Showing papers on "Mixed model published in 2007"

WOMBAT: a tool for mixed model analyses in quantitative genetics by restricted maximum likelihood (REML).

Abstract: WOMBAT is a software package for quantitative genetic analyses of continuous traits, fitting a linear, mixed model; estimates of covariance components and the resulting genetic parameters are obtained by restricted maximum likelihood. A wide range of models, comprising numerous traits, multiple fixed and random effects, selected genetic covariance structures, random regression models and reduced rank estimation are accommodated. WOMBAT employs up-to-date numerical and computational methods. Together with the use of efficient compilers, this generates fast executable programs, suitable for large scale analyses. Use of WOMBAT is illustrated for a bivariate analysis. The package consists of the executable program, available for LINUX and WINDOWS environments, manual and a set of worked example, and can be downloaded free of charge from (http://agbu. une.edu.au/~kmeyer/wombat.html).

How to separate genetic and environmental causes of similarity between relatives.

Abstract: Related individuals often have similar phenotypes, but this similarity may be due to the effects of shared environments as much as to the effects of shared genes. We consider here alternative approaches to separating the relative contributions of these two sources to phenotypic covariances, comparing experimental approaches such as cross-fostering, traditional statistical techniques and more complex statistical models, specifically the ‘animal model’. Using both simulation studies and empirical data from wild populations, we demonstrate the ability of the animal model to reduce bias due to shared environment effects such as maternal or brood effects, especially where pedigrees contain multiple generations and immigration rates are low. However, where common environment effects are strong, a combination of both cross-fostering and an animal model provides the best way to avoid bias. We illustrate ways of partitioning phenotypic variance into components of additive genetic, maternal genetic, maternal environment, common environment, permanent environment and temporal effects, but also show how substantial confounding between these different effects may occur. Whilst the flexibility of the mixed model approach is extremely useful for incorporating the spatial, temporal and social heterogeneity typical of natural populations, the advantages will inevitably be restricted by the quality of pedigree information and care needs to be taken in specifying models that are appropriate to the data.

Mixed Hidden Markov Models

Abstract: Hidden Markov models (HMMs) are a useful tool for capturing the behavior of overdispersed, autocorrelated data. These models have been applied to many different problems, including speech recognition, precipitation modeling, and gene finding and profiling. Typically, HMMs are applied to individual stochastic processes; HMMs for simultaneously modeling multiple processes—as in the longitudinal data setting—have not been widely studied. In this article I present a new class of models, mixed HMMs (MHMMs), where I use both covariates and random effects to capture differences among processes. I define the models using the framework of generalized linear mixed models and discuss their interpretation. I then provide algorithms for parameter estimation and illustrate the properties of the estimators via a simulation study. Finally, to demonstrate the practical uses of MHMMs, I provide an application to data on lesion counts in multiple sclerosis patients. I show that my model, while parsimonious, can describe the...

An empirical Bayes method for estimating epistatic effects of quantitative trait loci.

Abstract: The genetic variance of a quantitative trait is often controlled by the segregation of multiple interacting loci. Linear model regression analysis is usually applied to estimating and testing effects of these quantitative trait loci (QTL). Including all the main effects and the effects of interaction (epistatic effects), the dimension of the linear model can be extremely high. Variable selection via stepwise regression or stochastic search variable selection (SSVS) is the common procedure for epistatic effect QTL analysis. These methods are computationally intensive, yet they may not be optimal. The LASSO (least absolute shrinkage and selection operator) method is computationally more efficient than the above methods. As a result, it has been widely used in regression analysis for large models. However, LASSO has never been applied to genetic mapping for epistatic QTL, where the number of model effects is typically many times larger than the sample size. In this study, we developed an empirical Bayes method (E-BAYES) to map epistatic QTL under the mixed model framework. We also tested the feasibility of using LASSO to estimate epistatic effects, examined the fully Bayesian SSVS, and reevaluated the penalized likelihood (PENAL) methods in mapping epistatic QTL. Simulation studies showed that all the above methods performed satisfactorily well. However, E-BAYES appears to outperform all other methods in terms of minimizing the mean-squared error (MSE) with relatively short computing time. Application of the new method to real data was demonstrated using a barley dataset.

The accuracy of varietal selection using factor analytic models for multi-environment plant breeding trials

Abstract: Modeling of cultivar x trial effects for multienvironment trials (METs) within a mixed model framework is now common practice in many plant breeding programs The factor analytic (FA) model is a parsimonious form used to approximate the fully unstructured form of the genetic variance-covariance matrix in the model for MET data In this study, we demonstrate that the FA model is generally the model of best fit across a range of data sets taken from early generation trials in a breeding program In addition, we demonstrate the superiority of the FA model in achieving the most common aim of METs, namely the selection of superior genotypes Selection is achieved using best linear unbiased predictions (BLUPs) of cultivar effects at each environment, considered either individually or as a weighted average across environments In practice, empirical BLUPs (E-BLUPs) of cultivar effects must be used instead of BLUPs since variance parameters in the model must be estimated rather than assumed known While the optimal properties of minimum mean squared error of prediction (MSEP) and maximum correlation between true and predicted effects possessed by BLUPs do not hold for E-BLUPs, a simulation study shows that E-BLUPs perform well in terms of MSEP

Residual Analysis for Linear Mixed Models

Abstract: Residuals are frequently used to evaluate the validity of the assumptions of statistical models and may also be employed as tools for model selection. For standard (normal) linear models, for example, residuals are used to verify homoscedasticity, linearity of effects, presence of outliers, normality and independence of the errors. Similar uses may be envisaged for three types of residuals that emerge from the fitting of linear mixed models. We review some of the residual analysis techniques that have been used in this context and propose a standardization of the conditional residual useful to identify outlying observations and clusters. We illustrate the procedures with a practical example.

Fixed and Random Effects Selection in Linear and Logistic Models

Abstract: We address the problem of selecting which variables should be included in the fixed and random components of logistic mixed effects models for correlated data. A fully Bayesian variable selection is implemented using a stochastic search Gibbs sampler to estimate the exact model-averaged posterior distribution. This approach automatically identifies subsets of predictors having nonzero fixed effect coefficients or nonzero random effects variance, while allowing uncertainty in the model selection process. Default priors are proposed for the variance components and an efficient parameter expansion Gibbs sampler is developed for posterior computation. The approach is illustrated using simulated data and an epidemiologic example.

The Impact of Misspecifying the Within-Subject Covariance Structure in Multiwave Longitudinal Multilevel Models: A Monte Carlo Study

Abstract: This Monte Carlo study examined the impact of misspecifying the Σ matrix in longitudinal data analysis under both the multilevel model and mixed model frameworks. Under the multilevel model approach, under-specification and general-misspecification of the Σ matrix usually resulted in overestimation of the variances of the random effects (e.g., τ00, ττ11 ) and standard errors of the corresponding growth parameter estimates (e.g., SEβ 0, SEβ 1). Overestimates of the standard errors led to lower statistical power in tests of the growth parameters. An unstructured Σ matrix under the mixed model framework generally led to underestimates of standard errors of the growth parameter estimates. Underestimates of the standard errors led to inflation of the type I error rate in tests of the growth parameters. Implications of the compensatory relationship between the random effects of the growth parameters and the longitudinal error structure for model specification were discussed.

A Mixed Model Approach for Geoadditive Hazard Regression

Abstract: . Mixed model based approaches for semiparametric regression have gained much interest in recent years, both in theory and application. They provide a unified and modular framework for penalized likelihood and closely related empirical Bayes inference. In this article, we develop mixed model methodology for a broad class of Cox-type hazard regression models where the usual linear predictor is generalized to a geoadditive predictor incorporating non-parametric terms for the (log-)baseline hazard rate, time-varying coefficients and non-linear effects of continuous covariates, a spatial component, and additional cluster-specific frailties. Non-linear and time-varying effects are modelled through penalized splines, while spatial components are treated as correlated random effects following either a Markov random field or a stationary Gaussian random field prior. Generalizing existing mixed model methodology, inference is derived using penalized likelihood for regression coefficients and (approximate) marginal likelihood for smoothing parameters. In a simulation we study the performance of the proposed method, in particular comparing it with its fully Bayesian counterpart using Markov chain Monte Carlo methodology, and complement the results by some asymptotic considerations. As an application, we analyse leukaemia survival data from northwest England.

A Bayesian approach to joint analysis of longitudinal measurements and competing risks failure time data.

Abstract: Joint analysis of longitudinal measurements and survival data has received much attention in recent years. However, previous work has primarily focused on a single failure type for the event time. In this paper we consider joint modelling of repeated measurements and competing risks failure time data to allow for more than one distinct failure type in the survival endpoint which occurs frequently in clinical trials. Our model uses latent random variables and common covariates to link together the sub-models for the longitudinal measurements and competing risks failure time data, respectively. An EM-based algorithm is derived to obtain the parameter estimates, and a profile likelihood method is proposed to estimate their standard errors. Our method enables one to make joint inference on multiple outcomes which is often necessary in analyses of clinical trials. Furthermore, joint analysis has several advantages compared with separate analysis of either the longitudinal data or competing risks survival data. By modelling the event time, the analysis of longitudinal measurements is adjusted to allow for non-ignorable missing data due to informative dropout, which cannot be appropriately handled by the standard linear mixed effects models alone. In addition, the joint model utilizes information from both outcomes, and could be substantially more efficient than the separate analysis of the competing risk survival data as shown in our simulation study. The performance of our method is evaluated and compared with separate analyses using both simulated data and a clinical trial for the scleroderma lung disease.

Bayesian Inference for Skew-normal Linear Mixed Models

Abstract: Linear mixed models (LMM) are frequently used to analyze repeated measures data, because they are more flexible to modelling the correlation within-subject, often present in this type of data. The most popular LMM for continuous responses assumes that both the random effects and the within-subjects errors are normally distributed, which can be an unrealistic assumption, obscuring important features of the variations present within and among the units (or groups). This work presents skew-normal liner mixed models (SNLMM) that relax the normality assumption by using a multivariate skew-normal distribution, which includes the normal ones as a special case and provides robust estimation in mixed models. The MCMC scheme is derived and the results of a simulation study are provided demonstrating that standard information criteria may be used to detect departures from normality. The procedures are illustrated using a real data set from a cholesterol study.

Bivariate linear mixed models using SAS proc MIXED

Abstract: Bivariate linear mixed models are useful when analyzing longitudinal data of two associated markers. In this paper, we present a bivariate linear mixed model including random effects or first-order auto-regressive process and independent measurement error for both markers. Codes and tricks to fit these models using SAS Proc MIXED are provided. Limitations of this program are discussed and an example in the field of HIV infection is shown. Despite some limitations, SAS Proc MIXED is a useful tool that may be easily extendable to multivariate response in longitudinal studies.

Random-effects models for multivariate repeated measures:

Abstract: Mixed models are widely used for the analysis of one repeatedly measured outcome. If more than one outcome is present, a mixed model can be used for each one. These separate models can be tied together into a multivariate mixed model by specifying a joint distribution for their random effects. This strategy has been used for joining multivariate longitudinal profiles or other types of multivariate repeated data. However, computational problems are likely to occur when the number of outcomes increases. A pairwise modeling approach, in which all possible bivariate mixed models are fitted and where inference follows from pseudo-likelihood arguments, has been proposed to circumvent the dimensional limitations in multivariate mixed models. An analysis on 22-variate longitudinal measurements of hearing thresholds illustrates the performance of the pairwise approach in the context of multivariate linear mixed models. For generalized linear mixed models, a data set containing repeated measurements of seven aspects of psycho-cognitive functioning will be analyzed.

Model Building for Nonlinear Mixed Effects Models

Abstract: Nonlinear mixed-effects models involve both fixed effects and random effects. Model building for nonlinear mixed-effects models is the process of determining the characteristics of both the fixed and the random effects so as to give an adequate but parsimonious model. We describe procedures based on information criterion statistics for comparing different structures of the random effects component. These include procedures for determining which parameters in the model should be mixed effects and which should be purely fixed effects, as well as procedures for modeling the dependence of parameters on individual-specific covariates. We also consider procedures for assessing the variability in the parameter estimates, based on asymptotic theory and on likelihoodprofiling techniques. These methods are illustrated using the nonlinear mixed-effects methods and classes for S-plus and using data sets from forestry and pharmacokinetics studies.

Current Methods for Meta-Analysis

Abstract: . The bulk of conceptual and statistical developments as well as applications of meta-analysis have been published in the last 30 years. The methods for meta-analysis continue to be refined and new methods are applied to new types of research questions and data. Such current approaches, issues, and developments prevalent in the behavioral sciences are presented, reviewed, and discussed in this paper. The areas that are covered include: the fixed effects and random effects model of meta-analysis, new findings concerning effect sizes and their statistical properties, the comparison of different meta-analytic approaches, and multivariate procedures for meta-analysis. The latter also covers the stepwise combination of meta-analysis and structural equation modeling (MASEM).

Analysis of Litter Size and Average Litter Weight in Pigs Using a Recursive Model

Abstract: An analysis of litter size and average piglet weight at birth in Landrace and Yorkshire using a standard two-trait mixed model (SMM) and a recursive mixed model (RMM) is presented. The RMM establishes a one-way link from litter size to average piglet weight. It is shown that there is a one-to-one correspondence between the parameters of SMM and RMM and that they generate equivalent likelihoods. As parameterized in this work, the RMM tests for the presence of a recursive relationship between additive genetic values, permanent environmental effects, and specific environmental effects of litter size, on average piglet weight. The equivalent standard mixed model tests whether or not the covariance matrices of the random effects have a diagonal structure. In Landrace, posterior predictive model checking supports a model without any form of recursion or, alternatively, a SMM with diagonal covariance matrices of the three random effects. In Yorkshire, the same criterion favors a model with recursion at the level of specific environmental effects only, or, in terms of the SMM, the association between traits is shown to be exclusively due to an environmental (negative) correlation. It is argued that the choice between a SMM or a RMM should be guided by the availability of software, by ease of interpretation, or by the need to test a particular theory or hypothesis that may best be formulated under one parameterization and not the other.

Modeling group fMRI data

Abstract: The analysis of group fMRI data requires a statistical model known as the mixed effects model. This article motivates the need for a mixed effects model and outlines the different stages of the mixed model used to analyze group fMRI data. Different modeling options and their impact on analysis results are also described.

Nested generalized linear mixed models: an orthodox best linear unbiased predictor approach

Abstract: Summary. We introduce a new class of generalized linear mixed models based on the Tweedie exponential dispersion model distributions, accommodating a wide range of discrete, continuous and mixed data. Using the best linear unbiased predictor of random effects, we obtain an optimal estimating function for the regression parameters in the sense of Godambe, allowing an efficient common fitting algorithm for the whole class. Although allowing full parametric inference, our main results depend only on the first- and second-moment assumptions of unobserved random effects. In addition, we obtain consistent estimators for both regression and dispersion parameters. We illustrate the method by analysing the epilepsy data and cake baking data. Along with simulations and asymptotic justifications, this shows the usefulness of the method for analysis of clustered non-normal data.

Statistical tests with accurate size and power for balanced linear mixed models.

Abstract: The convenience of linear mixed models for Gaussian data has led to their widespread use. Unfortunately, standard mixed model tests often have greatly inflated test size in small samples. Many applications with correlated outcomes in medical imaging and other fields have simple properties which do not require the generality of a mixed model. Alternately, stating the special cases as a general linear multivariate model allows analysing them with either the univariate or multivariate approach to repeated measures (UNIREP, MULTIREP). Even in small samples, an appropriate UNIREP or MULTIREP test always controls test size and has a good power approximation, in sharp contrast to mixed model tests. Hence, mixed model tests should never be used when one of the UNIREP tests (uncorrected, Huynh-Feldt, Geisser-Greenhouse, Box conservative) or MULTIREP tests (Wilks, Hotelling-Lawley, Roy's, Pillai-Bartlett) apply. Convenient methods give exact power for the uncorrected and Box conservative tests. Simulations demonstrate that new power approximations for all four UNIREP tests eliminate most inaccuracy in existing methods. In turn, free software implements the approximations to give a better choice of sample size. Two repeated measures power analyses illustrate the methods. The examples highlight the advantages of examining the entire response surface of power as a function of sample size, mean differences, and variability.

Controlling for Individual Heterogeneity in Longitudinal Models, with Applications to Student Achievement

Abstract: Longitudinal data tracking repeated measurements on individuals are highly valued for research because they offer controls for unmeasured individual heterogeneity that might otherwise bias results. Random effects or mixed models approaches, which treat individual heterogeneity as part of the model error term and use generalized least squares to estimate model parameters, are often criticized because correlation between unobserved individual effects and other model variables can lead to biased and inconsistent parameter estimates. Starting with an examination of the relationship between random effects and fixed effects estimators in the standard unobserved effects model, this article demonstrates through analysis and simulation that the mixed model approach has a “bias compression” property under a general model for individual heterogeneity that can mitigate bias due to uncontrolled differences among individuals. The general model is motivated by the complexities of longitudinal student achievement measures, but the results have broad applicability to longitudinal modeling.

Bivariate random effect model using skew-normal distribution with application to HIV-RNA

Abstract: Correlated data arise in a longitudinal studies from epidemiological and clinical research. Random effects models are commonly used to model correlated data. Mostly in the longitudinal data setting we assume that the random effects and within subject errors are normally distributed. However, the normality assumption may not always give robust results, particularly if the data exhibit skewness. In this paper, we develop a Bayesian approach to bivariate mixed model and relax the normality assumption by using a multivariate skew-normal distribution. Specifically, we compare various potential models and illustrate the procedure using a real data set from HIV study.