Estimation of dynamic latent variable models using simulated nonparametric moments

Given a model that can be simulated, conditional moments at a trial parameter value can be calculated with high accuracy by applying kernel smoothing methods to a long simulation. With such conditional moments in hand, standard method of moments techniques can be used to estimate the parameter. Since conditional moments are calculated using kernel smoothing rather than simple averaging, it is not necessary that the model be simulable subject to the conditioning information that is used to define the moment conditions. For this reason, the proposed estimator is applicable to general dynamic latent variable models. Monte Carlo results show that the estimator performs well in comparison to other estimators that have been proposed for estimation of general DLV models.

Estimation of dynamic latent variable models using simulated nonparametric moments

Abstract. Given a model that can be simulated, conditional moments at a trial parameter value can be calculated with high accuracy by applying kernel smoothing methods to a long simulation. With such conditional moments in hand, standard method of moments techniques can be used to estimate the parameter. Because conditional moments are calculated using kernel smoothing rather than simple averaging, it is not necessary that the model be simulable subject to the conditioning information that is used to define the moment conditions. For this reason, the proposed estimator is applicable to general dynamic latent variable models. It is shown that as the number of simulations diverges, the estimator is consistent and a higher-order expansion reveals the stochastic difference between the infeasible GMM estimator based on the same moment conditions and the simulated version. In particular, we show how to adjust standard errors to account for the simulations. Monte Carlo results show how the estimator may be applied to a range of dynamic latent variable (DLV) models, and that it performs well in comparison to several other estimators that have been proposed for DLV models.

Life-Cycle Effects on Household Expenditures: A Latent-Variable Approach

Using data from the Spanish household budget survey, we investigate life- cycle effects on several product expenditures. A latent-variable model approach is adopted to evaluate the impact of income on expenditures, controlling for the number of members in the family. Two latent factors underlying repeated measures of monetary and non-monetary income are used as explanatory variables in the expenditure regression equations, thus avoiding possible bias associated to the measurement error in income. The proposed methodology also takes care of the case in which product expenditures exhibit a pattern of infrequent purchases. Multiple-group analysis is used to assess the variation of key parameters of the model across various household life-cycle typologies. The analysis discloses significant life-cycle effects on the mean levels of expenditures; it also detects significant life-cycle effects on the way expenditures are affected by income and family size. Asymptotic robust methods are used to account for possible non-normality of the data.

Lyfe-cycle effects on household expenditures: A latent-variable approach

Using data from the Spanish household budget survey, we investigate life-cycle effects on several product expenditures. A latent-variable model approach is adopted to evaluate the impact of income on expenditures, controlling for the number of members in the family. Two latent factors underlying repeated measures of monetary and non-monetary income are used as explanatory variables in the expenditure regression equations, thus avoiding possible bias associated to the measurement error in income. The proposed methodology also takes care of the case in which product expenditures exhibit a pattern of infrequent purchases. Multiple-group analysis is used to assess the variation of key parameters of the model across various household life-cycle typologies. The analysis discloses significant life-cycle effects on the mean levels of expenditures; it also detects significant life-cycle effects on the way expenditures are affected by income and family size. Asymptotic robust methods are used to account for possible non-normality of the data.

Latent Variable Models for Stochastic Discount Factors.

Latent variable models in finance originate both from asset pricing theory and time series analysis. These two strands of literature appeal to two different concepts of latent structures, which are both useful to reduce the dimension of a statistical model specified for a multivariate time series of asset prices. In the CAPM or APT beta pricing models, the dimension reduction is cross-sectional in nature, while in time-series state-space models, dimension is reduced longitudinally by assuming conditional independence between consecutive returns, given a small number of state variables. In this paper, we use the concept of Stochastic Discount Factor (SDF) or pricing kernel as a unifying principle to integrate these two concepts of latent variables. Beta pricing relations amount to characterize the factors as a basis of a vectorial space for the SDF. The coefficients of the SDF with respect to the factors are specified as deterministic functions of some state variables which summarize their dynamics. In beta pricing models, it is often said that only the factorial risk is compensated since the remaining idiosyncratic risk is diversifiable. Implicitly, this argument can be interpreted as a conditional cross-sectional factor structure, that is, a conditional independence between contemporaneous returns of a large number of assets, given a small number of factors, like in standard Factor Analysis. We provide this unifying analysis in the context of conditional equilibrium beta pricing as well as asset pricing with stochastic volatility, stochastic interest rates and other state variables. We address the general issue of econometric specifications of dynamic asset pricing models, which cover the modern literature on conditionally heteroskedastic factor models as well as equilibrium-based asset pricing models with an intertemporal specification of preferences and market fundamentals. We interpret various instantaneous causality relationships between state variables and market fundamentals as leverage effects and discuss their central role relative to the validity of standard CAPM-like stock pricing and preference-free option pricing.

Semiparametric Latent Variable Regression Models for Spatio-temporal Modeling of Mobile Source Particles in the Greater Boston Area

Traffic particle concentrations show considerable spatial variability within a metropolitan area. We consider latent variable semiparametric regression models for modeling the spatial and temporal variability of black carbon and elemental carbon concentrations in the greater Boston area. Measurements of these pollutants, which are markers of traffic particles, were obtained from several individual exposure studies conducted at specific household locations as well as 15 ambient monitoring sites in the city. The models allow for both flexible, nonlinear effects of covariates and for unexplained spatial and temporal variability in exposure. In addition, the different individual exposure studies recorded different surrogates of traffic particles, with some recording only outdoor concentrations of black or elemental carbon, some recording indoor concentrations of black carbon, and others recording both indoor and outdoor concentrations of black carbon. A joint model for outdoor and indoor exposure that specifies a spatially varying latent variable provides greater spatial coverage in the area of interest. We propose a penalised spline formation of the model that relates to generalised kringing of the latent traffic pollution variable and leads to a natural Bayesian Markov Chain Monte Carlo algorithm for model fitting. We propose methods that allow us to control the degress of freedom of the smoother in a Bayesian framework. Finally, we present results from an analysis that applies the model to data from summer and winter separately

A Mechanistic Latent Variable Model for Estimating Drug Concentrations in the Male Genital Tract

The purpose of this study is to develop statistical methodology to facilitate indirect estimation of the concentration of antiretroviral drugs and viral loads in the prostate gland and the seminal vesicle. The differences in antiretroviral drug concentrations in these organs may lead to suboptimal concentrations in one gland compared to the other. Suboptimal levels of the antiretroviral drugs will not be able to fully suppress the virus in that gland, lead to a source of sexually transmissible virus and increase the chance of selecting for drug resistant virus. This information may be useful selecting antiretroviral drug regimen that will achieve optimal concentrations in most of male genital tract glands. Using fractionally collected semen ejaculates, Lundquist (1949) measured levels of surrogate markers in each fraction that are uniquely produced by specific male accessory glands. To determine the original glandular concentrations of the surrogate markers, Lundquist solved a simultaneous series of linear equations. This method has several limitations. In particular, it does not yield a unique solution, it does not address measurement error, and it disregards inter-subject variability in the parameters. To cope with these limitations, we developed a mechanistic latent variable model based on the physiology of the male genital tract and surrogate markers. We employ a Bayesian approach and perform a sensitivity analysis with regard to the distributional assumptions on the random effects and priors. The model and Bayesian approach is validated on experimental data where the concentration of a drug should be (biologically) differentially distributed between the two glands. In this example, the Bayesian model-based conclusions are found to be robust to model specification and this hierarchical approach leads to more scientifically valid conclusions than the original methodology. In particular, unlike existing methods, the proposed model based approach was not affected by a common form of outliers.

The relation between cognitive and motor performance and their relevance for children’s transition to school: A latent variable approach

Both theoretically and empirically there is a continuous interest in understanding the specific relation between cognitive and motor development in childhood. In the present longitudinal study including three measurement points, this relation was targeted. At the beginning of the study, the participating children were 5-6-year-olds. By assessing participants' fine motor skills, their executive functioning, and their non-verbal intelligence, their cross-sectional and cross-lagged interrelations were examined. Additionally, performance in these three areas was used to predict early school achievement (in terms of mathematics, reading, and spelling) at the end of participants' first grade. Correlational analyses and structural equation modeling revealed that fine motor skills, non-verbal intelligence and executive functioning were significantly interrelated. Both fine motor skills and intelligence had significant links to later school achievement. However, when executive functioning was additionally included into the prediction of early academic achievement, fine motor skills and non-verbal intelligence were no longer significantly associated with later school performance suggesting that executive functioning plays an important role for the motor-cognitive performance link.

Relations among fluid intelligence, sensory discrimination and working memory in middle to late childhood – A latent variable approach

Two factors that have been suggested as key in explaining individual differences in fluid intelligence are working memory and sensory discrimination ability. A latent variable approach was used to explore the relative contributions of these two variables to individual differences in fluid intelligence in middle to late childhood. A sample of 263 children aged 7–12 years was examined. Correlational analyses showed that general discrimination ability (GDA)and working memory (WM) were related to each other and to fluid intelligence. Structural equation modeling showed that within both younger and older age groups and the sample as a whole, the relation between GDA and fluid intelligence could be accounted for by WM. While WM was able to predict variance in fluid intelligence above and beyond GDA, GDA was not able to explain significant amounts of variance in fluid intelligence, either in the whole sample or within the younger or older age group. We concluded that compared to GDA, WM should be considered the better predictor of individual differences in fluid intelligence in childhood. WM and fluid intelligence, while not being separable in middle childhood, develop at different rates, becoming more separable with age.

The application of latent variable models to the assessment of determinants of HIV risk behavior

Studies on the relationship between psychosocial determinants and HIV risk behaviors have produced little evidence to support hypotheses based on theoretical relationships. One limitation inherent in many articles in the literature is the method of measurement of the determinants and the analytic approach selected. ^ To reduce the misclassification associated with unit scaling of measures specific to internalized homonegativity, I evaluated the psychometric properties of the Reactions to Homosexuality scale in a confirmatory factor analytic framework. In addition, I assessed the measurement invariance of the scale across racial/ethnic classifications in a sample of men who have sex with men. The resulting measure contained eight items loading on three first-order factors. Invariance assessment identified metric and partial strong invariance between racial/ethnic groups in the sample. ^ Application of the updated measure to a structural model allowed for the exploration of direct and indirect effects of internalized homonegativity on unprotected anal intercourse. Pathways identified in the model show that drug and alcohol use at last sexual encounter, the number of sexual partners in the previous three months and sexual compulsivity all contribute directly to risk behavior. Internalized homonegativity reduced the likelihood of exposure to drugs, alcohol or higher numbers of partners. For men who developed compulsive sexual behavior as a coping strategy for internalized homonegativity, there was an increase in the prevalence odds of risk behavior. ^ In the final stage of the analysis, I conducted a latent profile analysis of the items in the updated Reactions to Homosexuality scale. This analysis identified five distinct profiles, which suggested that the construct was not homogeneous in samples of men who have sex with men. Lack of prior consideration of these distinct manifestations of internalized homonegativity may have contributed to the analytic difficulty in identifying a relationship between the trait and high-risk sexual practices. ^

Random error in willingness to pay measurement: A multiple indicators, latent variable approach to the reliability of contingent values

The reliability of measurement refers to unsystematic error in observed responses. Investigations of the prevalence of random error in stated estimates of willingness to pay (WTP) are important to an understanding of why tests of validity in CV can fail. However, published reliability studies have tended to adopt empirical methods that have practical and conceptual limitations when applied to WTP responses. This contention is supported in a review of contingent valuation reliability studies that demonstrate important limitations of existing approaches to WTP reliability. It is argued that empirical assessments of the reliability of contingent values may be better dealt with by using multiple indicators to measure the latent WTP distribution. This latent variable approach is demonstrated with data obtained from a WTP study for stormwater pollution abatement. Attitude variables were employed as a way of assessing the reliability of open-ended WTP (with benchmarked payment cards) for stormwater pollution abatement. The results indicated that participants' decisions to pay were reliably measured, but not the magnitude of the WTP bids. This finding highlights the need to better discern what is actually being measured in VVTP studies, (C) 2003 Elsevier B.V. All rights reserved.

EM optimization of latent-variable density models

There is currently considerable interest in developing general non-linear density models based on latent, or hidden, variables. Such models have the ability to discover the presence of a relatively small number of underlying `causes' which, acting in combination, give rise to the apparent complexity of the observed data set. Unfortunately, to train such models generally requires large computational effort. In this paper we introduce a novel latent variable algorithm which retains the general non-linear capabilities of previous models but which uses a training procedure based on the EM algorithm. We demonstrate the performance of the model on a toy problem and on data from flow diagnostics for a multi-phase oil pipeline.