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72
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 58 (8 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.
Robust Detection of Degenerate Configurations whilst Estimating the Fundamental Matrix
, 1998
"... We present a new method for the detection of multiple solutions or degeneracy when estimating the Fundamental Matrix, with specific emphasis on robustness to data contamination (mismatches). The Fundamental Matrix encapsulates all the information on camera motion and internal parameters available f ..."
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Cited by 31 (3 self)
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We present a new method for the detection of multiple solutions or degeneracy when estimating the Fundamental Matrix, with specific emphasis on robustness to data contamination (mismatches). The Fundamental Matrix encapsulates all the information on camera motion and internal parameters available from image feature correspondences between two views. It is often used as a first step in structure from motion algorithms. If the set of correspondences is degenerate, then this structure cannot be accurately recovered and many solutions explain the data equally well. It is essential that we are alerted to such eventualities. As current feature matchers are very prone to mismatching the degeneracy detection method must also be robust to outliers. In this paper a definition of degeneracy is given and all two view nondegenerate and degenerate cases are catalogued in a logical way by introducing the language of varieties from algebraic geometry. It is then shown how each of the cases can be ro...
Bayesian model selection in structural equation models
, 1993
"... A Bayesian approach to model selection for structural equation models is outlined. This enables us to compare individual models, nested or nonnested, and also to search through the (perhaps vast) set of possible models for the best ones. The approach selects several models rather than just one, whe ..."
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Cited by 29 (10 self)
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A Bayesian approach to model selection for structural equation models is outlined. This enables us to compare individual models, nested or nonnested, and also to search through the (perhaps vast) set of possible models for the best ones. The approach selects several models rather than just one, when appropriate, and so enables us to take account, both informally and formally, of uncertainty about model structure when making inferences about quantities of interest. The approach tends to select simpler models than strategies based on multiple Pvaluebased tests. It may thus help to overcome the criticism of structural
People Are Variables Too: Multilevel Structural Equations Modeling
"... The article uses confirmatory factor analysis (CFA) as a template to explain didactically multilevel structural equation models (MLSEM) and to demonstrate the equivalence of general mixedeffects models and MLSEM. An intuitively appealing graphical representation of complex MLSEMs is introduced t ..."
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Cited by 8 (0 self)
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The article uses confirmatory factor analysis (CFA) as a template to explain didactically multilevel structural equation models (MLSEM) and to demonstrate the equivalence of general mixedeffects models and MLSEM. An intuitively appealing graphical representation of complex MLSEMs is introduced that succinctly describes the underlying model and its assumptions. The use of definition variables (i.e., observed variables used to fix model parameters to individual specific data values) is extended to the case of MLSEMs for clustered data with random slopes. Empirical examples of multilevel CFA and MLSEM with random slopes are provided along with scripts for fitting such models in SAS Proc Mixed, Mplus, and Mx. Methodological issues regarding estimation of complex MLSEMs and the evaluation of model fit are discussed. Further potential applications of MLSEMs are explored.
Distinguishing between latent classes and continuous factors: Resolution by maximum likelihood? Multivariate Behavioral Research
 Multivariate Behavioral Research
, 2006
"... Latent variable models exist with continuous, categorical, or both types of latent variables. The role of latent variables is to account for systematic patterns in the observed responses. This article has two goals: (a) to establish whether, based on observed responses, it can be decided that an und ..."
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Cited by 8 (2 self)
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Latent variable models exist with continuous, categorical, or both types of latent variables. The role of latent variables is to account for systematic patterns in the observed responses. This article has two goals: (a) to establish whether, based on observed responses, it can be decided that an underlying latent variable is continuous or categorical, and (b) to quantify the effect of sample size and class proportions on making this distinction. Latent variable models with categorical, continuous, or both types of latent variables are fitted to simulated data generated under different types of latent variable models. If an analysis is restricted to fitting continuous latent variable models assuming a homogeneous population and data stem from a heterogeneous population, overextraction of factors may occur. Similarly, if an analysis is restricted to fitting latent class models, overextraction of classes may occur if covariation between observed variables is due to continuous factors. For the datagenerating models used in this study, comparing the fit of different exploratory factor mixture models usually allows one to distinguish correctly between categorical and/or continuous latent variables. Correct model choice depends on class separation and withinclass sample size. Starting with the introduction of factor analysis by Spearman (1904), different types of latent variable models have been developed in various areas of the social sciences. Apart from proposed estimation methods, the most obvious differences between these early latent variable models concern the assumed distribution of the Correspondence concerning this article should be addressed to Gitta H. Lubke, Department of Psychology,
MML and Bayesianism: Similarities and Differences (Introduction to Minimum Encoding Inference  Part II)
, 1994
"... This paper continues the introduction to minimum encoding inference given by Oliver and Hand. This series of papers were written with the objective of providing an introduction to this area for statisticians. We examine the relationship between Bayesianism and Minimum Message Length (MML) inference. ..."
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Cited by 6 (0 self)
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This paper continues the introduction to minimum encoding inference given by Oliver and Hand. This series of papers were written with the objective of providing an introduction to this area for statisticians. We examine the relationship between Bayesianism and Minimum Message Length (MML) inference. We argue that MML augments Bayesian methods by providing a sound Bayesian method for point estimation which is invariant under nonlinear transformations. We explore the issues of invariance of estimators under nonlinear transformations, the role of the Fisher Information matrix in MML inference, and the apparent similarity between MML and the adoption of a Jeffreys' Prior. We then compare MML to an approximate method of Bayesian Model Class Selection. Despite apparent similarities in their expressions, the properties of the two approaches can be different.
Univariate and Bivariate Loglinear Models for Discrete Test Score Distributions
, 2000
"... The welldeveloped theory of exponential families of distributions is applied to the problem of fitting the univariate histograms and discrete bivariate frequency distributions that often arise in the analysis of test scores. These models are powerful tools for many forms of parametric data smoothi ..."
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Cited by 5 (0 self)
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The welldeveloped theory of exponential families of distributions is applied to the problem of fitting the univariate histograms and discrete bivariate frequency distributions that often arise in the analysis of test scores. These models are powerful tools for many forms of parametric data smoothing and are particularly wellsuited to problems in which there is little or no theory to guide a choice of probability models, e.g., smoothing a distribution to eliminate roughness and zero frequencies in order to equate scores from different tests. Attention is given to efficient computation of the maximum likelihood estimates of the parameters using Newton's Method and to computationally efficient methods for obtaining the asymptotic standard errors of the fitted frequencies and proportions. We discuss tools that can be used to diagnose the quality of the fitted frequencies for both the univariate and the bivariate cases. Five examples, using real data, are used to illustrate the methods of this paper.
Simultaneous genetic analysis of longitudinal means and covariance structure in the simplex model using twin data
 Behavior Genetics
, 1991
"... A longitudinal model based on the simplex model is presented to analyze simultaneously means and covariance structure using univariate longitudinal twin data. The objective of the model is to decompose the mean trend into components which can be attributed to those genetic and environmental factors ..."
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Cited by 4 (3 self)
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A longitudinal model based on the simplex model is presented to analyze simultaneously means and covariance structure using univariate longitudinal twin data. The objective of the model is to decompose the mean trend into components which can be attributed to those genetic and environmental factors which give rise to phenotypic individual differences and a component of unknown constitution which does not involve individual differences. Illustrations are given using simulated data and repeatedly measured weight obtained in a sample of 82 female twin pairs on sbc occasions. KEY WORDS: repeated measures; genetic and environmental covariance structure; mean trend; longitudinal twin data; genetic simplex mode; LISREL.
Traffic congestion and trucking managers’ use of automated routing and scheduling
 Transportation Research Part E: Logistics and Transportation Review
, 2001
"... Using data from a 2001 survey of managers of 700 trucking companies operating in California, we tested competing hypotheses about the relationship between managers’ perceptions of the impact of traffic congestion on their operations and their companies’ adoption of routing and scheduling software. D ..."
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Cited by 4 (1 self)
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Using data from a 2001 survey of managers of 700 trucking companies operating in California, we tested competing hypotheses about the relationship between managers’ perceptions of the impact of traffic congestion on their operations and their companies’ adoption of routing and scheduling software. Demand for automated routing and scheduling was found to be influenced directly by the need to reroute drivers, and indirectly by the need, generated by customers ’ schedules, to operate during congested periods. We were also able to identify which types of trucking companies are most affected by congestion and which types are more likely to adopt such software.
Bayesian Model Selection in Factor Analytic Models
"... Factor analytic models are widely used in social science applications to study latent traits, such as intelligence, creativity, stress and depression, that cannot be accurately measured with a single variable. In recent years, there has been a rise in the popularity of factor models due to their fle ..."
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Cited by 4 (1 self)
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Factor analytic models are widely used in social science applications to study latent traits, such as intelligence, creativity, stress and depression, that cannot be accurately measured with a single variable. In recent years, there has been a rise in the popularity of factor models due to their flexibility in characterizing multivariate data. For example, latent factor