Showing papers on "Latent variable model published in 1999"

Probabilistic Principal Component Analysis

Abstract: Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based upon a probability model. In this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum-likelihood estimation of parameters in a latent variable model closely related to factor analysis. We consider the properties of the associated likelihood function, giving an EM algorithm for estimating the principal subspace iteratively, and discuss the advantages conveyed by the definition of a probability density function for PCA.

Mixtures of probabilistic principal component analyzers

Abstract: Principal component analysis (PCA) is one of the most popular techniques for processing, compressing, and visualizing data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a combination of local linear PCA projections. However, conventional PCA does not correspond to a probability density, and so there is no unique way to combine PCA models. Therefore, previous attempts to formulate mixture models for PCA have been ad hoc to some extent. In this article, PCA is formulated within a maximum likelihood framework, based on a specific form of gaussian latent variable model. This leads to a well-defined mixture model for probabilistic principal component analyzers, whose parameters can be determined using an expectationmaximization algorithm. We discuss the advantages of this model in the context of clustering, density modeling, and local dimensionality reduction, and we demonstrate its application to image compression and handwritten digit recognition.

Finite Mixture Modeling with Mixture Outcomes Using the EM Algorithm

Abstract: Summary. This paper discusses the analysis of an extended finite mixture model where the latent classes corresponding to the mixture components for one set of observed variables influence a second set of observed variables. The research is motivated by a repeated measurement study using a random coefficient model to assess the influence of latent growth trajectory class membership on the probability of a binary disease outcome. More generally, this model can be seen as a combination of latent class modeling and conventional mixture modeling. The EM algorithm is used for estimation. As an illustration, a random-coefficient growth model for the prediction of alcohol dependence from three latent classes of heavy alcohol use trajectories among young adults is analyzed.

Robustness of partial least-squares method for estimating latent variable quality structures

Abstract: Latent variable structural models and the partial least-squares (PLS) estimation procedure have found increased interest since being used in the context of customer satisfaction measurement. The well-known property that the estimates of the inner structure model are inconsistent implies biased estimates for finite sample sizes. A simplified version of the structural model that is used for the Swedish Customer Satisfaction Index (SCSI) system has been used to generate simulated data and to study the PLS algorithm in the presence of three inadequacies: (i) skew instead of symmetric distributions for manifest variables; (ii) multi-collinearity within blocks of manifest and between latent variables; and (iii) misspecification of the structural model (omission of regressors). The simulation results show that the PLS method is quite robust against these inadequacies. The bias that is caused by the inconsistency of PLS estimates is substantially increased only for extremely skewed distributions and for the erron...

Local instrumental variables and latent variable models for identifying and bounding treatment effects.

Abstract: This paper examines the relationship between various treatment parameters within a latent variable model when the effects of treatment depend on the recipient’s observed and unobserved characteristics. We show how this relationship can be used to identify the treatment parameters when they are identified and to bound the parameters when they are not identified.

Integration of Choice and Latent Variable Models

Abstract: This paper presents a general methodology and framework for including latent variables—in particular, attitudes and perceptions—in choice models. This is something that has long been deemed necessary by behavioral researchers, but is often either ignored in statistical models, introduced in less than optimal ways (e.g., sequential estimation of a latent variable model then a choice model, which produces inconsistent estimates), or introduced for a narrowly defined model structure. The paper is focused on the use of psychometric data to explicitly model attitudes and perceptions and their influences on choices. The methodology requires the estimation of an integrated multi-equation model consisting of a discrete choice model and the latent variable model’s structural and measurement equations. The integrated model is estimated simultaneously using a maximum likelihood estimator, in which the likelihood function includes complex multi-dimensional integrals. The methodology is applicable to any situation in which one is modeling choice behavior (with any type and combination of choice data) where (1) there are important latent variables that are hypothesized to influence the choice and (2) there exist indicators (e.g., responses to survey questions) for the latent variables. Three applications of the methodology provide examples and demonstrate the flexibility of the approach, the resulting gain in explanatory power, and the improved specification of discrete choice models.

Latent state–trait theory and research in personality and individual differences

Abstract: Latent state–trait (LST) theory is a generalization of classical test theory designed to take account of the fact that psychological measurement does not take place in a situational vacuum. The basic concepts of latent state–trait theory (LST theory) are introduced. The core of LST theory consists of two decompositions: (a) the decomposition of any observed score into latent state and measurement error, and (b) the decomposition of any latent state into latent trait and latent state residual representing situational and/or interaction effects. Latent states and latent traits are defined as special conditional expectations. A score on a latent state variable is defined as the expectation of an observable variable Yik given a person in a situation whereas a score on a latent trait variable is the expectation of Yik given a person. The theory also comprises the definition of consistency, occasion specificity, reliability, and stability coefficients. An overview of different models of LST theory is given. It is shown how different research questions of personality psychology can be and have been analysed within the LST framework and why research in personality and individual differences can profit from LST theory and methodology. Copyright © 1999 John Wiley & Sons, Ltd.

Modeling Uncertainty in Latent Class Membership: A Case Study in Criminology

Abstract: Social scientists are commonly interested in relating a latent trait (e.g., criminal tendency) to measurable individual covariates (e.g., poor parenting) to understand what defines or perhaps causes the latent trait. In this article we develop an efficient and convenient method for answering such questions. The basic model presumes that two types of variables have been measured: Response variables (possibly longitudinal) that partially determine the latent class membership, and covariates or risk factors that we wish to relate to these latent class variables. The model assumes that these observable variables are conditionally independent, given the latent class variable. We use a mixture model for the joint distribution of the observables. We apply this model to a longitudinal dataset assembled as part of the Cambridge Study of Delinquent Development to test a fundamental theory of criminal development. This theory holds that crime is committed by two distinct groups within the population: Adoles...

Estimating Multiple Classification Latent Class Models.

Abstract: This paper presents a new class of models for persons-by-items data. The essential new feature of this class is the representation of the persons: every person is represented by its membership tomultiple latent classes, each of which belongs to onelatent classification. The models can be considered as a formalization of the hypothesis that the responses come about in a process that involves the application of a number ofmental operations. Two algorithms for maximum likelihood (ML) and maximum a posteriori (MAP) estimation are described. They both make use of the tractability of the complete data likelihood to maximize the observed data likelihood. Properties of the MAP estimators (i.e., uniqueness and goodness-of-recovery) and the existence of asymptotic standard errors were examined in a simulation study. Then, one of these models is applied to the responses to a set of fraction addition problems. Finally, the models are compared to some related models in the literature.

Extended Framework for Modeling Choice Behavior

Abstract: We review the case against the standard model of rational behavior and discuss the consequences of various ‘anomalies’ of preference elicitation. A general theoretical framework that attempts to disentangle the various psychological elements in the decision-making process is presented. We then present a rigorous and general methodology to model the theoretical framework, explicitly incorporating psychological factors and their influences on choices. This theme has long been deemed necessary by behavioral researchers, but is often ignored in demand models. The methodology requires the estimation of an integrated multi-equation model consisting of a discrete choice model and the latent variable model system. We conclude with a research agenda to bring the theoretical framework into fruition.

Variational principal components

Abstract: One of the central issues in the use of principal component analysis (PCA) for data modelling is that of choosing the appropriate number of retained components. This problem was recently addressed through the formulation of a Bayesian treatment of PCA in terms of a probabilistic latent variable model. A central feature of this approach is that the effective dimensionality of the latent space is determined automatically as part of the Bayesian inference procedure. In common with most non-trivial Bayesian models, however, the required marginalizations are analytically intractable, and so an approximation scheme based on a local Gaussian representation of the posterior distribution was employed. In this paper we develop an alternative, variational formulation of Bayesian PCA, based on a factorial representation of the posterior distribution. This approach is computationally efficient, and unlike other approximation schemes, it maximizes a rigorous lower bound on the marginal log probability of the observed data.

Modelling the hidden economy and the tax-gap in new zealand

Abstract: This paper develops and estimates a structural, latent variable, model for the hidden economy in New Zealand, and a separate currency-demand model. The estimated latent variable model is used to generate an historical time-series index of hidden economic activity, which is calibrated via the information from the currency-demand model. Special attention is paid to data non-stationarity, and to diagnostic testing. Over the period 1968 to 1994, the size of the hidden economy is found to vary between 6.8% and 11.3% of measured GDP. This, in turn, implies that the total tax-gap is of the order of 6.4% to 10.2% of total tax liability in that country. Of course, not all of this foregone revenue would be recoverable, as not all of the activity in the underground economy is responsive to changes in taxation or other policies.

Evaluation of ADHD Typology in Three Contrasting Samples: A Latent Class Approach

Abstract: Objective To identify subtypes of attention-deficit/hyperactivity disorder (ADHD) and characterize them as either categorical or continuous, to investigate tamilial resemblance for ADHD among sibling pairs; and to test the robustness of all results by using contrasting data sets. Method Latent class analysis was applied to the ADHD symptom profiles obtained from parents or best informant about their offspring in 3 samples: a population-based set of female adolescent twins (724 monozygotic pairs, 594 dizygotic pairs) and male ( N = 425) and female ( N = 430) child and adolescent offspring ascertained from high-risk alcoholic families. Results Latent class analysis revealed 2 categories of clinically significant ADHD which were replicated in all 3 study groups: a subtype with high endorsements of ADHD inattention symptoms and a second combined type with high endorsements of both inattention and hyperactivity-impulsivity items. Both appeared to be continuous across all 3 data groups. The high-risk families contained a class in which members heavily endorsed the ADHD "fidget" item but not other ADHD items. A large proportion of the monozygotic sibs (80%) versus a smaller proportion of dizygotic sibs (52%) were assigned to the same latent class. Among the high-risk children and adolescents, 51% of the female and 41% of the male siblings were concordant for class membership. Conclusions The pattern of latent classes suggested that ADHD consists of an inattentive and a combined subtype, within each of which lies a dimensional domain. These analyses further support that genetic factors are significant determinants of latent class membership. J. Am. Acad. Child Adolesc Psychiatry, 1999. 38(1):25–33.

Latent variable models for neural data analysis

Abstract: The brain is perhaps the most complex system to have ever been subjected to rigorous scientific investigation The scale is staggering: over 10^11 neurons, each making an average of 10^3 synapses, with computation occurring on scales ranging from a single dendritic spine, to an entire cortical area Slowly, we are beginning to acquire experimental tools that can gather the massive amounts of data needed to characterize this system However, to understand and interpret these data will also require substantial strides in inferential and statistical techniques This dissertation attempts to meet this need, extending and applying the modern tools of latent variable modeling to problems in neural data analysis It is divided into two parts The first begins with an exposition of the general techniques of latent variable modeling A new, extremely general, optimization algorithm is proposed - called Relaxation Expectation Maximization (REM) - that may be used to learn the optimal parameter values of arbitrary latent variable models This algorithm appears to alleviate the common problem of convergence to local, sub-optimal, likelihood maxima REM leads to a natural framework for model size selection; in combination with standard model selection techniques the quality of fits may be further improved, while the appropriate model size is automatically and efficiently determined Next, a new latent variable model, the mixture of sparse hidden Markov models, is introduced, and approximate inference and learning algorithms are derived for it This model is applied in the second part of the thesis The second part brings the technology of part I to bear on two important problems in experimental neuroscience The first is known as spike sorting; this is the problem of separating the spikes from different neurons embedded within an extracellular recording The dissertation offers the first thorough statistical analysis of this problem, which then yields the first powerful probabilistic solution The second problem addressed is that of characterizing the distribution of spike trains recorded from the same neuron under identical experimental conditions A latent variable model is proposed Inference and learning in this model leads to new principled algorithms for smoothing and clustering of spike data

Latent Class Scaling Analysis

Abstract: Introduction and Overview Latent Class Models Extreme-Types Models Linear Scales Joint Scales Multiple Groups Analysis Concomitant-Variable Models

Discrete-Time Discrete-State Latent Markov Models with Time-Constant and Time-Varying Covariates

Abstract: Discrete-time discrete-state Markov chain models can be used to describe individual change in categorical variables. But when the observed states are subject to measurement error, the observed transitions between two points in time will be partially spurious. Latent Markov models make it possible to separate true change from measurement error. The standard latent Markov model is, however, rather limited when the aim is to explain individual differences in the probability of occupying a particular state at a particular point in time. This paper presents a flexible logit regression approach which allows to regress the latent states occupied at the various points in time on both timeconstant and time-varying covariates. The regression approach combines features of causal log-linear models and latent class models with explanatory variables. In an application pupils' interest in physics at different points in time is explained by the time-constant covariate sex and the time-varying covariate physics grade. Results of both the complete and partially observed data are presented.

[Principles & Practice of Structural Equation Modelling]

Abstract: Structural equation modeling (SEM) is one of the most rapidly growing analytic techniques in use today. Proponents of the approach have virtually declared the advent of a statistical revolution, while skeptics worry about the widespread misuse of complex and often poorly understood analytic methods. Despite the growing interest in and use of structural equation models, few individuals using these techniques have benefitted from any formal training. Indeed, most graduate programs provide no courses on SEM. Individuals interested in acquiring skills in this technique must eider attend expensive training seminars or plow through technical books and manuals on their own.The two new books under renew are therefore timely. Both are valuable, but differ in important ways. Kevin Kelloway's book is directed at the researcher with little knowledge of structural equation modeling and is intricately linked to one of the more popular structural equation modeling programs, LISREL. For researchers keen to begin analyzing data quickly, this book is an invaluable resource that will speed one's introduction to SEM.On the other hand, the volume written by Rex Kline represents one of the most comprehensive of available introductions to the application, execution, and interpretation of this technique. The book is written for both students and researchers who do not have extensive quantitative background. It is especially attentive to quantitative issues common to most structural equation applications.Kelloway's book is designed for the researcher unfamiliar with structural equation modeling and structural equation software. Chapter 1 provides a brief overview of the book and differentiates among historical concepts such as path analysis and latent variable model. Although the focus of the book is on using LISREL, the book offers two of the most clearly written and concise introductory chapters on SEM that I have ever read. They provide an ideal introduction to the relevant basic concepts of the technique.The theory behind the basic steps of structural equation modeling is reviewed in Chapter 2 and includes model specification, identification, estimation, testing fit, and respecification. The author emphasizes the importance of specifying the model. Indeed, this is the fundamental step in SEM that allows researchers to test hypotheses about the relation among a number of variables, and that makes structural equation modeling an inherently confirmatory technique. How a model is specified influences other issues such as identification and testing fit. Currently, there are over 20 indices of fit computed by most programs. Chapter 3 provides an overview of three general classes of fit indices, namely those assessing absolute fit, comparative fit, and parsimonious fit. Absolute fit indices assess the ability of the specified model to reproduce accurately the manner in which observed variables actually covary. Comparative fit indices assess the ability of the proposed model to account for the observed data relative to a less complex restricted model. Parsimonious fit indices recognize that better fit is usually achieved simply by increasing the number of parameters estimated. Parsimonious fit indices compensate by evaluating the benefit achieved, given the cost of estimating additional parameters.Chapter 4, the most technical chapter of the book, explains the various algebraic components and matrices required in fitting a structural equation model. Although no understanding of the algebraic components associated with fitting a structural equation model is needed to run the most recent versions of LISREL, EQS, and AMOS, this overview is useful. Indeed, the author has prudently avoided directing the book towards "point-and-click" users. This chapter provides sufficient information to novice users to appreciate the complexity of fitting a structural equation model without discouraging them.Chapters 5, 6, and 7 are devoted to the three most common applications of SEM, namely confirmatory factor analysis, observed variable path analysis, and latent variable path analysis. …

A state-space model for multivariate longitudinal count data

Abstract: SUMMARY We propose a nonstationary state space model for multivariate longitudinal count data driven by a latent gamma Markov process. The Poisson counts are assumed to be conditionally independent given the latent process, both over time and across categories. We consider a regression model where time-varying covariates may enter via either the Poisson model or the latent gamma process. Estimation is based on the Kalman smoother, and we consider analysis of residuals from both the Poisson model and the latent process. A reanalysis of Zeger's (1988) polio data shows that the choice between a stationary and nonstationary model is crucial for the correct assessment of the evidence of a long-term decrease in the rate of U.S. polio infection.

Probit Latent Class Analysis with Dichotomous or Ordered Category Measures: Conditional Independence/Dependence Models.

Abstract: Flexible methods that relax restrictive conditional independence assumptions of latent classanalysis (LCA) are described. Dichotomous and ordered category manifest variables are viewed asdiscretized latent continuous variables. The latent continuous variables are assumed to have a mixtureofmultivariate-normals distribution. Within a latent class, conditional dependence is modeled as the mutual association of all or some latent continuous variables with a continuous latent trait (or in special cases, multiple latent traits). The relaxation of conditional independence assumptions allows LCA to better model natural taxa. Comparisons of specific restricted and unrestricted models permit statistical tests of specific aspects of latent taxonic structure. Latent class, latent trait, and latent distribution analysis can be viewed as special cases of the mixed latent trait model. The relationship between the multivariate probit mixture model proposed here and Rost’s mixed Rasch (1990, 1991) model is discussed. Two...

The stochastic conditional duration model: a latent factor model for the analysis of financial durations

Abstract: A new model for the analysis of durations, the stochastic conditional duration (SCD) model, is introduced This model is based of the assumption that the durations are generated by a latent stochastic factor that follows a first order autoregressive process The latent factor is pertubed multiplicatively by an innovation distributed as aWeibull or gamma variable The model can capture a wide range of shapes of hazard functions The estimation of the parameters is performed by quasi-maximum likelihood, after transforming the original nonlinear model into a space state representation and using the Kalman filter The model is applied to stock market price-durations, looking at the relation between price durations, volume, spread and trading intensity

Symmetric pattern models: a latent variable approach to item non-response in attitude scales

Abstract: Summary. This paper proposes a new approach to the treatment of item non-response in attitude scales. It combines the ideas of latent variable identification with the issues of non-response adjustment in sample surveys. The latent variable approach allows missing values to be included in the analysis and, equally importantly, allows information about attitude to be inferred from nonresponse. We present a symmetric pattern methodology for handling item non-response in attitude scales. The methodology is symmetric in that all the variables are given equivalent status in the analysis (none is designated a ‘dependent’ variable) and is pattern based in that the pattern of responses and non-responses across individuals is a key element in the analysis. Our approach to the problem is through a latent variable model with two latent dimensions: one to summarize response propensity and the other to summarize attitude, ability or belief. The methodology presented here can handle binary, metric and mixed (binary and metric) manifest items with missing values. Examples using both artificial data sets and two real data sets are used to illustrate the mechanism and the advantages of the methodology proposed.

Multivariate linear mixed models for multiple outcomes

Abstract: We propose a multivariate linear mixed (MLMM) for the analysis of multiple outcomes, which generalizes the latent variable model of Sammel and Ryan. The proposed model assumes a flexible correlation structure among the multiple outcomes, and allows a global test of the impact of exposure across outcomes. In contrast to the Sammel-Ryan model, the MLMM separates the mean and correlation parameters so that the mean estimation will remain reasonably robust even if the correlation is misspecified. The model is applied to birth defects data, where continuous data on the size of infants who were exposed to anticonvulsant medications in utero are compared to controls.

Longitudinal analysis of activity and travel pattern dynamics using generalized mixed markov latent class models

Abstract: Understanding the dynamics of time allocation by households and their household members is becoming increasingly important for travel demand forecasting. A unique opportunity to understand day-to-day and year-to-year behavioral change, is provided by data from multi-day travel diaries combined with yearly observation of the same individuals over time (panel surveys). In fact, the “repeated” nature of the data allows to distinguish units that over time change their behavior from those that are not and to uncover the underlying stochastic behavior generating the data. In this paper data from the Puget Sound Transportation Panel (PSTP) are analyzed to identify change in the patterns of time allocation by the panel participants (i.e., patterns of activity participation and travel). The data analyzed are sequences of states in categorical data from reported individuals' daily activity participation and travel indicators. This is done separately for activity participation and trip making using probabilistic models that generalize the restrictive Markov chain models by incorporating unobserved variables of change. The PSTP data analysis here suggests the more likely presence of multiple paths of change for time allocation to activities, non-stationary switching of activity participation from one year to the next, and day-to-day stationarity in activity participation pattern switching. Travel pattern change is best explained by a single path of change with stationary day-to-day pattern transition probabilities that are different from their year-to-year counterparts.

On the Utilization of Sample Weights in Latent Variable Models.

Abstract: The purpose of this article is to examine the use of sample weights in the latent variable modeling context. A sample weight is the inverse of the probability that the unit in question was sampled and is used to obtain unbiased estimates of population parameters when units have unequal probabilities of inclusion in a sample. Although sample weights are discussed at length in survey research literature, virtually no discussion of sample weights can be found in the latent variable modeling literature. This article examines sample weights in latent variable models applied to the case where a simple random sample is drawn from a population containing a mixture of strata. A bootstrap simulation study is used to compare raw and normalized sample weights to conditions where weights are ignored. The results show that ignoring weights can lead to serious bias in latent variable model parameters and that this bias is mitigated by the incorporation of sample weights. Standard errors appear to be underestimated when ...

Additional construct validity of the Schwartz Cancer Fatigue Scale.

Abstract: The purpose of this article is to report the results of additional construct validity testing of the Schwartz Cancer Fatigue Scale. Latent variable modeling was used to determine the best fit of the data to the model. Testing with a heterogeneous sample (n = 303) did not support the proposed model. Using exploratory techniques a six-item, two-factor scale was formed which demonstrated that all measures of fit were consistently strong, and that the standardized solution factors loaded strongly. Reliabilities for the total scale and subscales were all greater than 0.80. These results provide preliminary support for the reliability and validity of the two-factor model of the six-item Schwartz Cancer Fatigue Scale.

A hierarchical latent variable model for ordinal data from a customer satisfaction survey with no answer responses

Abstract: We propose an item response theory model for ordinal customer satisfaction data where the probability of each response is a function of latent person and question parameters and of cutoffs for the ordinal response categories. This structure was incorporated into a Bayesian hierarchical model by Albert and Chib. We extend this formulation by modeling item nonresponse, coded as “no answer” (NA), as due to either lack of a strong opinion or indifference to the entire question. Because the probability of an NA is related to the latent opinion, the missing-data model is nonignorable. In our hierarchical Bayesian framework, prior means for the person and item effects are related to observed covariates. This structure supports model inferences about satisfaction of individual customers and about associations between customer characteristics and satisfaction levels or propensity to respond. We contrast this with exploratory and standard regression analyses that do not fully support these inferences. Our ...