Random Effects Components Research Articles

A Bayesian Approach for Capturing Daily Heterogeneity in Intra-Daily Durations Time Series: The Mixed Autoregressive Conditional Duration Model

Intra-daily financial durations time series typically exhibit evidence of long range dependence. This has motivated the introduction of models able to reproduce this stylized fact, like the Fractionally Integrated Autoregressive Conditional Duration Model. In this work we introduce a novel specification able to capture long range dependence. We propose a three component model that consists of an autoregressive daily random effect, a semiparametric time-of-day effect and an intra-daily dynamic component: the Mixed Autoregressive Conditional Duration (Mixed ACD) model. The random effect component allows for heterogeneity in mean reversal within a day and captures low frequency dynamics in the duration time series.The joint estimation of the model parameters is carried out using MCMC techniques based on the Bayesian formulation of the model. The empirical application to a set of widely traded US tickers shows that the model is able to capture low frequency dependence in duration time series. We also find that the degree of dependence and dispersion of low frequency dynamics is higher in periods of higher financial distress.

Fixed Rank Filtering for Spatio-Temporal Data

Datasets from remote-sensing platforms and sensor networks are often spatial, temporal, and very large. Processing massive amounts of data to provide current estimates of the (hidden) state from current and past data is challenging, even for the Kalman filter. A large number of spatial locations observed through time can quickly lead to an overwhelmingly high-dimensional statistical model. Dimension reduction without sacrificing complexity is our goal in this article. We demonstrate how a Spatio-Temporal Random Effects (STRE) component of a statistical model reduces the problem to one of fixed dimension with a very fast statistical solution, a methodology we call Fixed Rank Filtering (FRF). This is compared in a simulation experiment to successive, spatial-only predictions based on an analogous Spatial Random Effects (SRE) model, and the value of incorporating temporal dependence is quantified. A remote-sensing dataset of aerosol optical depth (AOD), from the Multi-angle Imaging SpectroRadiometer (MISR) instrument on the Terra satellite, is used to compare spatio-temporal FRF with spatial-only prediction. FRF achieves rapid production of optimally filtered AOD predictions, along with their prediction standard errors. In our case, over 100,000 spatio-temporal data were processed: Parameter estimation took 64.4 seconds and optimal predictions and their standard errors took 77.3 seconds to compute. Supplemental materials giving complete details on the design and analysis of a simulation experiment, the simulation code, and the MISR data used are available on-line.

Detection of imprinting and heterogeneous maternal effects on high blood pressure using Framingham Heart Study data

Both imprinting and maternal effects could lead to parent-of-origin patterns in complex traits of human disorders. Statistical methods that differentiate these two effects and identify them simultaneously by using family-based data from retrospective studies are available. The usual data structures include case-parents triads and nuclear families with multiple affected siblings. We develop a likelihood-based method to detect imprinting and maternal effects simultaneously using data from prospective studies. The proposed method utilizes both affected and unaffected siblings in nuclear families by modeling familial genotypes and offspring's disease status jointly. Maternal effect is usually modeled as a fixed effect under the assumption that maternal variant allele(s) has (have) identical effect on any offspring. However, recent studies report that different people may carry different amounts of substances encoded by the mother's variant allele(s) (called maternal microchimerism), which could result in heterogeneity of maternal effects. The proposed method incorporates the heterogeneity of maternal effects by adding a random component to the logit of the penetrance. Our method was applied to the Framingham Heart Study data in two steps to detect single-nucleotide polymorphisms (SNPs) that may be associated with high blood pressure. In the first step, SNPs that affect susceptibility of high blood pressure through minor allele, genomic imprinting, or maternal effects were identified by using the proposed model without the random effect component. In the second step, we fitted the mixed effect model to the identified SNPs that have significant maternal effect to detect heterogeneity of the maternal effects.

Fixed and random effect analysis of multi-subject fMRI data using wavelet transform

We propose a new method to estimate the random effect variance in group analysis of fMRI data. In the first level of analysis, general linear model (GLM) is used to estimate a parameter map (“effect”) for each subject. After applying discrete wavelet transform to the “effect” maps, noise is reduced through a vertical energy thresholding (VET). The fixed effect component in each coefficient is derived by averaging the wavelet coefficients along all subjects. Then, the wavelet coefficients containing significant random effect are identified by their higher sample variance along the subjects. Wavelet coefficients containing random effect component in each subject are used to reconstruct the random effect maps through an inverse wavelet transform. Random effect variance is obtained from random effect maps for use in random effect analysis. The proposed method and other methods like GLM group analysis and variance ratio smoothing are applied to both experimental and artificial fMRI data. ROC curves, obtained from the simulated data, show improved group activation detection compared to existing random effect analysis methods. For the experimental data, the proposed method shows its high sensitivity by detecting multiple activation regions, namely visual cortex, cuneus, precuneus, thalamus, and cerebellum. From these regions, precuneus and cerebellum are not detected by majority of the previously published methods.

Stochastic Simulation of Forest Regeneration Establishment Using a Multilevel Multivariate Model

Abstract Here we present a method for simulating high unexplained variation in establishment of tree seedlings in planted Norway spruce (Picea abies [L.] Karst.) stands. The simulation method is based on an existing hierarchical multilevel multivariate model for establishment of regeneration (Miina, J., and T. Saksa. 2006. New For. 32:265–283). The model includes seven simultaneously estimated models for numbers and heights of tree seedlings on 20-m2 plots within a regeneration area. The variation in plot-level expectations is described by fixed effects and two nested multivariate normal random effects. Conditionally, given the expected values, one of the count variables is underdispersed and four are overdispersed relative to Poisson law. The conditional distributions of the square roots of the height variables are normal. For the conditional joint distribution, the model defines the product-moment cross-correlation matrix, which includes both positive and negative cross-correlations. The first two moments do not, however, uniquely define the marginal distributions of the count variables or the joint distribution of all seven variables. We applied binomial distribution for the underdispersed Poisson variation and negative binomial distribution for the overdispersed Poisson variation. The conditional joint distribution was defined by a multivariate normal copula and the marginal distributions. Despite relatively low cross-correlations among responses, if the cross-correlations among random components of the responses were ignored in stochastic simulations, the amount and costs of precommercial thinning (i.e., cleaning out competing broadleaves) were greatly underestimated. If all random effect components in model parameters were dropped, the error increased markedly.

Retrospective analysis of chronic hepatitis C in untreated patients with nonlinear mixed effects model

It is well known that viral load of the hepatitis C virus (HCV) is related to the efficacy of interferon therapy. The complex biological parameters that impact on viral load are essentially unknown. The current knowledge of the hepatitis C virus does not provide a mathematical model for viral load dynamics within untreated patients. We car-ried out an empirical modelling to investigate whether different fluctuation patterns exist and how these patterns (if exist) are related to host-specific factors. Data was prospectively col-lected from 147 untreated patients chronically infected with hepatitis C, each contributing be-tween 2 to 10 years of measurements. We pro-pose to use a three parameter logistic model to describe the overall pattern of viral load fluctua-tion based on an exploratory analysis of the data. To incorporate the correlation feature of longitu-dinal data and patient to patient variation, we introduced random effects components into the model. On the basis of this nonlinear mixed ef-fects modelling, we investigated effects of host-specific factors on viral load fluctuation by in-corporating covariates into the model. The pro-posed model provided a good fit for describing fluctuations of viral load measured with varying frequency over different time intervals. The aver-age viral load growth time was significantly dif-ferent between infection sources. There was a large patient to patient variation in viral load as-ymptote.

Modelling Exposure in Flour Processing Sectors in The Netherlands: a Baseline Measurement in the Context of an Intervention Program

Recent studies have shown that even low exposure levels to flour dust and related allergens can cause severe respiratory symptoms. In The Netherlands the Dutch government and responsible branch organizations [from bakeries (traditional & industrial), flour mills and bakery ingredient producers] signed a covenant to reduce exposure to flour dust and decrease the prevalence of work-related occupational airway disease. This paper describes a sector wide survey to measure exposure to flour dust, wheat allergens and fungal alpha-amylase. The results are being used to underpin various elements of the covenant. A dataset containing 910 personal measurements was compiled from four field studies containing information on exposure and potential determinants. The dataset represents a baseline estimate of exposure for four major flour processing sectors in The Netherlands. Exposure models for all sectors and agents were generated, based on job, tasks and company size, taking into account worker and company as random effect components. Use of control measures and, where possible, their effect were evaluated. Flour dust and enzyme exposures vary strongly between sectors. The job performed and specific tasks were identified as important determinants of exposure. The number of identified control measures during walk-through surveys, and their effectiveness in reduction of dust exposure was generally limited. The exposure models explained significant exposure variability between companies and workers but performed poorly in explaining day to day differences in exposure. The dataset serves as a baseline estimate and will be compared with a post intervention survey in the near future. The information obtained on control measures can be used to optimize the intervention scenarios that will be implemented in the different sectors by external occupational hygienists. The predictive exposure models will provide a relevant measure of average personal exposure that will be used in the sector wide health surveillance system.

A Mixture model with random-effects components for clustering correlated gene-expression profiles

The clustering of gene profiles across some experimental conditions of interest contributes significantly to the elucidation of unknown gene function, the validation of gene discoveries and the interpretation of biological processes. However, this clustering problem is not straightforward as the profiles of the genes are not all independently distributed and the expression levels may have been obtained from an experimental design involving replicated arrays. Ignoring the dependence between the gene profiles and the structure of the replicated data can result in important sources of variability in the experiments being overlooked in the analysis, with the consequent possibility of misleading inferences being made. We propose a random-effects model that provides a unified approach to the clustering of genes with correlated expression levels measured in a wide variety of experimental situations. Our model is an extension of the normal mixture model to account for the correlations between the gene profiles and to enable covariate information to be incorporated into the clustering process. Hence the model is applicable to longitudinal studies with or without replication, for example, time-course experiments by using time as a covariate, and to cross-sectional experiments by using categorical covariates to represent the different experimental classes. We show that our random-effects model can be fitted by maximum likelihood via the EM algorithm for which the E(expectation)and M(maximization) steps can be implemented in closed form. Hence our model can be fitted deterministically without the need for time-consuming Monte Carlo approximations. The effectiveness of our model-based procedure for the clustering of correlated gene profiles is demonstrated on three real datasets, representing typical microarray experimental designs, covering time-course, repeated-measurement and cross-sectional data. In these examples, relevant clusters of the genes are obtained, which are supported by existing gene-function annotation. A synthetic dataset is considered too. A Fortran program blue called EMMIX-WIRE (EM-based MIXture analysis WIth Random Effects) is available on request from the corresponding author.

Bayesian spatial analysis and disease mapping: tools to enhance planning and implementation of a schistosomiasis control programme in Tanzania

To predict the spatial distributions of Schistosoma haematobium and S. mansoni infections to assist planning the implementation of mass distribution of praziquantel as part of an on-going national control programme in Tanzania. Bayesian geostatistical models were developed using parasitological data from 143 schools. In the S. haematobium models, although land surface temperature and rainfall were significant predictors of prevalence, they became non-significant when spatial correlation was taken into account. In the S. mansoni models, distance to water bodies and annual minimum temperature were significant predictors, even when adjusting for spatial correlation. Spatial correlation occurred over greater distances for S. haematobium than for S. mansoni. Uncertainties in predictions were examined to identify areas requiring further data collection before programme implementation. Bayesian geostatistical analysis is a powerful and statistically robust tool for identifying high prevalence areas in a heterogeneous and imperfectly known environment.

Spatio-temporal modeling of fine particulate matter

Studies indicate that even short-term exposure to high concentrations of fine atmospheric particulate matter (PM2.5) can lead to long-term health effects. In this article, we propose a random effects model for PM2.5 concentrations. In particular, we anticipate urban/rural differences with regard to both mean levels and variability. Hence we introduce two random effects components, one for rural or background levels and the other as a supplement for urban areas. These are specified in the form of spatio-temporal processes. Weighting these processes through a population density surface results in nonstationarity in space. We analyze daily PM2.5 concentrations in three midwestern U.S. states for the year 2001. A fully Bayesian model is implemented, using MCMC techniques, which enables full inference with regard to process unknowns as well as predictions in time and space.

Estimation of genetic and environmental factors for melanoma onset using population‐based family data

Estimation of genetic and environmental contributions to cancers falls in the framework of generalized linear mixed modelling with several random effect components. Computational challenges remain, however, in dealing with binary or survival phenotypes. In this paper, we consider the analysis of melanoma onset in a population of 2.6 million nuclear families in Sweden, for which none of the current survival-based methodologies is feasible. We treat the disease outcome as a binary phenotype, so that the standard proportional hazard model leads to a generalized linear model with the complementary-log link function. For rare diseases this link is very close to the probit link, and thus allows the use of marginal likelihood for the estimation of the variance components. We correct for the survival length bias by censoring the parent generation within each family at the time they attain the same cumulative hazard as the child generation, thus improving the validity of the estimates. Our finding that childhood shared environment in addition to genetic factors had a considerable effect on the development of melanoma is consistent with epidemiological studies.

Testing in mixed-effects FANOVA models

We consider the testing problem in the mixed-effects functional analysis of variance models. We develop asymptotically optimal (minimax) testing procedures for testing the significance of functional global trend and the functional fixed effects based on the empirical wavelet coefficients of the data. Wavelet decompositions allow one to characterize various types of assumed smoothness conditions on the response function under the nonparametric alternatives. The distribution of the functional random-effects component is defined in the wavelet domain and captures the sparseness of wavelet representation for a wide variety of functions. The simulation study presented in the paper demonstrates the finite sample properties of the proposed testing procedures. We also applied them to the real data from the physiological experiments.

Formal Statistical Models for Estimating Radiocarbon Calibration Curves

We report on the development and implementation of a model-based statistical method for the estimation of radiocarbon calibration curves using diverse data. The method takes account of uncertainty on both the 14C and calendar scales, coherently integrating data, the calendar age estimates of which arise from different dating methods. It also allows for correlation between observations, if they have particular sources of uncertainty in common. We adopt an approach based on a random walk model, tailoring it to take account of possible calendar age offsets between different data sources by adding a random effect component. The latter allows us to use the same modeling framework for constructing the new calibration curve IntCal04, the comparison curve NotCal04, the Southern Hemisphere curve SHCal04, and the marine calibration curve Marine04.

Random effects selection in linear mixed models.

We address the important practical problem of how to select the random effects component in a linear mixed model. A hierarchical Bayesian model is used to identify any random effect with zero variance. The proposed approach reparameterizes the mixed model so that functions of the covariance parameters of the random effects distribution are incorporated as regression coefficients on standard normal latent variables. We allow random effects to effectively drop out of the model by choosing mixture priors with point mass at zero for the random effects variances. Due to the reparameterization, the model enjoys a conditionally linear structure that facilitates the use of normal conjugate priors. We demonstrate that posterior computation can proceed via a simple and efficient Markov chain Monte Carlo algorithm. The methods are illustrated using simulated data and real data from a study relating prenatal exposure to polychlorinated biphenyls and psychomotor development of children.

Using hierarchical modeling to measure ICU quality

To determine whether hierarchical modeling agrees with conventional logistic regression modeling on the identity of ICU quality outliers within a large multi-institutional database. Retrospective database analysis. Subset of the Project IMPACT database consisting of 40435 adult patients admitted to surgical, medical, and mixed surgical-medical ICUs ( n=55) between 1997 and 1999 who met inclusion criteria for SAPS II. The SAPS II score was customized to this database using conventional logistic regression and using a hierarchical (random coefficients) model. Both models exhibited excellent discrimination ( Cstatistic) and calibration (Hosmer-Lemeshow statistic). The hierarchical and nonhierarchical models had C statistics of.870 and.865, and HL statistics of 3.71 ( p>.88, df=8) and 8.94 ( p>.35, df=8), respectively. Since the random effects component of the hierarchical model accounts for between-hospital variability, only the fixed-effects coefficients were used to calculate the expected mortality rate based on the hierarchical model. The ratio and 95% confidence intervals of the observed to expected mortality rate were calculated using both models for each ICU. ICUs whose observed/expected ratio was either less than 1 or greater than 1, and whose 95% confidence interval did not include 1 were labeled as either high-performance or low-performance outliers, respectively. Analysis using kappa statistic revealed almost perfect agreement between the two models (nonhierarchical vs. hierarchical) on the identity of ICU quality outliers. Models obtained by customizing SAPS II using a nonhierarchical and a hierarchical approach exhibit excellent agreement on the identity of ICU quality outliers.

A Nonparametric Approach to Identifying Latent Relationships in Hierarchical Models

This paper provides a method for nonparametrically modeling the relationship between consumer preference for product features, such as reliability or durability, and covariates that describe consumers and how they use the product. This relationship is of interest to firms designing and delivering products to a market because the extent to which consumers are sensitive to particular features determines the potential profitability of product offerings, and affects decisions relating to appropriate distribution outlets and advertising strategies. The successful identification of these relationships also aids in efficiently targeting marketing activities to specific segments of the consumer population. The relationship between consumer preference for product features and observable covariates is important but is typically unknown. In addition, these relationships are often deeply embedded in a model hierarchy and are not observed directly. For example, in models of household choice, the observed outcomes are multinomial with probabilities driven by latent utilities or values that consumers place on the choice alternatives. These utilities are in turn a function of characteristics, such as price and product features, which are differentially valued. Of primary interest is the relationship between consumer sensitivity to product characteristics and readily observed covariates such as household demographics or aspects of product usage. Because the relationships of interest are not directly observed, it is difficult to draw inferences about them without formal statistical models. This paper presents a three-level hierarchical Bayes model for modeling binary consumer preferences as a function of observable covariates. The hierarchical model nonparametrically estimates the relationships between consumer preferences for product features and the covariates without assuming a specific functional form. A nonparametric model is particularly useful in the exploratory analysis of consumer data in which the primary purpose of the analysis is to generate further questions rather than provide specific answers to well-posed questions. This type of analysis is frequently encountered in marketing where a series of studies are commissioned to better understand the nature of demand. The first level of the hierarchy in the Bayesian model relates the binary consumer choice to the sensitivities of the consumer to product attributes such as brand name, price, reliability, and durability. The second level of the hierarchy models the heterogeneity across consumers using functions that relate attribute sensitivities to observable covariates. This level of the hierarchy also allows each respondent to have unique demand coefficients by introducing random effect components. The third level of the hierarchy specifies a smoothness prior for each of the unknown functions used in the second level. The approach is flexible and works well both when the unknown function can be closely approximated by a linear function and when it cannot be. A Bayesian model selection technique is used to determine which functions can be modeled using a linear function and which ones should be modeled nonparametrically to provide the necessary flexibility to estimate the function accurately. The proposed methodology is illustrated using data from a survey of consumer preferences for features of marine outboard engines that was collected as part of a consulting project. Our analysis focuses on measuring consumer preferences for engine features and their relationships to two variables related to boat length and engine size. Consumer preferences for engine features were obtained through a national survey conducted over the telephone. Preferences were elicited by means of a pairwise evaluation in which respondents chose between two engines that were identical in every respect except for two engine features. The methodology can be modified to allow for more complex comparisons such as conjoint data collected in full profiles. The application of a Bayesian model selection procedure indicates that 4 of the 28 covariate relationships in the model are nonlinear, while the other 24 are linear. The preferences associated with these four functions are involved in 56% of the pairwise comparisons in the study. Therefore, in practice, if the nonlinear functions are not properly estimated there is the potential to draw misleading inferences regarding 56% of the pairwise choices. Firms can use the estimates of the functions relating preferences to covariates in a number of ways. First, they can use the covariates to determine the total number of consumers who have high demand for a particular product feature, and then they can target communication efforts to those individuals. Alternatively, the empirical results can be used as a basis of subsequent analysis to obtain a more complete characterization of a market segment.

Reference Bayesian Methods for Generalized Linear Mixed Models

Bayesian methods furnish an attractive approach to inference in generalized linear mixed models. In the absence of subjective prior information for the random-effect variance components, these analyses are typically conducted using either the standard invariant prior for normal responses or diffuse conjugate priors. Previous work has pointed out serious difficulties with both strategies, and we show here that as in normal mixed models, the standard invariant prior leads to an improper posterior distribution for generalized linear mixed models. This article proposes and investigates two alternative reference (i.e., “objective” or “noninformative”) priors: an approximate uniform shrinkage prior and an approximate Jeffreys's prior. We give conditions for the existence of the posterior distribution under any prior for the variance components in conjunction with a uniform prior for the fixed effects. The approximate uniform shrinkage prior is shown to satisfy these conditions for several families of distributions, in some cases under mild constraints on the data. Simulation studies conducted using a logit-normal model reveal that the approximate uniform shrinkage prior improves substantially on a plug-in empirical Bayes rule and fully Bayesian methods using diffuse conjugate specifications. The methodology is illustrated on a seizure dataset.

Modelling binary data: a gibbs sampling approach

For a generalized linear model with random effects, Zeger and Karim used the Gibbs sampler to estimate the model parameters. However their methods of estimation have some drawbacks; especially in estimating the random effect components which, as stated in their paper, have 20 to 30 percent bias in the posterior mean of the random effect variances. Here we use the adaptive rejection sampling method proposed by Gilks and Wild. The adaptive rejection sampling (ARS) algorithm is an efficient and direct method to sample from complicated log-concave densities often encountered in Gibbs sampling. Good results are obtained from simulations. We applied this model to analyze data obtained from experiments on the quality of telephone connection. For diagnostic checking of our models, we used the concept of latent residuals introduced by Albert and Chib.

Robust nonparametrics in mixed-MANOCOVA models

In robust and nonparametric MANOVA models, the basic assumptions of independence, homoscedasticity and multinormality of the error components have been relaxed to a certain extent. In mixed-effects MANOVA models, the random effects components (due to concomitant variates) rest on the linearity of the regression function and some other distributional homogeneity conditions that may not hold universally, and avoidance of such regularity conditions generally introduce complications. Some of these difficulties are eliminated here through a conditional functional estimation approach, and in this setup, improved estimation of the fixed effects parameters is presented in a unified manner. Robustness and efficacy of these nonparametric procedures are appraised, and the picture is compared with their parametric as well as semiparametric counterparts.

Between Algorithms: A “Short Cut” Restricted Maximum Likelihood Procedure to Estimate Variance Components

A restricted maximum likelihood procedure is described to estimate variance and covariance components in a multivariate mixed model when records are missing for some traits. The algorithm combines features of an expectation-maximization algorithm to estimate the within random effects components with the method of scoring to estimate the between random effects components. The procedure is computationally less demanding per round of iteration than the method of scoring, although the number of iterates required to reach convergence is increased. A computing strategy is described for the example of estimating genetic parameters for first and later lactations of dairy cows.