 (0 self)
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We propose a new method for analyzing factor analysis models using a Bayesian approach. Normal theory is used for the sampling distribution, and we adopt a model with a full disturbance covariance matrix. Using vague and natural conjugate priors for the parameters, we find that the marginal posterior distribution of the factor scores is approximately a matrix Tdistribution, in large samples. This explicit result permits simple interval estimation and hypothesis testing of the factor scores. Explicit point and interval estimators of the factor score elements, in large samples, are obtained as means as means of the respective marginal posterior distributions. Factor loadings are estimated as joint modes (with factor scores), or alternatively as means or modes of the distribution of the factor loadings conditional upon the estimated factor scores. Disturbance variances and covariances are estimated conditional upon the estimated factor scores and factor loadings. This revision includes the correction of some typographical errors and some revised computations, plus an appendix that provides some intermediate results. 1
A SAS Interface for Bayesian Analysis With WinBUGS
, 2008
"... This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan or sublicensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express ..."
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This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan or sublicensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. Structural Equation Modeling, 15:705–728, 2008 Copyright © Taylor & Francis Group, LLC ISSN: 10705511 print/15328007 online
A BAYES IAN APPROACH TO NONLINEAR LATENT VARIABLE MODELS US ING THE G IBBS SAMPLER AND THE METROPOLISHAST INGS ALGORITHM
, 1998
"... Nonlinear latent variable models are specified that include quadratic forms and interactions of latent regressor variables as pecial cases. To estimate the parameters, the models are put in a Bayesian framework with conjugate priors for the parameters. The posterior distributions f the parameters an ..."
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Nonlinear latent variable models are specified that include quadratic forms and interactions of latent regressor variables as pecial cases. To estimate the parameters, the models are put in a Bayesian framework with conjugate priors for the parameters. The posterior distributions f the parameters and the latent variables are estimated using Markov chain Monte Carlo methods uch as the Gibbs sampler and the MetropolisHastings algorithm. The proposed estimation methods are illustrated by two simulation studies and by the estimation of a nonlinear model for the dependence of performance on task complexity and goal specificity using empirical data.
Dealing with rotational invariance in Bayesian confirmatory factor analysis ∗
, 2011
"... on an earlier draft of the paper and on the R code. 1 Dealing with rotational invariance in Bayesian confirmatory factor analysis A wellknown inherent ambiguity in factor models is that factors and factor loadings can only be identified up to an orthogonal rotation. In confirmatory factor analysis ..."
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on an earlier draft of the paper and on the R code. 1 Dealing with rotational invariance in Bayesian confirmatory factor analysis A wellknown inherent ambiguity in factor models is that factors and factor loadings can only be identified up to an orthogonal rotation. In confirmatory factor analysis (CFA), different options exist for placing constraints aimed at ensuring unique identification of the model parameters. For simple CFA structures, when each observed variable loads on exactly one factor, different sets of constraints are equivalent with respect to model fit. However, this may no longer be the case when some variables are permitted to load on more than one factor. Following a Bayesian approach to factor analysis, we illustrate that naive implementation of rotational constraints can be problematic for Bayesian inference. Dealing with rotational invariance by constraining some loadings to be one or positive may result in nontrivial multimodality in the likelihood and in modeswitching behavior with Markov chain Monte Carlo samplers. We present a simple approach for dealing with rotational invariance in Bayesian confirmatory factor analysis. We demonstrate our approach on simulated data and further illustrate it on a classic bifactor data set.