Showing papers on "Latent variable model published in 2009"

Using PLS path modeling for assessing hierarchial construct models: guidelines and impirical illustration

Abstract: In this paper, the authors show that PLS path modeling can be used to assess a hierarchical construct model. They provide guidelines outlining four key steps to construct a hierarchical construct model using PLS path modeling. This approach is illustrated empirically using a reflective, fourth-order latent variable model of online experiential value in the context of online book and CD retailing. Moreover, the guidelines for the use of PLS path modeling to estimate parameters in a hierarchical construct model are extended beyond the scope of the empirical illustration. The findings of the empirical illustration are used to discuss the use of covariance-based SEM versus PLS path modeling. The authors conclude with the limitations of their study and suggestions for future research.

Latent Class and Latent Transition Analysis: With Applications in the Social, Behavioral, and Health Sciences

Abstract: List of Figures. List of Tables. Acknowledgments. Acronyms. Part I Fundamentals. 1. General Introduction. 1.1 Overview. 1.2 Conceptual foundation and brief history of the latent class model. 1.3 Why select a categorical latent variable approach? 1.4 Scope of this book. 1.5 Empirical example of LCA: Adolescent delinquency. 1.6 Empirical example of LTA: Adolescent delinquency. 1.7 About this book. 1.8 The examples in this book. 1.9 Software. 1.10 Additional resources: The book's web site. 1.11 Suggested supplemental readings. 1.12 Points to remember. 1.13 What's next. 2. The latent class model. 2.1 Overview. 2.2 Empirical example: Pubertal development. 2.3 The role of item-response probabilities to label the latent classes in the pubertal development example. 2.4 Empirical example: Health risk behaviors. 2.5 LCA: Model and notation. 2.6 Suggested supplemental readings. 2.7 Points to remember. 2.8 What's next. 3. The relation between the latent variable and its indicators. 3.1 Overview. 3.2 The latent class measurement model. 3.3 Homogeneity and latent class separation. 3.4 The precision with which the observed variables measure the latent variable. 3.5 Expressing the degree of uncertainty: Mean posterior probabilities and entropy. 3.6 Points to remember. 3.7 What's next. 4. Parameter estimation and model selection. 4.1 Overview. 4.2 Maximum Likelihood estimation. 4.3 Model fit and model selection. 4.4 Finding the ML solution. 4.5 Empirical example of using many starting values. 4.6 Empirical examples of selecting the number of latent classes. 4.7 More about parameter restrictions. 4.8 Standard errors. 4.9 Suggested supplemental readings. 4.10 Points to remember. 4.11 What's next. Part II Advanced LCA. 5. Multiple-group LCA. 5.1 Overview. 5.2 Introduction. 5.3 Multiple-group LCA: Model and notation. 5.4 Computing the number of parameters estimated. 5.5 Expressing group differences in the LCA model. 5.6 Measurement invariance. 5.7 Establishing whether the number of latent classes is identical across groups. 5.8 Establishing invariance of item-response probabilities across groups. 5.9 Interpretation when measurement invariance does not hold. 5.10 Strategies when measurement invariance does not hold. 5.11 Significant differences and important differences. 5.12 Testing equivalence of latent class prevalences across groups. 5.13 Suggested supplemental readings. 5.14 Points to remember. 5.15 What's next. 6. LCA with Covariates. 6.1 Overview. 6.2 Empirical example: Positive health behaviors. 6.3 Preparing to conduct LCA with covariates. 6.4 LCA with covariates: Model and notation. 6.5 Hypothesis testing in LCA with covariates. 6.6 Interpretation of the intercepts and regression coefficients. 6.7 Empirical examples of LCA with a single covariate. 6.8 Empirical example of multiple covariates and interaction terms. 6.9 Multiple-group LCA with covariates: Model and notation. 6.10 Grouping variable or covariate? 6.11 Use of a Bayesian prior to stabilize estimation. 6.12 Binomial logistic regression. 6.13 Suggested supplemental readings. 6.14 Points to remember. 6.15 What's next. Part III Latent Class Models for Longitudinal Data. 7. RMLCA and LTA. 7.1 Overview. 7.2 RMLCA. 7.3 LTA. 7.4 LTA model parameters. 7.5 LTA: Model and notation. 7.6 Degrees of freedom associated with latent transition models. 7.7 Empirical example: Adolescent depression. 7.8 Empirical example: Dating and sexual risk behavior. 7.9 Interpreting what a latent transition model reveals about change. 7.10 Parameter restrictions in LTA. 7.11 Testing the hypotheses of measurement invariance across times. 7.12 Testing the hypotheses about change between times. 7.13 Relation between RMLCA and LTA. 7.14 Invariance of the transition probability matrix. 7.15 Suggested supplemental readings. 7.16 Points to remember. 7.17 What's next. 8. Multiple-Group LTA and LTA with Covariates. 8.1 Overview. 8.2 LTA with a grouping variable. 8.3 Multiple-group LTA: Model and notation. 8.4 Computing the number of parameters estimated in multiple-group latent transition models. 8.5 Hypothesis tests concerning group differences: General consideration. 8.6 Overall hypothesis tests about group differences in LTA. 8.7 Testing the hypothesis of equality of latent status prevalences. 8.8 Testing the hypothesis of equality of transition probabilities. 8.9 Incorporating covariates in LTA. 8.10 LTA with covariates: Model and notation. 8.11 Hypothesis testing in LTA with covariates. 8.12 Including both a grouping variable and a covariate in LTA. 8.13 Binomial logistic regression. 8.14 The relation between multiple-group LTA and LTA with a covariate. 8.15 Suggested supplemental readings. 8.16 Points to remember. Topic Index. Author Index.

Latent Variable Modeling of Differences and Changes with Longitudinal Data

Abstract: This review considers a common question in data analysis: What is the most useful way to analyze longitudinal repeated measures data? We discuss some contemporary forms of structural equation models (SEMs) based on the inclusion of latent variables. The specific goals of this review are to clarify basic SEM definitions, consider relations to classical models, focus on testable features of the new models, and provide recent references to more complete presentations. A broader goal is to illustrate why so many researchers are enthusiastic about the SEM approach to data analysis. We first outline some classic problems in longitudinal data analysis, consider definitions of differences and changes, and raise issues about measurement errors. We then present several classic SEMs based on the inclusion of invariant common factors and explain why these are so important. This leads to newer SEMs based on latent change scores, and we explain why these are useful.

Understanding and Using Factor Scores: Considerations for the Applied Researcher

Abstract: Following an exploratory factor analysis, factor scores may be computed and used in subsequent analyses. Factor scores are composite variables which provide information about an individual’s placement on the factor(s). This article discusses popular methods to create factor scores under two different classes: refined and non-refined. Strengths and considerations of the various methods, and for using factor scores in general, are discussed. Exploratory factor analysis (EFA) has been used as an analytical tool in educational research. The methods may be used with novel or exploratory research scenarios as a precursor to latent variable modeling or confirmatory factor analyses (CFA) (Schumaker & Lomax, 2004). However, in many research situations, EFA is used as the focal methodology. Practitioners may use EFA for a variety of purposes such as reducing a large number of items from a questionnaire or survey instrument to a smaller number of components, uncovering latent dimensions underlying a data set, or examining which items have the strongest association with a given factor. Once a researcher has used EFA and has identified the number of factors or components underlying a data set, he/she may wish to use the information about the factors in subsequent analyses (Gorsuch, 1983). For example, researchers may want to identify an individual’s placement or ranking on the factor(s), use the information with hypothesis tests to determine how factor scores differ between groups, or to incorporate factor information as part of a regression or predictive analysis. To use EFA information in follow-up studies, the researcher must create scores to represent each individual’s placement on the factor(s) identified from the EFA. These

Latent class and latent transition analysis.

Abstract: Often quantities of interest in psychology cannot be observed directly. These unobservable quantities are known as latent variables. By using multiple items as indicators of the latent variable, we can obtain a more complete picture of the construct of interest and estimate measurement error. One approach to latent variable modeling is latent class analysis, a method appropriate for examining the relationship between discrete observed variables and a discrete latent variable. The present chapter will introduce latent class analysis, its extension to repeated measures, and recent developments further extending the latent class model. First, the concept of a latent class and the mathematical model are presented. This is followed by a discussion of parameter restrictions, model fit, and the measurement quality of categorical items. Second, latent class analysis is demonstrated through an examination of the prevalence of depression types in adolescents. Third, longitudinal extensions of the latent class model are presented. This section also contains an empirical example on adolescent depression types, where the previous analysis is extended to examine the stability and change in depression types over time. Finally, several recent developments that further extend the latent class model are introduced. Keywords: categorical variables; depression types; latent class analysis; latent transition analysis; latent variables; longitudinal

12 Structural Equation Modeling in Management Research: A Guide for Improved Analysis

Abstract: A large segment of management research in recent years has used structural equation modeling (SEM) as an analytical approach that simultaneously combines factor analysis and linear regression models for theory testing. With this approach, latent variables (factors) represent the concepts of a theory, and data from measures (indicators) are used as input for statistical analyses that provide evidence about the relationships among latent variables. This chapter first provides a brief introduction to SEM and its concepts and terminology. We then discuss four issues related to the measurement component of such models, including how indicators are developed, types of relationships between indicators and latent variables, approaches for multidimensional constructs, and analyses needed when data from multiple time points or multiple groups are examined. In our second major section, we focus on six issues related to the structural component of structural equation models, including how to examine mediatio...

On‐line expectation–maximization algorithm for latent data models

Abstract: In this contribution, we propose a generic online (also sometimes called adaptive or recursive) version of the Expectation-Maximisation (EM) algorithm applicable to latent variable models of independent observations. Compared to the algorithm of Titterington (1984), this approach is more directly connected to the usual EM algorithm and does not rely on integration with respect to the complete data distribution. The resulting algorithm is usually simpler and is shown to achieve convergence to the stationary points of the Kullback-Leibler divergence between the marginal distribution of the observation and the model distribution at the optimal rate, i.e., that of the maximum likelihood estimator. In addition, the proposed approach is also suitable for conditional (or regression) models, as illustrated in the case of the mixture of linear regressions model.

Defining a Family of Cognitive Diagnosis Models Using Log-Linear Models with Latent Variables

Abstract: This paper uses log-linear models with latent variables (Hagenaars, in Loglinear Models with Latent Variables, 1993) to define a family of cognitive diagnosis models. In doing so, the relationship between many common models is explicitly defined and discussed. In addition, because the log-linear model with latent variables is a general model for cognitive diagnosis, new alternatives to modeling the functional relationship between attribute mastery and the probability of a correct response are discussed.

Complex working memory span tasks and higher-order cognition: A latent-variable analysis of the relationship between processing and storage

Abstract: Complex span tasks, assumed by many to measure an individual’s working memory capacity, are predictive of several aspects of higher-order cognition. However, the underlying cause of the relationships between ‘‘processing-and-storage’’ tasks and cognitive abilities is still hotly debated nearly 30 years after the tasks were first introduced. The current study utilised latent constructs across verbal, numerical, and spatial content domains to examine a number of questions regarding the predictive power of complex span tasks. In particular, the relations among processing time, processing accuracy, and storage accuracy from the complex span tasks were examined, in combination with their respective relationships with fluid intelligence. The results point to a complicated pattern of unique and shared variance among the constructs. Implications for various theories of working memory are discussed.

Tracking Executive Function Across the Transition to School: A Latent Variable Approach

Abstract: This longitudinal study of executive function (EF) addressed three questions. These concerned: (i) the validity of EF as a latent construct underpinning performance at ages 4 and 6 on tests of planning, inhibitory control, and working memory; (ii) developmental change in EF across these time-points, which straddled children's transition to school; and (iii) verbal ability and family income as predictors of base-line individual differences and variation in the slopes of EF development. Confirmatory factor analyses of data from a socially diverse sample of 191 children supported the validity of a single EF construct at both time-points; a MIMIC (multiple indicators, multiple causes) model showed equally good fit for boys and girls. Latent growth models demonstrated that verbal mental age and family income predicted EF intercepts, but EF slopes were only related to verbal mental age. Across the transition to school, less able children (but not children from low income families) showed greater gains in EF than their peers.

Nonparametric Bayes Modeling of Multivariate Categorical Data

Abstract: Modeling of multivariate unordered categorical (nominal) data is a challenging problem, particularly in high dimensions and cases in which one wishes to avoid strong assumptions about the dependence structure. Commonly used approaches rely on the incorporation of latent Gaussian random variables or parametric latent class models. The goal of this article is to develop a nonparametric Bayes approach, which defines a prior with full support on the space of distributions for multiple unordered categorical variables. This support condition ensures that we are not restricting the dependence structure a priori. We show this can be accomplished through a Dirichlet process mixture of product multinomial distributions, which is also a convenient form for posterior computation. Methods for nonparametric testing of violations of independence are proposed, and the methods are applied to model positional dependence within transcription factor binding motifs.

Multiplicative latent factor models for description and prediction of social networks

Abstract: We discuss a statistical model of social network data derived from matrix representations and symmetry considerations. The model can include known predictor information in the form of a regression term, and can represent additional structure via sender-specific and receiver-specific latent factors. This approach allows for the graphical description of a social network via the latent factors of the nodes, and provides a framework for the prediction of missing links in network data.

Evaluation of Scale Reliability for Unidimensional Measures Using Latent Variable Modeling

Abstract: This article outlines a readily and widely applicable procedure of reliability evaluation for scales with unidimensional measures. The method is developed within the framework of the popular latent...

Analysis of Gene Sets Based on the Underlying Regulatory Network

Abstract: Networks are often used to represent the interactions among genes and proteins. These interactions are known to play an important role in vital cell functions and should be included in the analysis of genes that are differentially expressed. Methods of gene set analysis take advantage of external biological information and analyze a priori defined sets of genes. These methods can potentially preserve the correlation among genes; however, they do not directly incorporate the information about the gene network. In this paper, we propose a latent variable model that directly incorporates the network information. We then use the theory of mixed linear models to present a general inference framework for the problem of testing the significance of subnetworks. Several possible test procedures are introduced and a network based method for testing the changes in expression levels of genes as well as the structure of the network is presented. The performance of the proposed method is compared with methods ...

A negative binomial model for time series of counts

Abstract: We study generalized linear models for time series of counts, where serial dependence is introduced through a dependent latent process in the link function. Conditional on the covariates and the latent process, the observation is modelled by a negative binomial distribution. To estimate the regression coefficients, we maximize the pseudolikelihood that is based on a generalized linear model with the latent process suppressed. We show the consistency and asymptotic normality of the generalized linear model estimator when the latent process is a stationary strongly mixing process. We extend the asymptotic results to generalized linear models for time series, where the observation variable, conditional on covariates and a latent process, is assumed to have a distribution from a one-parameter exponential family. Thus, we unify in a common framework the results for Poisson log-linear regression models of Davis et al. (2000), negative binomial logit regression models and other similarly specified generalized linear models. Language: en

Modeling conditional dependence between diagnostic tests: a multiple latent variable model.

Abstract: Applications of latent class analysis in diagnostic test studies have assumed that all tests are measuring a common binary latent variable, the true disease status. In this article we describe a new approach that recognizes that tests based on different biological phenomena measure different latent variables, which in turn measure the latent true disease status. This allows for adjustment of conditional dependence between tests within disease categories. The model further allows for the inclusion of measured covariates and unmeasured random effects affecting test performance within latent classes. We describe a Bayesian approach for model estimation and describe a new posterior predictive check for evaluating candidate models. The methods are motivated and illustrated by results from a study of diagnostic tests for Chlamydia trachomatis.

Latent Variable Modeling in Congruence Research Current Problems and Future Directions

Abstract: During the past decade, the use of polynomial regression has become increasingly prevalent in congruence research. One drawback of polynomial regression is that it relies on the assumption that variables are measured without error. This assumption is relaxed by structural equation modeling with latent variables. One application of structural equation modeling to congruence research is the latent congruence model (LCM). Although the LCM takes measurement error into account and allows tests of measurement equivalence, it is framed around the mean and algebraic difference of the components of congruence (e.g., the person and organization), which creates various interpretational problems. This article discusses problems with the LCM and shows how these problems are resolved by a linear structural equation model that uses the components of congruence as predictors and outcomes. Extensions of the linear model to quadratic equations used in polynomial regression analysis are discussed.

Latent variable perceptron algorithm for structured classification

Abstract: We propose a perceptron-style algorithm for fast discriminative training of structured latent variable model, and analyzed its convergence properties. Our method extends the perceptron algorithm for the learning task with latent dependencies, which may not be captured by traditional models. It relies on Viterbi decoding over latent variables, combined with simple additive updates. Compared to existing probabilistic models of latent variables, our method lowers the training cost significantly yet with comparable or even superior classification accuracy.

A Discriminative Latent Variable Chinese Segmenter with Hybrid Word/Character Information

Abstract: Conventional approaches to Chinese word segmentation treat the problem as a character-based tagging task. Recently, semi-Markov models have been applied to the problem, incorporating features based on complete words. In this paper, we propose an alternative, a latent variable model, which uses hybrid information based on both word sequences and character sequences. We argue that the use of latent variables can help capture long range dependencies and improve the recall on segmenting long words, e.g., named-entities. Experimental results show that this is indeed the case. With this improvement, evaluations on the data of the second SIGHAN CWS bakeoff show that our system is competitive with the best ones in the literature.

A Latent Variable Model of Synchronous Syntactic-Semantic Parsing for Multiple Languages

Abstract: Motivated by the large number of languages (seven) and the short development time (two months) of the 2009 CoNLL shared task, we exploited latent variables to avoid the costly process of hand-crafted feature engineering, allowing the latent variables to induce features from the data. We took a pre-existing generative latent variable model of joint syntactic-semantic dependency parsing, developed for English, and applied it to six new languages with minimal adjustments. The parser's robustness across languages indicates that this parser has a very general feature set. The parser's high performance indicates that its latent variables succeeded in inducing effective features. This system was ranked third overall with a macro averaged F1 score of 82.14%, only 0.5% worse than the best system.

Variation in working memory capacity, fluid intelligence, and episodic recall: A latent variable examination of differences in the dynamics of free recall

Abstract: A latent variable analysis was conducted to examine the nature of individual differences in the dynamics of free recall and cognitive abilities. Participants performed multiple measures of free recall, working memory capacity (WMC), and fluid intelligence (gF). For each free recall task, recall accuracy, recall latency, and number of intrusion errors were determined, and latent factors were derived for each. It was found that recall accuracy was negatively related to both recall latency and number of intrusions, and recall latency and number of intrusions were positively related. Furthermore, latent WMC and gF factors were positively related to recall accuracy, but negatively related to recall latency and number of intrusions. Finally, a cluster analysis revealed that subgroups of participants with deficits in focusing the search had deficits in recovering degraded representations or deficits in monitoring the products of retrieval. The results are consistent with the idea that variation in the dynamics of free recall, WMC, and gF are primarily due to differences in search set size, but differences in recovery and monitoring are also important.

Shared Kernel Information Embedding for discriminative inference

Abstract: Latent variable models (LVM), like the shared-GPLVM and the spectral latent variable model, help mitigate over-fitting when learning discriminative methods from small or moderately sized training sets. Nevertheless, existing methods suffer from several problems: (1) complexity; (2) the lack of explicit mappings to and from the latent space; (3) an inability to cope with multi-modality; and (4) the lack of a well-defined density over the latent space. We propose a LVM called the shared kernel information embedding (sKIE). It defines a coherent density over a latent space and multiple input/output spaces (e.g., image features and poses), and it is easy to condition on a latent state, or on combinations of the input/output states. Learning is quadratic, and it works well on small datasets. With datasets too large to learn a coherent global model, one can use sKIE to learn local online models. sKIE permits missing data during inference, and partially labelled data during learning. We use sKIE for human pose inference.

Learning GP-BayesFilters via Gaussian process latent variable models

Abstract: GP-BayesFilters are a general framework for integrating Gaussian process prediction and observation models into Bayesian filtering techniques, including particle filters and extended and unscented Kalman filters. GP-BayesFilters have been shown to be extremely well suited for systems for which accurate parametric models are difficult to obtain. GP-BayesFilters learn non-parametric models from training data containing sequences of control inputs, observations, and ground truth states. The need for ground truth states limits the applicability of GP-BayesFilters to systems for which the ground truth can be estimated without significant overhead. In this paper we introduce GPBF-Learn, a framework for training GP-BayesFilters without ground truth states. Our approach extends Gaussian Process Latent Variable Models to the setting of dynamical robotics systems. We show how weak labels for the ground truth states can be incorporated into the GPBF-Learn framework. The approach is evaluated using a difficult tracking task, namely tracking a slotcar based on inertial measurement unit (IMU) observations only. We also show some special features enabled by this framework, including time alignment, and control replay for both the slotcar, and a robotic arm.

Latent variable models for multivariate longitudinal ordinal responses.

Abstract: The paper proposes a full information maximum likelihood estimation method for modelling multivariate longitudinal ordinal variables. Two latent variable models are proposed that account for dependencies among items within time and between time. One model fits item-specific random effects which account for the between time points correlations and the second model uses a common factor. The relationships between the time-dependent latent variables are modelled with a non-stationary autoregressive model. The proposed models are fitted to a real data set.

System and Method for the Model Predictive Control of Batch Processes using Latent Variable Dynamic Models

Abstract: A computer implemented method for modeling and controlling batch or transitional processes is disclosed including collecting, or initiating the collection of measurements on a plurality of process variables. The method may include creating, or initiating the creation of, a latent variable model predictive controller based on the collected measurements. The method further provides for applying or initiating the application of, the model predictive controller to predict and control at least one of the process variables to track a desired trajectory, by operation of at least one computer including one or more computer processors. A related system for implementing the method is disclosed as is a computer program operable with this method.