Showing papers on "Latent variable model published in 2006"

Confirmatory Factor Analysis for Applied Research

Abstract: "With its emphasis on practical and conceptual aspects, rather than mathematics or formulas, this accessible book has established itself as the go-to resource on confirmatory factor analysis (CFA). Detailed, worked-through examples drawn from psychology, management, and sociology studies illustrate the procedures, pitfalls, and extensions of CFA methodology. The text shows how to formulate, program, and interpret CFA models using popular latent variable software packages (LISREL, Mplus, EQS, SAS/CALIS); understand the similarities and differences between CFA and exploratory factor analysis (EFA); and report results from a CFA study. It is filled with useful advice and tables that outline the procedures. The companion website offers data and program syntax files for most of the research examples, as well as links to CFA-related resources. New to This Edition *Updated throughout to incorporate important developments in latent variable modeling. *Chapter on Bayesian CFA and multilevel measurement models. *Addresses new topics (with examples): exploratory structural equation modeling, bifactor analysis, measurement invariance evaluation with categorical indicators, and a new method for scaling latent variables. *Utilizes the latest versions of major latent variable software packages"--

ltm: An R Package for Latent Variable Modeling and Item Response Theory Analyses

Abstract: The R package ltm has been developed for the analysis of multivariate dichotomous and polytomous data using latent variable models, under the Item Response Theory approach. For dichotomous data the Rasch, the Two-Parameter Logistic, and Birnbaum’s Three-Parameter models have been implemented, whereas for polytomous data Semejima’s Graded Response model is available. Parameter estimates are obtained under marginal maximum likelihood using the Gauss-Hermite quadrature rule. The capabilities and features of the package are illustrated using two real data examples.

On the Merits of Orthogonalizing Powered and Product Terms: Implications for Modeling Interactions Among Latent Variables

Abstract: The goals of this article are twofold: (a) briefly highlight the merits of residual centering for representing interaction and powered terms in standard regression contexts (e.g., Lance, 1988), and (b) extend the residual centering procedure to represent latent variable interactions. The proposed method for representing latent variable interactions has potential advantages over extant procedures. First, the latent variable interaction is derived from the observed covariation pattern among all possible indicators of the interaction. Second, no constraints on particular estimated parameters need to be placed. Third, no recalculations of parameters are required. Fourth, model estimates are stable and interpretable. In our view, the orthogonalizing approach is technically and conceptually straightforward, can be estimated using any structural equation modeling software package, and has direct practical interpretation of parameter estimates. Its behavior in terms of model fit and estimated standard errors is v...

A Non-arbitrary Method of Identifying and Scaling Latent Variables in SEM and MACS Models

Abstract: A non-arbitrary method for the identification and scale setting of latent variables in general structural equation modeling is introduced This particular technique provides identical model fit as traditional methods (eg, the marker variable method), but it allows one to estimate the latent parameters in a nonarbitrary metric that reflects the metric of the measured indicators This technique, therefore, is particularly useful for mean and covariance structures (MACS) analyses, where the means of the indicators and latent constructs are of key interest By introducing this alternative method of identification and scale setting, researchers are provided with an additional tool for conducting MACS analyses that provides a meaningful and nonarbitrary scale for the estimates of the latent variable parameters Importantly, this tool can be used with single-group single-occasion models as well as with multiple-group models, multiple-occasion models, or both

Estimating Generalizability to a Latent Variable Common to All of a Scale's Indicators: A Comparison of Estimators for ωh

Abstract: The extent to which a scale score generalizes to a latent variable common to all of the scale’s indicators is indexed by the scale’s general factor saturation. Seven techniques for estimating this parameter—omegahierarchical (ωh)—are compared in a series of simulated data sets. Primary comparisons were based on 160 artificial data sets simulating perfectly simple and symmetric structures that contained four group factors, and an additional 200 artificial data sets confirmed large standard deviations for two methods in these simulations when a general factor was absent. Major findings were replicated in a series of 40 additional artificial data sets based on the structure of a real scale widely believed to contain three group factors of unequal size and less than perfectly simple structure. The results suggest that alpha and methods based on either the first unrotated principal factor or component should be rejected as estimates of ωh. Index terms: generalizability, alpha, omega, factor analysis, measurement, reliability. Many scales are assumed by their developers and users to be primarily a measure of one latent variable. When it is also assumed that the scale conforms to the effect indicator model of measurement (as is almost always the case in psychological assessment), it is important to support such an interpretation with evidence regarding the internal structure of that scale (Bollen & Lennox, 1991). In particular, it is important to examine two related properties pertaining to the internal structure of such a scale. The first property relates to whether all the indicators forming the scale measure a latent variable in common. The second internal structural property pertains to the proportion of variance in the scale scores (derived from summing or averaging the indicators) accounted for by this latent variable that is common to all the indicators (Cronbach, 1951; McDonald, 1999; Revelle, 1979). That is, if an effect indicator scale is primarily a measure of one latent variable common to all the indicators forming the scale, then that latent variable should account for the majority of the variance in the scale scores. Put differently, this variance ratio provides important information about the sampling fluctuations when estimating individuals’ standing on a latent variable common to all the indicators arising from the sampling of indicators (i.e., when dealing with either Type 2 or

Distinguishing Between Latent Classes and Continuous Factors: Resolution by Maximum Likelihood?

Abstract: 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 data-generating...

Variational Bayesian multinomial probit regression with Gaussian process priors

Abstract: It is well known in the statistics literature that augmenting binary and polychotomous response models with gaussian latent variables enables exact Bayesian analysis via Gibbs sampling from the parameter posterior. By adopting such a data augmentation strategy, dispensing with priors over regression coefficients in favor of gaussian process (GP) priors over functions, and employing variational approximations to the full posterior, we obtain efficient computational methods for GP classification in the multiclass setting. The model augmentation with additional latent variables ensures full a posteriori class coupling while retaining the simple a priori independent GP covariance structure from which sparse approximations, such as multiclass informative vector machines (IVM), emerge in a natural and straightforward manner. This is the first time that a fully variational Bayesian treatment for multiclass GP classification has been developed without having to resort to additional explicit approximations to the nongaussian likelihood term. Empirical comparisons with exact analysis use Markov Chain Monte Carlo (MCMC) and Laplace approximations illustrate the utility of the variational approximation as a computationally economic alternative to full MCMC and it is shown to be more accurate than the Laplace approximation.

Learning the Structure of Linear Latent Variable Models

Abstract: We describe anytime search procedures that (1) find disjoint subsets of recorded variables for which the members of each subset are d-separated by a single common unrecorded cause, if such exists; (2) return information about the causal relations among the latent factors so identified. We prove the procedure is point-wise consistent assuming (a) the causal relations can be represented by a directed acyclic graph (DAG) satisfying the Markov Assumption and the Faithfulness Assumption; (b) unrecorded variables are not caused by recorded variables; and (c) dependencies are linear. We compare the procedure with standard approaches over a variety of simulated structures and sample sizes, and illustrate its practical value with brief studies of social science data sets. Finally, we consider generalizations for non-linear systems.

A Probabilistic Latent Variable Model for Acoustic Modeling

Abstract: In this paper we describe a model developed for the analysis of acoustic spectra. Unlike decompositions techniques that can result in difficult to interpret results this model explicitly models spectra as distributions and extracts sets of additive and semantically useful components that facilitate a variety of applications ranging from source separation, denoising, music transcription and sound recognition. This model is probabilistic in nature and is easily extended to produce sparse codes, and discover transform invariant components which can be optimized for particular applications.

Comparing groups on latent variables: A structural equation modeling approach

Abstract: Structural equation modeling (SEM) provides a dependable framework for testing differences among groups on latent variables (constructs, factors). The purpose of this article is to illustrate SEM-based testing for group mean differences on latent variables. Related procedures of confirmatory factor analysis and testing for measurement invariance across compared groups are also presented in the context of rehabilitation research.

Building a better model: an introduction to structural equation modelling.

Abstract: Confirmatory factor analysis (CFA) and structural equation modelling (SEM) are powerful extensions of path analysis, which was described in a previous article in this series. CFA differs from the more traditional exploratory factor analysis in that the relations among the variables are specified a priori, which permits more powerful tests of construct validity for scales. It can also be used to compare different versions of a scale (for example, English and French) and to determine whether the scale performs equivalently in different groups (for example, men and women). SEM expands on path analysis by allowing paths to be drawn between latent variables (which, in other techniques, are called factors or hypothetical constructs), that is, variables that are not seen directly but, rather, through their effect on observable variables, such as questionnaires and behavioural measures. Each latent variable and its associated measured variables form small CFAs, with the added advantage that the correlations among the variables can be corrected for the unreliability of the measures.

Book Review: Latent Variable Models: An Introduction to Factor, Path, and Structural Equation Analysis (4th ed.)

Abstract: The first edition of the book, published in 1987, was one of the early and popular texts on factor, path, and structural models. In its fourth edition, it remains an excellent text on basic principles and analyses of covariance structures for researchers in the fields of education, psychology, and social sciences. In recent decades, confirmatory factor analysis, path analysis, and structural equation modeling (SEM) have become basic research tools. Loehlin argues that these methods are ‘‘at heart’’ one, and the path diagram approach makes these methods accessible to students who are not very mathematical. This book explains a number of statistical methods, such as factor analysis, path analysis, and structural equation models, and does so in a clear, easy-to-grasp manner and with fully worked-out examples. The book represents an approach that is neither too mathematical nor merely simplistic, focused on the mechanics of running analyses. Loehlin uses path diagrams with a minimum of equations to present structural equation and factor analysis models. The book departs from other introductory texts because it is not based on any particular software (e.g., AMOS, EQS, or LISREL) and provides examples from several widely used software programs. The style of the book is easy to understand, and notes at the end of each chapter provide additional technical references for the interested readers. For those familiar with previous editions of the book, the overall contents of the book would look familiar. New material in the fourth edition includes missing data, nonnormality, mediation, and factorial invariance. Following are this reviewer’s comments on the contents of the book. Chapter 1 focuses on underlying relationships in models via path diagrams and introduces the reader to path models with observed and latent variables equations of path analysis, underand overdetermination of path models, and factor models. It provides a lucid coverage on basic ideas about path models via diagrams and sets the stage for further elucidation of statistical methods to study relationships among variables using factor, path, and structural models. Chapter 2 describes how models are fit to data, giving the reader a feel for an iterative minimization process. Topics addressed in the chapter are matrix formulation of path models, modelfitting programs (with examples from LISREL-SIMPLIS, EQS, and Mx), fit functions, chi-square tests, root mean square error of approximation (RMSEA), power to reject an incorrect model, and treatment of missing data. These topics apply to all models and provide the reader a firm grasp on what the author refers to as latent variable analysis.

Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities.

Abstract: The purpose of this paper is to introduce a new method for fitting item response theory models with the latent population distribution estimated from the data using splines. A spline-based density estimation system provides a flexible alternative to existing procedures that use a normal distribution, or a different functional form, for the population distribution. A simulation study shows that the new procedure is feasible in practice, and that when the latent distribution is not well approximated as normal, two-parameter logistic (2PL) item parameter estimates and expected a posteriori scores (EAPs) can be improved over what they would be with the normal model. An example with real data compares the new method and the extant empirical histogram approach.

Bayesian dynamic modeling of latent trait distributions

Abstract: SUMMARY Studies of latent traits often collect data for multiple items measuring different aspects of the trait. For such data, it is common to consider models in which the different items are manifestations of a normal latent variable, which depends on covariates through a linear regression model. This article proposes a flexible Bayesian alternative in which the unknown latent variable density can change dynamically in location and shape across levels of a predictor. Scale mixtures of underlying normals are used in order to model flexibly the measurement errors and allow mixed categorical and continuous scales. A dynamic mixture of Dirichlet processes is used to characterize the latent response distributions. Posterior computation proceeds via a Markov chain Monte Carlo algorithm, with predictive densities used as a basis for inferences and evaluation of model fit. The methods are illustrated using data from a study of DNA damage in response to oxidative stress.

Latent Variable Models for Semantic Orientations of Phrases

Abstract: We propose models for semantic orientations of phrases as well as classification methods based on the models. Although each phrase consists of multiple words, the semantic orientation of the phrase is not a mere sum of the orientations of the component words. Some words can invert the orientation. In order to capture the property of such phrases, we introduce latent variables into the models. Through experiments, we show that the proposed latent variable models work well in the classification of semantic orientations of phrases and achieved nearly 82% classification accuracy.

Ramsay-curve item response theory (RC-IRT) to detect and correct for nonnormal latent variables.

Abstract: Popular methods for fitting unidimensional item response theory (IRT) models to data assume that the latent variable is normally distributed in the population of respondents, but this can be unreasonable for some variables. Ramsay-curve IRT (RC-IRT) was developed to detect and correct for this nonnormality. The primary aims of this article are to introduce RC-IRT less technically than it has been described elsewhere; to evaluate RC-IRT for ordinal data via simulation, including new approaches for model selection; and to illustrate RC-IRT with empirical examples. The empirical examples demonstrate the utility of RC-IRT for real data, and the simulation study indicates that when the latent distribution is skewed, RC-IRT results can be more accurate than those based on the normal model. Along with a plot of candidate curves, the Hannan-Quinn criterion is recommended for model selection.

On the Use of Structural Equation Modeling in Health Communication Research

Abstract: Structural equation modeling (SEM) is a multivariate technique suited for testing proposed relations between variables. In this article, the authors discuss the potential for SEM as a tool to advance health communication research both statistically and conceptually. Specifically, the authors discuss the advantages that latent variable modeling in SEM affords researchers by extracting measurement error. In addition, they argue that SEM is useful in understanding communication as a complex set of relations between variables. Moreover, the authors articulate the possibility for examining communication as an agent, mediator, and an outcome. Finally, they review the application of SEM to recursive models, interactions, and confirmatory factor analysis.

Sampling Correlation Matrices in Bayesian Models With Correlated Latent Variables

Abstract: Hierarchical model specifications using latent variables are frequently used to reflect correlation structure in data. Motivated by the structure of a Bayesian multivariate probit model, we demonstrate a parameter-extended Metropolis-Hastings algorithm for sampling from the posterior distribution of a correlation matrix. Our sampling algorithms lead directly to two readily interpretable families of prior distributions for a correlation matrix. The methodology is illustrated through a simulation study and through an application with repeated binary outcomes on individuals from a study of a suicide prevention intervention.

Explanatory Item Response Models: A Generalized Linear and Nonlinear Approach by P. de Boeck and M. Wilson and Generalized Latent Variable Modeling: Multilevel, Longitudinal and Structural Equation Models by A. Skrondal and S. Rabe-Hesketh

Abstract: 2004 saw the publication of two interesting and useful books on the general topic of complex statistical models for behavioral science data. This review discusses both, comparing and contrasting them. The first book is an edited volume by Paul de Boeck (KU-Leuven) and Mark Wilson (UC-Berkeley), titled Explanatory item response modeling: A generalized linear and nonlinear approach (henceforth EIRM). The second is by Anders Skrondal (Norwegian Institute of Public Health) and Sophia Rabe-Hesketh (UC-Berkeley), titled Generalized latent variable modeling: Multilevel, longitudinal and structural equation models (henceforth GLVM). The general focus of both books is to provide an integrative framework for the disparate set of models existing in psychometrics, econometrics, biometrics, and statistics. As the authors of GLVM note in the Introduction, there is a substantial degree of balkanization of these disciplines, even though the needs of practitioners in them are often similar. This is unfortunate (if, perhaps, unavoidable) because it leads to frequent reinvention of the wheel. For instance, econometricians have developed a number of interesting statistical models for modeling discrete choice behavior— many of which are built explicitly on choice models in psychology—that are in turn very similar to models from educational measurement, signal detection, or bioassay. Technologies developed by the different groups of researchers often prove useful in addressing problems faced in all literatures. However, because developments exist in largely parallel bodies of work, this fact often goes unrecognized and so different groups are left to reinvent developments that may well be old somewhere else, possibly even superseded by better techniques. Similar things could be said about the literatures on multilevel models or, indeed, any number of other areas. GLVM has as its explicit focus the unification of these literatures. EIRM is less ambitious but still has as its goal the synthesis of the truly vast number of models falling under the banner of item response theory in terms of the generalized linear and nonlinear mixed models.

Classification using Hierarchical Naïve Bayes models

Abstract: Classification problems have a long history in the machine learning literature. One of the simplest, and yet most consistently well-performing set of classifiers is the Naive Bayes models. However, an inherent problem with these classifiers is the assumption that all attributes used to describe an instance are conditionally independent given the class of that instance. When this assumption is violated (which is often the case in practice) it can reduce classification accuracy due to "information double-counting" and interaction omission. In this paper we focus on a relatively new set of models, termed Hierarchical Naive Bayes models. Hierarchical Naive Bayes models extend the modeling flexibility of Naive Bayes models by introducing latent variables to relax some of the independence statements in these models. We propose a simple algorithm for learning Hierarchical Naive Bayes models in the context of classification. Experimental results show that the learned models can significantly improve classification accuracy as compared to other frameworks.

Noisy-OR Component Analysis and its Application to Link Analysis

Abstract: We develop a new component analysis framework, the Noisy-Or Component Analyzer (NOCA), that targets high-dimensional binary data. NOCA is a probabilistic latent variable model that assumes the expression of observed high-dimensional binary data is driven by a small number of hidden binary sources combined via noisy-or units. The component analysis procedure is equivalent to learning of NOCA parameters. Since the classical EM formulation of the NOCA learning problem is intractable, we develop its variational approximation. We test the NOCA framework on two problems: (1) a synthetic image-decomposition problem and (2) a co-citation data analysis problem for thousands of CiteSeer documents. We demonstrate good performance of the new model on both problems. In addition, we contrast the model to two mixture-based latent-factor models: the probabilistic latent semantic analysis (PLSA) and latent Dirichlet allocation (LDA). Differing assumptions underlying these models cause them to discover different types of structure in co-citation data, thus illustrating the benefit of NOCA in building our understanding of high-dimensional data sets.

Analysing Demand for Suburban Trips: A Mixed RP/SP Model with Latent Variables and Interaction Effects

Abstract: We analyse mode choice behaviour for suburban trips in the Grand Canary island using mixed revealed preference (RP)/stated preference (SP) information. The SP choice experiment allowed for interactions among the main policy variables: travel cost, travel time and frequency, and also to test the influence of latent variables such as comfort. It also led to discuss additional requirements on the size and sign of the estimated model parameters, to assess model quality when interactions are present. The RP survey produced data on actual trip behaviour and was used to adapt the SP choice experiment. During the specification searches we detected the presence of income effect and were able to derive willingness-to-pay measures, such as the subjective value of time, which varied among individuals. We also studied the systematic heterogeneity in individual tastes through the specification of models allowing for interactions between level-of-service and socio-economic variables. We con- cluded examining the sensitivity of travellers' behaviour to various policy scenarios. In particular, it seems that contrary to political opinion, in a crowded island policies penalising the use of the private car seem to have a far greater impact in terms of bus patronage than policies implying direct improvements to the public transport service.

Advances in behavioral genetics modeling using Mplus: applications of factor mixture modeling to twin data.

Abstract: This article discusses new latent variable techniques developed by the authors. As an illustration, a new factor mixture model is applied to the monozygotic-dizygotic twin analysis of binary items measuring alcohol-use disorder. In this model, heritability is simultaneously studied with respect to latent class membership and within-class severity dimensions. Different latent classes of individuals are allowed to have different heritability for the severity dimensions. The factor mixture approach appears to have great potential for the genetic analyses of heterogeneous populations. Generalizations for longitudinal data are also outlined.

Likelihood inference for a class of latent Markov models under linear hypotheses on the transition probabilities

Abstract: Summary. For a class of latent Markov models for discrete variables having a longitudinal structure, we introduce an approach for formulating and testing linear hypotheses on the transition probabilities of the latent process. For the maximum likelihood estimation of a latent Markov model under hypotheses of this type, we outline an EM algorithm that is based on well-known recursions in the hidden Markov literature. We also show that, under certain assumptions, the asymptotic null distribution of the likelihood ratio statistic for testing a linear hypothesis on the transition probabilities of a latent Markov model, against a less stringent linear hypothesis on the transition probabilities of the same model, is of X2 type. As a particular case, we derive the asymptotic distribution of the likelihood ratio statistic between a latent class model and its latent Markov version, which may be used to test the hypothesis of absence of transition between latent states. The approach is illustrated through a series of simulations and two applications, the first of which is based on educational testing data that have been collected within the National Assessment of Educational Progress 1996, and the second on data, concerning the use of marijuana, which have been collected within the National Youth Survey 19761980.

A Class of Latent Marginal Models for Capture–Recapture Data With Continuous Covariates

Abstract: We introduce a new family of latent class models for the analysis of capture–recapture data where continuous covariates are available. The present approach exploits recent advances in marginal parameterizations to model simultaneously, and conditionally on individual covariates, the size of the latent classes, the marginal probabilities of being captured by each list given the latent, and possible higher-order marginal interactions among lists conditionally on the latent. An EM algorithm for maximum likelihood estimation is described, and an expression for the expected information matrix is derived. In addition, a new method for computing confidence intervals for the size of the population having given covariate configurations is proposed and its asymptotic properties are derived. Applications to data on patients with human immunodeficiency virus, in the region of Veneto, Italy, and to new cases of cancer in Tuscany are discussed.

The EM Algorithm for Factor Analyzers:An Extension with Latent Variable

Abstract: This paper assume that the continuous latent variable(common factor) is related to an observed covariates through the multivariate linear regression model on the basis of traditional factor analyzers(FA).EM algorithm is used to estimate model parameters.A detailed derivation of its is proposed in the context.

Information-Theoretic Latent Distribution Modeling: Distinguishing Discrete and Continuous Latent Variable Models.

Abstract: Distinguishing between discrete and continuous latent variable distributions has become increasingly important in numerous domains of behavioral science. Here, the authors explore an information-theoretic approach to latent distribution modeling, in which the ability of latent distribution models to represent statistical information in observed data is emphasized. The authors conclude that loss of statistical information with a decrease in the number of latent values provides an attractive basis for comparing discrete and continuous latent variable models. Theoretical considerations as well as the results of 2 Monte Carlo simulations indicate that information theory provides a sound basis for modeling latent distributions and distinguishing between discrete and continuous latent variable models in particular.

Aligning music audio with symbolic scores using a hybrid graphical model

Abstract: We present a new method for establishing an alignment between a polyphonic musical score and a corresponding sampled audio performance. The method uses a graphical model containing both latent discrete variables, corresponding to score position, as well as a latent continuous tempo process. We use a simple data model based only on the pitch content of the audio signal. The data interpretation is defined to be the most likely configuration of the hidden variables, given the data, and we develop computational methodology to identify or approximate this configuration using a variant of dynamic programming involving parametrically represented continuous variables. Experiments are presented on a 55-minute hand-marked orchestral test set.