Showing papers on "Mixed model published in 1998"
TL;DR: This paper is written as a step-by-step tutorial that shows how to fit the two most common multilevel models: (a) school effects models, designed for data on individuals nested within naturally occurring hierarchies (e.g., students within classes); and (b) individual growth models,designed for exploring longitudinal data (on individuals) over time.
Abstract: SAS PROC MIXED is a flexible program suitable for fitting multilevel models, hierarchical linear models, and individual growth models. Its position as an integrated program within the SAS statistic...
2,903 citations
TL;DR: This procedure implements random effects in the statistical model and permits modeling the covariance structure of the data, and can compute efficient estimates of fixed effects and valid standard errors of the estimates in the SAS System.
Abstract: Mixed linear models were developed by animal breeders to evaluate genetic potential of bulls. Application of mixed models has recently spread to all areas of research, spurred by availability of advanced computer software. Previously, mixed model analyses were implemented by adapting fixed-effect methods to models with random effects. This imposed limitations on applicability because the covariance structure was not modeled. This is the case with PROC GLM in the SAS® System. Recent versions of the SAS System include PROC MIXED. This procedure implements random effects in the statistical model and permits modeling the covariance structure of the data. Thereby, PROC MIXED can compute efficient estimates of fixed effects and valid standard errors of the estimates. Modeling the covariance structure is especially important for analysis of repeated measures data because measurements taken close in time are potentially more highly correlated than those taken far apart in time.
2,770 citations
TL;DR: The paper takes the reader through the relevant practicalities of model fitting, interpretation and criticism and demonstrates that, in a simple case such as this, analyses based upon these model-based approaches produce reassuringly similar inferences to standard analysesbased upon more conventional methods.
Abstract: Much of the research in epidemiology and clinical science is based upon longitudinal designs which involve repeated measurements of a variable of interest in each of a series of individuals. Such designs can be very powerful, both statistically and scientifically, because they enable one to study changes within individual subjects over time or under varied conditions. However, this power arises because the repeated measurements tend to be correlated with one another, and this must be taken into proper account at the time of analysis or misleading conclusions may result. Recent advances in statistical theory and in software development mean that studies based upon such designs can now be analysed more easily, in a valid yet flexible manner, using a variety of approaches which include the use of generalized estimating equations, and mixed models which incorporate random effects. This paper provides a particularly simple illustration of the use of these two approaches, taking as a practical example the analysis of a study which examined the response of portable peak expiratory flow meters to changes in true peak expiratory flow in 12 children with asthma. The paper takes the reader through the relevant practicalities of model fitting, interpretation and criticism and demonstrates that, in a simple case such as this, analyses based upon these model-based approaches produce reassuringly similar inferences to standard analyses based upon more conventional methods.
627 citations
Book•
30 Jan 1998
TL;DR: One-sample problems as mentioned in this paper have been used to evaluate the robustness of estimates of location in linear models with respect to the number of false positives and false negatives of the estimated locations.
Abstract: One-Sample Problems Introduction Location Model Geometry and Inference in the Location Model Examples Properties of Norm-Based Inference Robustness Properties of Norm-Based Inference Inference and the Wilcoxon Signed-Rank Norm Inference Based on General Signed-Rank Norms Ranked Set Sampling L1 Interpolated Confidence Intervals Two-Sample Analysis Two-Sample Problems Introduction Geometric Motivation Examples Inference Based on the Mann-Whitney-Wilcoxon General Rank Scores L1 Analyses Robustness Properties Proportional Hazards Two-Sample Rank Set Sampling (RSS) Two-Sample Scale Problem Behrens-Fisher Problem Paired Designs Linear Models Introduction Geometry of Estimation and Tests Examples Assumptions for Asymptotic Theory Theory of Rank-Based Estimates Theory of Rank-Based Tests Implementation of the R Analysis L1 Analysis Diagnostics Survival Analysis Correlation Model High Breakdown (HBR) Estimates Diagnostics for Differentiating between Fits Rank-Based Procedures for Nonlinear Models Experimental Designs: Fixed Effects Introduction One-Way Design Multiple Comparison Procedures Two-Way Crossed Factorial Analysis of Covariance Further Examples Rank Transform Models with Dependent Error Structure Introduction General Mixed Models Simple Mixed Models Arnold Transformations General Estimating Equations (GEE) Time Series Multivariate Multivariate Location Model Componentwise Spatial Methods Affine Equivariant and Invariant Methods Robustness of Estimates of Location Linear Model Experimental Designs Appendix: Asymptotic Results References Index
505 citations
TL;DR: In this paper, a class of models for an additive decomposition of groups of curves stratified by crossed and nested factors is introduced, and the model parameters are estimated using a highly efficient implementation of the EM algorithm for restricted maximum likelihood (REML) estimation based on a preliminary eigenvector decomposition.
Abstract: We introduce a class of models for an additive decomposition of groups of curves stratified by crossed and nested factors, generalizing smoothing splines to such samples by associating them with a corresponding mixed-effects model. The models are also useful for imputation of missing data and exploratory analysis of variance. We prove that the best linear unbiased predictors (BLUPs) from the extended mixed-effects model correspond to solutions of a generalized penalized regression where smoothing parameters are directly related to variance components, and we show that these solutions are natural cubic splines. The model parameters are estimated using a highly efficient implementation of the EM algorithm for restricted maximum likelihood (REML) estimation based on a preliminary eigenvector decomposition. Variability of computed estimates can be assessed with asymptotic techniques or with a novel hierarchical bootstrap resampling scheme for nested mixed-effects models. Our methods are applied to me...
425 citations
TL;DR: The problem of detecting influential subjects in the context of longitudinal data is considered, following the approach of local influence proposed by Cook.
Abstract: The linear mixed model has become an important tool in modelling, partially due to the introduction of the SAS procedure MIXED, which made the method widely available to practising statisticians. Its growing popularity calls for data-analytic methods to check the underlying assumptions and robustness. Here, the problem of detecting influential subjects in the context of longitudinal data is considered, following the approach of local influence proposed by Cook.
262 citations
TL;DR: In this paper, the authors show that the smoothing spline estimates evaluated at design points are best linear unbiased prediction (BLUP) estimates and that the GML estimates of smoothing parameters an...
Abstract: Spline-smoothing techniques are commonly used to estimate the mean function in a nonparametric regression model. Their performances depend greatly on the choice of smoothing parameters. Many methods of selecting smoothing parameters such as generalized maximum likelihood (GML), generalized cross-validation (GCV), and unbiased risk (UBR), have been developed under the assumption of independent observations. They tend to underestimate smoothing parameters when data are correlated. In this article, I assume that observations are correlated and that the correlation matrix depends on a parsimonious set of parameters. I extend the GML, GCV, and UBR methods to estimate the smoothing parameters and the correlation parameters simultaneously. I also relate a smoothing spline model to three mixed-effects models. These relationships show that the smoothing spline estimates evaluated at design points are best linear unbiased prediction (BLUP) estimates and that the GML estimates of the smoothing parameters an...
250 citations
Book•
01 Jan 1998
TL;DR: A comparison of Random Models with Unequal Cell Frequencies in the Last Stage with Balanced Random and Mixed Models and Multivariate Mixed and Random Models shows that the latter are more prone to bias than the former.
Abstract: Nature of Exact and Optimum Tests in Mixed Linear Models. Balanced Random and Mixed Models. Measures of Data Imbalance. Unbalanced One-Way and Two-Way Random Models. Random Models with Unequal Cell Frequencies in the Last Stage. Tests in Unbalanced Mixed Models. Recovery of Inter-Block Information. Split-Plot Designs Under Mixed and Random Models. Tests Using Generalized P-Values. Multivariate Mixed and Random Models. Appendix. General Bibliography. Indexes.
191 citations
TL;DR: In this article, a general family of nonparametric mixed effects models is proposed, where smoothing splines are used to model the fixed effects and are estimated by maximizing the penalized likelihood function, and the random effects are modeled parametrically by assuming that the covariance function depends on a parsimonious set of parameters.
Abstract: We propose a general family of nonparametric mixed effects models. Smoothing splines are used to model the fixed effects and are estimated by maximizing the penalized likelihood function. The random effects are generic and are modelled parametrically by assuming that the covariance function depends on a parsimonious set of parameters. These parameters and the smoothing parameter are estimated simultaneously by the generalized maximum likelihood method. We derive a connection between a nonparametric mixed effects model and a linear mixed effects model. This connection suggests a way of fitting a nonparametric mixed effects model by using existing programs. The classical two-way mixed models and growth curve models are used as examples to demonstrate how to use smoothing spline analysis-of-variance decompositions to build nonparametric mixed effects models. Similarly to the classical analysis of variance, components of these nonparametric mixed effects models can be interpreted as main effects and interactions. The penalized likelihood estimates of the fixed effects in a two-way mixed model are extensions of James-Stein shrinkage estimates to correlated observations. In an example three nested nonparametric mixed effects models are fitted to a longitudinal data set.
179 citations
TL;DR: It is shown by cross-validation using five real data sets (oilseed rape, Brassica napus L.) that the predictive accuracy of BLUPs based on models with multiplicative terms may be better than that of least-squares estimators based on the same models and also better than BLUPS based on ANOVA models.
Abstract: Results of multi-environment trials to evaluate new plant cultivars may be displayed in a two-way table of genotypes by environments. Different estimators are available to fill the cells of such tables. It has been shown previously that the predictive accuracy of the simple genotype by environment mean is often lower than that of other estimators, e.g. least-squares estimators based on multiplicative models, such as the additive main effects multiplicative interaction (AMMI) model, or empirical best-linear unbiased predictors (BLUPs) based on a two-way analysis-of-variance (ANOVA) model. This paper proposes a method to obtain BLUPs based on models with multiplicative terms. It is shown by cross-validation using five real data sets (oilseed rape, Brassica napus L.) that the predictive accuracy of BLUPs based on models with multiplicative terms may be better than that of least-squares estimators based on the same models and also better than BLUPs based on ANOVA models.
163 citations
TL;DR: In this paper, the authors consider generalized linear mixed models (GLMMs) for clustered data when one of the predictors is measured with error and show that the observed data also follow a GLMM but with a different fixed effects structure from the original model, a different and more complex random effects structure, and restrictions on the parameters.
Abstract: We consider generalized linear mixed models (GLMMs) for clustered data when one of the predictors is measured with error. When the measurement error is additive and normally distributed and the error-prone predictor is itself normally distributed, we show that the observed data also follow a GLMM but with a different fixed effects structure from the original model, a different and more complex random effects structure, and restrictions on the parameters. This characterization enables us to compute the biases that result in common GLMMs when one ignores measurement error. For instance, in one common situation the biases in parameter estimates become larger as the number of observations within a cluster increases, both for regression coefficients and for variance components. Parameter estimation is described using the SIMEX method, a relatively new functional method that makes no assumptions about the structure of the unobservable predictors. Simulations and an example illustrate the results.
TL;DR: The mixed model approach to the analysis of repeated measurements allows users to model the covariance structure of their data as mentioned in this paper, rather than using a univariate or a multivariate test statistic for analyzing effects.
Abstract: The mixed model approach to the analysis of repeated measurements allows users to model the covariance structure of their data. That is, rather than using a univariate or a multivariate test statistic for analyzing effects, tests that assume a particular form for the covariance structure, the mixed model approach allows the data to determine the appropriate structure. Using the appropriate covariance structure should result in more powerful tests of the repeated measures effects according to advocates of the mixed model approach. SAS’ (SAS Institute, 1996) mixed model program, PROC MIXED, provides users with two information Criteria for selecting the ‘best’ covariance structure, Akaike (1974) and Schwarz (1978). Our study compared these log likelihood tests to see how effective they would be for detecting various population covariance structures. In particular, the criteria were compared in nonspherical repeated measures designs having equal/unequal group sizes and covariance matrices when data were both ...
TL;DR: In this paper, a simple method based on simulated moments is proposed for estimating the fixed-effects and variance components in a generalized linear mixed model (GLMM), which is not only computationally attractive but also leads to consistent estimators.
Abstract: A simple method based on simulated moments is proposed for estimating the fixed-effects and variance components in a generalized linear mixed model (GLMM). It is shown that the method is not only computationally attractive but also leads to consistent estimators. On the other hand, simulation shows that the method can be quite inefficient.
TL;DR: This paper applies the ‘working parameter’ approach to derive alternative EM‐type implementations for fitting mixed effects models, which it is shown empirically can be hundreds of times faster than the common EM‐ type implementations.
Abstract: The mixed effects model, in its various forms, is a common model in applied statistics. A useful strategy for fitting this model implements EM-type algorithms by treating the random effects as missing data. Such implementations, however, can be painfully slow when the variances of the random effects are small relative to the residual variance. In this paper, we apply the ‘working parameter’ approach to derive alternative EM-type implementations for fitting mixed effects models, which we show empirically can be hundreds of times faster than the common EM-type implementations. In our limited simulations, they also compare well with the routines in S-PLUS® and Stata® in terms of both speed and reliability. The central idea of the working parameter approach is to search for efficient data augmentation schemes for implementing the EM algorithm by minimizing the augmented information over the working parameter, and in the mixed effects setting this leads to a transfer of the mixed effects variances into the regression slope parameters. We also describe a variation for computing the restricted maximum likelihood estimate and an adaptive algorithm that takes advantage of both the standard and the alternative EM-type implementations.
TL;DR: The generalized linear mixed effects model with normal errors is extended by allowing the random effects to have a non-parametric prior distribution, using a Dirichlet process prior for the general distribution of therandom effects.
Abstract: The linear mixed effects model with normal errors is a popular model for the analysis of repeated measures and longitudinal data. The generalized linear model is useful for data that have non-normal errors but where the errors are uncorrelated. A descendant of these two models generates a model for correlated data with non-normal errors, called the generalized linear mixed model (GLMM). Frequentist attempts to fit these models generally rely on approximate results and inference relies on asymptotic assumptions. Recent advances in computing technology have made Bayesian approaches to this class of models computationally feasible. Markov chain Monte Carlo methods can be used to obtain 'exact' inference for these models, as demonstrated by Zeger and Karim. In the linear or generalized linear mixed model, the random effects are typically taken to have a fully parametric distribution, such as the normal distribution. In this paper, we extend the GLMM by allowing the random effects to have a non-parametric prior distribution. We do this using a Dirichlet process prior for the general distribution of the random effects. The approach easily extends to more general population models. We perform computations for the models using the Gibbs sampler.
TL;DR: In this paper, the authors extend Cox's idea of differential gradients within columns of a Latin square to within blocks for incomplete block and row-column designed experiments and, in addition, treat them as random effects.
Abstract: Spatial analysis and blocking analysis of experimental results are treated separately in the literature. Here we combine these analyses into a single analysis. The information arising from the random nature of different gradients within incomplete blocks is used to adjust treatment means. We extend Cox's (1958, Journal of the Royal Statistical Society, Series B 20, 193-204) idea of differential gradients within columns of a Latin square to within blocks for incomplete block and row-column designed experiments and, in addition, treat them as random effects. With this analysis, the restrictions on randomization due to blocking are taken into consideration whereas they are often ignored in spatial analysis literature. Some comments on designing experiments and analyzing experimental results to control heterogeneity are presented. A numerical example illustrates the computational procedure and indicates effect of alternative analyses. The class of augmented experiment designs has been found useful for experiments involving comparisons of standard check treatments with a set of new and untried treatments, usually with one replicate. Interreplicate, interblock, interrow, and/or intercolumn information is available to use in obtaining solutions for new treatment effects. Since the new treatment effects are often considered to be random effects, their distributional properties may be used to increase the efficiency of the experiment. We demonstrate the statistical procedures for recovering this information in block and row-column designs using mixed model procedures.
01 Jan 1998
TL;DR: In this paper, the best linear unbiased estimators (BLUE) of fixed effects, with unknown variance components substituted by the REML estimates, are jointly asymptotically normal with the estimates.
Abstract: We show in a general mixed model the best linear unbiased estimators (BLUE) of fixed effects, with unknown variance components substituted by the REML estimates, are jointly asymptotically normal with the REML estimates. We also prove that given sufficient information the empirical distributions of the best linear unbiased predictors (BLUP) of random effects, again with REML-estimated variance components, converge to the true distributions of the corresponding ran- dom effects. As a consequence, we obtain a consistent estimate of the asymptotic variance-covariance matrix of the REML estimates. The results require neither that the data is normally distributed nor that the model is hierarchical (nested).
TL;DR: In this article, a simple example illustrates how very critical the approximations can be for the performance of the variance component estimators, i.e., intra-class correlation or heritability.
Abstract: Evaluation of the likelihood in mixed models for non-normal data, e.g. dependent binary data, involves high dimensional integration, which offers severe numerical problems. Penalized quasi-likelihood, iterative re-weighted restricted maximum likelihood and adjusted profile h-likelihood estimation are methods which avoid numerical integration. They will be derived by approximation of the maximum likelihood equations. For binary data, these estimation procedures may yield seriously biased estimates for components of variance, intra-class correlation or heritability. An analytical evaluation of a simple example illustrates how very critical the approximations can be for the performance of the variance component estimators.
TL;DR: In this article, the authors present a methodology for simultaneously modeling three components of a general mixed-model approach to robust design: location (fixed) effects, dispersion effects, and random effects.
Abstract: This article presents a methodology for simultaneously modeling three components of a general mixed-model approach to robust design—location (fixed) effects, dispersion effects, and random effects. Control, noise, and random factors can be accommodated with this approach. Parameters associated with all three are estimated jointly using residual maximum likelihood and assuming normality. Simulated and real datasets illustrate the key concepts and advantages over previously proposed approaches.
TL;DR: In this article, a method for the analysis of censored records based on a Gaussian mixed effects model is presented, which uses the Gibbs sampler and data augmentation, and examples are presented using the motorette data of Schmee & Hahn plus other simulated data sets that illustrate animal breeding applications.
Abstract: Adopting a Bayesian viewpoint, a method is presented for the analysis of censored records based on a Gaussian mixed effects model. The method uses the Gibbs sampler and data augmentation. Examples are presented using the motorette data of Schmee & Hahn (1979, Technometrics 21, 417–432) plus other simulated data sets that illustrate animal breeding applications.
TL;DR: If the residuals from a longitudinal fit for the time-varying covariate behave like measurement errors, the original parameters can be estimated without the need for additional validation or reliability studies.
Abstract: We explore the effects of measurement error in a time-varying covariate for a mixed model applied to a longitudinal study of plasma levels and dietary intake of beta-carotene. We derive a simple expression for the bias of large sample estimates of the variance of random effects in a longitudinal model for plasma levels when dietary intake is treated as a time-varying covariate subject to measurement error. In general, estimates for these variances made without consideration of measurement error are biased positively, unlike estimates for the slope coefficients which tend to be ‘attenuated’ If we can assume that the residuals from a longitudinal fit for the time-varying covariate behave like measurement errors, we can estimate the original parameters without the need for additional validation or reliability studies. We propose a method to test this assumption and show that the assumption is reasonable for the example data. We then use a likelihood-based method of estimation that involves a simple extension of existing methods for fitting mixed models. Simulations illustrate the properties of the proposed estimators. © 1998 John Wiley & Sons, Ltd.
TL;DR: The empirical semi-variogram of ordinary least squares residuals is extended to non-stationary models which include random effects other than intercepts, and will be applied to prostate cancer data, taken from the Baltimore Longitudinal Study of Aging.
Abstract: Diggle (1988) described how the empirical semi-variogram of ordinary least squares residuals can be used to suggest an appropriate serial correlation structure in stationary linear mixed models. In this paper, this approach is extended to non-stationary models which include random effects other than intercepts, and will be applied to prostate cancer data, taken from the Baltimore Longitudinal Study of Aging. A simulation study demonstrates the effectiveness of this extended variogram for improving the covariance structure of the linear mixed model used to describe the prostate data.
TL;DR: In this article, a simulation-based approach for determining Bayesian tolerance intervals in variance component models is presented, which handles different kinds of tolerance intervals and is easily tailored to particular applications.
Abstract: This article presents a simulation-based approach for determining Bayesian tolerance intervals in variance component models. The approach handles different kinds of tolerance intervals in a straightforward fashion and is easily tailored to particular ap..
TL;DR: This article proposed a two-step approximate likelihood approach (AL) for the estimation of three types of parameters (fixed effect parameters, random effects and their variance component) in the Poisson mixed model.
Abstract: The application of the Poisson mixed model has been hampered by the difficulty of computation in evaluating the marginal likelihood of the parameters involved. Many approximate approaches have recently been proposed for inference about the generalized linear mixed model which refers to the Poisson mixed model as a special case, for example, the penalized quasi-likelihood (PQL) approach of Breslow and Clayton (1993), and the generalized estimating function (GEF) approach of Waclawiw and Liang (1993). We show in the thesis that both the PQL and GEF produce inconsistent inference for the variance component in the Poisson mixed model. The thesis then proposes a two-step approximate likelihood approach (AL) for the estimation of three types of parameters (fixed effect parameters, random effects and their variance component) in the Poisson mixed model. In the first step, an approximate likelihood function of count data is constructed to estimate the fixed effect parameters and the variance component by applying a conjugate Bayesian theorem. In the second step, the random effects are estimated by minimizing their approximate posterior mean square error. Our estimates are always consistent for both the fixed effect parameters and the variance component. When the actual variance component is near zero, our estimates are almost efficient for both the fixed effect parameters and the variance component, and are almost optimal for the random effects. When the actual variance component is away from zero, our estimates are always asymptotically unbiased for the fixed effect parameters, whereas our estimate is asymptotically negative biased for the variance component. Another desirable merit is that, unlike the existing approaches mentioned above, our estimates for both the fixed effect parameters and the variance component only depend on the distribution of random effects rather than the estimates of random effects. An important finding is that the asymptotic covariance of our estimates for the fixed effect parameters will become smaller in general as the variance component, an index of the intra-cluster association, increases, and can be noticeably reduced by assigning the values of the fixed effect covariates as different as possible among different observations in any cluster. However, if the fixed effect covariate has the same or almost equal values among different observations in any cluster, the asymptotic variance of the estimate for the corresponding fixed effect parameter may increase as the variance component gets larger. This feature may be useful in designing a valid experiment or sampling for the Poisson mixed model. Unless the variance component is small, the fixed effect covariates should be designed to have values as different as possible among different observations in any cluster. It is further shown, through simulation, the proposed approach performs better than the PQL and GEF approaches.
TL;DR: In this article, the authors present an approach for estimating the order of disability events in activities of daily living using Discrete Longitudinal Data using fixed and mixed models with application to longitudinal data.
Abstract: Generalized Linear Models.- Linear Models, Vector Spaces, and Residual Likelihood.- An Assessment of Approximate Maximum Likelihood Estimators in Generalized Linear Models.- Scaled Link Functions for Heterogeneous Ordinal Response Data.- Longitudinal Data Analysis.- Software Design for Longitudinal Data Analysis.- Asymptotic Properties of Nonlinear Mized-Effects Models.- Structured Antedependence Models for Longitudinal Data.- Effect of Confounding and Other Misspecification in Models for Longitudinal Data.- The Linear Mixed Model. A Critical Investigation in the Context of Longitudinal Data.- Modelling the Order of Disability Events in Activities of Daily Living Using Discrete Longitudinal Data.- Estimation of Subject Means in Fixed and Mixed Models with Application to Longitudinal Data.- Modeling Toxicological Multivariate Mortality Data: a Bayesian Perspective.- Comparison of Methods for General Nonlinear Mixed-Effects Models.- Repeated Measures Analysis Using Mixed Models: Some Simulation Results.- Spatial Data Analysis.- Object Identification Using Markov Random Field Segmentation Models at Multiple Resolutions of a Rectangular Lattice.- Comparison of Some Sampling Designs for Spatially Clustered Populations.- Using Geostatistical Techniques to Map the Distribution of Tree Species from Ground Inventory Data.- Global Analysis of Ozone Data Based on Spherical Splines.- Bounded Influence Estimation in a Spatial Linear Mixed Model.- Spatial Correlation Models as Applied to Evolutionary Biology.- Rainfall Modelling Using a Latent Guassian Variable.- Estimation of Individual Exposure Following a Chemical Spill in Superior, Wisconsin.- Flexible Response Surface Methods via Spatial Regression and EBLUPS.- Robust Semivariogram Estimation in the Presence of Influential Spatial Data Values.- Modelling Spatio-Temporal Processes.- Elephant Seal Movements: Dive Types and Their Sequences.- Models for Continuous Stationary Space-time Processes.- A Comparison of Two Spatio-temporal Semivariograms with Use in Agriculture.- Structuring Correlation Within Hierarchical Spatio-temporal Models for Disease Rates.- Modelling Messy Data.- Generalized Linear Mixed Measurement Error Models:.- Calculating the Appropriate Information Matrix for Log-linear Models When Data Are Missing at Random.- Nonparametric Regression in the Presence of Correlated Errors.- Exploratory Modelling of Multiple Non-Stationary Time Series: Latent Process Structure and Decompositions.- Modelling Correlations Between Diagnostic Tests in Efficacy Studies With an Imperfect Reference Test.- Special Topics and Future Directions.- Combining Standard Block Analyses with Spatial Analyses Under a Random Effects Model.- Spatial and Longitudinal Data Analysis: Two Histories with a Common Future?.
TL;DR: In this article, the authors apply the Kalman filter to the analysis of multi-unit variance components models where each unit's response profile follows a state space model and use the signal extraction approach to smooth individual profiles.
Abstract: We apply the Kalman Filter to the analysis of multi-unit variance components models where each unit's response profile follows a state space model. We use mixed model results to obtain estimates of unit-specific random effects, state disturbance terms and residual noise terms. We use the signal extraction approach to smooth individual profiles. We show how to utilize the Kalman Filter to efficiently compute the restricted loglikelihood of the model. For the important special case where each unit's response profile follows a continuous structural time series model with known transition matrix we derive an EM algorithm for the restricted maximum likelihood (REML) estimation of the variance components. We present details for the case where individual profiles are modeled as local polynomial trends or polynomial smoothing splines.
TL;DR: A method for model identification of biological systems described by stochastic linear differential equations using a new computational technique for statistical Bayesian inference, namely mixed graphical models in the sense of Lauritzen and Wermuth, is presented.
TL;DR: This paper presents techniques of parameter estimation in heteroskedastic mixed models having i) heterogeneous log residual variances which are described by a linear model of explanatory covariates and ii) log residual and log u-components linearly related which makes the intraclass correlation a monotonic function of the residual variance.
Abstract: This paper presents techniques of parameter estimation in heteroskedastic mixed models having i) heterogeneous log residual variances which are described by a linear model of explanatory covariates and ii) log residual and log u-components linearly related. This makes the intraclass correlation a monotonic function of the residual variance. Cases of a homogeneous variance ratio and of a homogeneous u-component of variance are also included in this parameterization. Estimation and testing procedures of the corresponding dispersion parameters are based on restricted maximum likelihood procedures. Estimating equations are derived using the standard and gradient EM. The analysis of a small example is outlined to illustrate the theory. © Inra/Elsevier, Paris
TL;DR: In this paper, the best linear unbiased predictor (BLUP) was developed for individual measurement prediction under a mixed linear model, where the fixed and random effects and the missing observations were taken into account.
Abstract: The problem of predicting individual measurement is considered. This paper develops the Best Linear Unbiased Predictor (BLUP) of the fixed and random effects and the missing observations, under a mixed linear model The mean square errors are also obtained.
Journal Article•
TL;DR: A new approach is used to evaluate three current nonlinear models of development of human stature allowing for individual variation in the estimation of model parameters in a population average model of growth, more parsimonious than previous techniques.
Abstract: The modern mixed model approach is used to evaluate three current nonlinear models of development of human stature. By combining both fixed and random effects in the same model, the mixed approach incorporates variability between subjects in the estimation of the mean parameter values. This allows us to provide a single statistical test for the differences between each pair of statistical models. Asymptotic growth models from Preece and Baines (1978), Jolicoeur et al. (1988, 1991,1992), and Kanefuji and Shohoji (1990) were applied to height data collected from 28 males and 25 females. The NLINMIX Macro from SAS was used to evaluate the fit of each model allowing for two random components in addition to the fixed mean parameter values. In every case, the addition of random parameters improved the fit of each growth model. Models were evaluated by the calculation of the Akaike Information Criterion, differences in -2 log likelihood, and determination of the residual variance. For males, the Jolicoeur et al. model was superior, while for females, the Kanefuji and Shohoji model provided the best fit. This new approach is more parsimonious than previous techniques by allowing for individual variation in the estimation of model parameters in a population average model of growth.