Variance Components Of Random Effects Research Articles

Remarks on asymptotic efficient estimation for regression effects in stationary and nonstationary models for panel count data

In a panel count data setup, repeated counts of an individual are assumed to be influenced by the individual’s random effect. Consequently, conditional on the random effect, the repeated responses of the individual are assumed to be serially correlated. Under the assumption that the random effects of the individuals follow a normal distribution, Jowaheer and Sutradhar (Statist. Probab. Letters 79 (2009) 1928–1934) have demonstrated that the generalized quasi-likelihood (GQL) estimation approach produces more efficient estimates than the so-called generalized method of moments (GMM) approach for both regression effects and the variance component of the normal random effects. For the cases where the distribution of the random effects is unknown, there exist two estimation approaches, namely the conditional maximum likelihood (CML) and instrumental variables based GMM (IVGMM) approaches, for the estimation of the regression effects. The purpose of this paper is to examine the asymptotic efficiency performances of the CML and IVGMM approaches as compared to the GQL approach for the regression estimation. When the covariates are stationary, that is, time independent, it is, however, known that the CML and IVGMM approaches are useless for the regression estimation, whereas the GQL approach does not encounter any such limitations. For the general case, that is, when the covariates are time dependent, the IVGMM approach appears to be computationally expensive and hence it is not included in efficiency comparison. Between the CML and GQL approaches, it is found through exact asymptotic variance calculations that the GQL approach is asymptotically more efficient than the CML approach in estimating the regression effects. This makes the GQL as a unified efficient approach irrespective of the cases whether the panel count data are stationary or nonstationary.

Testing for random effect in the Fuller–Battese model

We consider the Fuller–Battese model where random effects are allowed to be from non-normal universes. The asymptotic distribution of the F-statistic in this model is derived as the number of groups tends to infinity (is large) and sample size from any group is either fixed or large. The result is used to establish an approximate test for the significance of the random effect variance component. Robustness of the established approximate test is given.

Permutation tests for centre effect on survival endpoints with application in an acute myeloid leukaemia multicentre study

When analysing multicentre data, it may be of interest to test whether the distribution of the endpoint varies among centres. In a mixed-effect model, testing for such a centre effect consists in testing to zero a random centre effect variance component. It has been shown that the usual asymptotic χ(2) distribution of the likelihood ratio and score statistics under the null does not necessarily hold. In the case of censored data, mixed-effects Cox models have been used to account for random effects, but few works have concentrated on testing to zero the variance component of the random effects. We propose a permutation test, using random permutation of the cluster indices, to test for a centre effect in multilevel censored data. Results from a simulation study indicate that the permutation tests have correct type I error rates, contrary to standard likelihood ratio tests, and are more powerful. The proposed tests are illustrated using data of a multicentre clinical trial of induction therapy in acute myeloid leukaemia patients.

Estimating Adjusted Associations between Random Effects from Multilevel Models: The Reffadjust Package

We describe a method to estimate associations between random effects from multilevel models. We provide two new postestimation commands, reffadjustsim and reffadjust4nlcom, which are distributed as the reffadjust package. These commands produce the estimates and their associated confidence intervals. The commands are used after official Stata multilevel model estimation commands mixed, meqrlogit, and meqrpoisson (formerly named xtmixed, xtmelogit, and xtmepoisson, respectively, before Stata 13) and with models fit in the MLwiN statistical software package via the runmlwin command. We demonstrate our commands with several simulated datasets and for a bivariate outcome model investigating the relationship between weight and mean arterial pressure in pregnant women using data from the Avon Longitudinal Study of Parents and Children. Our method and commands help to improve the interpretability of estimated random-effects variance components from multilevel models.

Haplotype Kernel Association Test as a Powerful Method to Identify Chromosomal Regions Harboring Uncommon Causal Variants

For most complex diseases, the fraction of heritability that can be explained by the variants discovered from genome-wide association studies is minor. Although the so-called "rare variants" (minor allele frequency [MAF] < 1%) have attracted increasing attention, they are unlikely to account for much of the "missing heritability" because very few people may carry these rare variants. The genetic variants that are likely to fill in the "missing heritability" include uncommon causal variants (MAF < 5%), which are generally untyped in association studies using tagging single-nucleotide polymorphisms (SNPs) or commercial SNP arrays. Developing powerful statistical methods can help to identify chromosomal regions harboring uncommon causal variants, while bypassing the genome-wide or exome-wide next-generation sequencing. In this work, we propose a haplotype kernel association test (HKAT) that is equivalent to testing the variance component of random effects for distinct haplotypes. With an appropriate weighting scheme given to haplotypes, we can further enhance the ability of HKAT to detect uncommon causal variants. With scenarios simulated according to the population genetics theory, HKAT is shown to be a powerful method for detecting chromosomal regions harboring uncommon causal variants.

Parametric bootstrap tests for unbalanced nested designs under heteroscedasticity

In this article, we consider the two-factor unbalanced nested design model without the assumption of equal error variance. For the problem of testing ‘main effects’ of both factors, we propose a parametric bootstrap (PB) approach and compare it with the existing generalized F (GF) test. The Type I error rates of the tests are evaluated using Monte Carlo simulation. Our studies show that the PB test performs better than the GF test. The PB test performs very satisfactorily even for small samples while the GF test exhibit poor Type I error properties when the number of factorial combinations or treatments goes up. It is also noted that the same tests can be used to test the significance of the random effect variance component in a two-factor mixed effects nested model under unequal error variances.

Variational Bayesian mixed-effects inference for classification studies

Multivariate classification algorithms are powerful tools for predicting cognitive or pathophysiological states from neuroimaging data. Assessing the utility of a classifier in application domains such as cognitive neuroscience, brain-computer interfaces, or clinical diagnostics necessitates inference on classification performance at more than one level, i.e., both in individual subjects and in the population from which these subjects were sampled. Such inference requires models that explicitly account for both fixed-effects (within-subjects) and random-effects (between-subjects) variance components. While models of this sort are standard in mass-univariate analyses of fMRI data, they have not yet received much attention in multivariate classification studies of neuroimaging data, presumably because of the high computational costs they entail. This paper extends a recently developed hierarchical model for mixed-effects inference in multivariate classification studies and introduces an efficient variational Bayes approach to inference. Using both synthetic and empirical fMRI data, we show that this approach is equally simple to use as, yet more powerful than, a conventional t-test on subject-specific sample accuracies, and computationally much more efficient than previous sampling algorithms and permutation tests. Our approach is independent of the type of underlying classifier and thus widely applicable. The present framework may help establish mixed-effects inference as a future standard for classification group analyses.

The Use of Permutation Tests for Variance Components in Linear Mixed Models

Standard asymptotic chi-square distribution of the likelihood ratio and score statistics under the null hypothesis does not hold when the parameter value is on the boundary of the parameter space. In mixed models it is of interest to test for a zero random effect variance component. Some available tests for the variance component are reviewed and a new test within the permutation framework is presented. The power and significance level of the different tests are investigated by means of a Monte Carlo simulation study. The proposed test has a significance level closer to the nominal one and it is more powerful.

돼지의 번식형질과 산육형질에 대한 유전모수 추정

본 연구는 국내 특정 종돈장에서 보유하고 있는 종돈에 대한 번식형질 및 산육형질들에 대한 유전변이를 추정하고자 연구를 실시하였다. 본 분석에 이용된 자료는 2000년부터 2008년까지 개량을 진행한 국내 모종돈장에 있는 돼지(Landrace, Large white, Duroc) 2,447두에서 조사된 9,886복의 번식자료(실산자수, 이유자 돈수)와 10,181두의 산육검정자료(등심단면적, 90 kg 도달일령, 등 지방두께, 정육률)을 이용하여 분석을 실시하였다. 번식형질 및 산육형질에 적합한 모형을 찾기 위해 분산분석을 실시하였으며, 그 결과 번식형질에서 품종효과, 교배웅돈효과, 산차효과, 분만시 년도-계절효과, 산육형질에서 품종효과, 분만시 년도-계절효과, 성의 효과, 모산차 등이 환경요인으로 작용하는 것으로 나타나 이들을 혼합모형방정식에 적합시켜 유전모수를 추정하였다. 그 결과, 번식 형질의 실산자수에 대한 유전력은 0.07, 모체 유전효과에 대한 유전력은 0.02로 추정되었고 이유자돈수의 유전력은 0.03, 모체 유전효과에서 0.02로 추정되었으며 이들 두 형질 간의 유전상관은 0.14, 모체 유전효과에 대한 상관은 0.06로 추정되었다. 또한 등심 면적의 경우 0.19, 90 kg 도달일령은 0.39, 등지방두께 및 정육률은 각각 0.36 및 0.43으로 번식형질에 비해 높은 유전력을 나타내는 것으로 추정되었다. 또한 등심단면적과 등지방두께 간에는 0.04로 유전적 상관관계가 없으며, 등심단면적과 정육률 간에는 0.35로 중도의 유전적 상관관계를 갖는 것으로 추정되었다. 반면에 등지방 두께와 정육률 간은 -0.42로 중도의 부의 상관관계를 나타냈으며, 등지방두께와 90 kg 도달일령 간에는 유전상관이 없는 것(0.00)으로 추정되었다. 또한 번식형질과 산육형질 간 유전상관은 등지방두께를 제외한 나머지 산육형질에서 번식형질과의 부의 상관을 보여, 번식형질 또는 산육형질을 독자적으로 개량하고자 할 때, 부의 관계가 있는 형질과의 유전적 관계를 고려한 개량목표 설정이 필요할 것으로 사료된다. The purpose of this study was to estimate heritabilities and genetic correlations for reproductive and productive traits and to apply their estimates to selection strategies in a swine population. Reproductive and productive traits considered in this study were number of born alive piglet (NBA), number of weaned piglet (NW), loin eye area (LEA), days to 90 kg (D90KG), back fat thickness (BF), and lean meat content (LEAN). Data were collected from 9,886 litters on 2,447 sows for reproductive traits and 10,181 gilts and boars for productive traits from Jan. 2000 to Dec. 2008 in a swine GGP farm. The statistical model to estimate genetic parameters for considering traits was a multiple traits animal model with including animal and maternal additive effects and litter effects on reproductive traits and animal additive effects on productive traits as random as well as some of fixed effects. For estimating (co) variance components of several random effects, restricted maximum likelihood methodology was used on this assumed model. The estimated heritabilities by animal additive effects and maternal effects were 0.07 and 0.02 for NBA and 0.03 and 0.02 for NW, respectively. Genetic correlation estimate for direct genetic effects between NBA and NW was 0.14. Heritability estimates for direct genetic effects were 0.19, 0.39, 0.36, and 0.43 for LEA, D90KG, BF and LEAN, respectively. The genetic correlation of LEA with LEAN was 0.35. Productive traits were antagonistically correlated with reproductive traits. From these results it is concluded that, if selection is done for strong positive effects of reproductive traits, then this would decline productive performance.

Moment-based method for random effects selection in linear mixed models

The selection of random effects in linear mixed models is an important yet challenging problem in practice. We propose a robust and unified framework for automatically selecting random effects and estimating covariance components in linear mixed models. A moment-based loss function is first constructed for estimating the covariance matrix of random effects. Two types of shrinkage penalties, a hard thresholding operator and a new sandwich-type soft-thresholding penalty, are then imposed for sparse estimation and random effects selection. Compared with existing approaches, the new procedure does not require any distributional assumption on the random effects and error terms. We establish the asymptotic properties of the resulting estimator in terms of its consistency in both random effects selection and variance component estimation. Optimization strategies are suggested to tackle the computational challenges involved in estimating the sparse variance-covariance matrix. Furthermore, we extend the procedure to incorporate the selection of fixed effects as well. Numerical results show promising performance of the new approach in selecting both random and fixed effects and, consequently, improving the efficiency of estimating model parameters. Finally, we apply the approach to a data set from the Amsterdam Growth and Health study.

Effect of the number of categories, number of time-points, and sample size on the recovery of random-effect ordinal regression model parameters

The random-effect ordinal regression model (REORM) is formulated as a special case of the hierarchical generalized linear model to analyze the effect of a cluster randomized trial on the ordinal responses measured at several occasions. The random-effect model takes the dependency between observations based on the same cluster or subject into account by introducing one or more random effects. The parameters in the REORM can be estimated using the computer program WinBUGS, which adopts Markov chain Monte Carlo (MCMC) algorithms. An analysis of real data is provided as an example. Simulations were conducted to examine parameter recovery based on the best-fitting model in the empirical example. The results show that increasing sample size improved the accuracy of the random-effect variance component recovery. Increasing the number of categories and sample sizes improved the accuracy of threshold recovery, and increasing the number of time-points improved the accuracy of regression parameter recovery.

Therapist effects in routine psychotherapy practice: An account from chronic fatigue syndrome

The effect of therapists in psychotherapy is a much debated topic, with a number of studies showing therapist variance being large while other studies show little or no variability in outcomes due to therapists. The aim of this study was to investigate therapist effects in a well-defined sample of patients and therapists from an outpatient service which specializes in providing cognitive behaviour therapy (CBT) for patients with chronic fatigue syndrome (CFS). Therapy was provided in a highly specialized clinical setting for CFS and was delivered by qualified CBT therapists with at least 2 years experience with this client group. Three hundred and seventy-four patients with CFS and 12 cognitive behavioural psychotherapists took part. Therapist effects on the primary outcomes of fatigue and disability were investigated with multilevel random effects models and variance component analysis. Different models were computed and compared. Results showed a reduction in fatigue and disability scores after therapy. Variance explained by therapists, when demographic covariates were accounted for, was 0% for fatigue and under 2% for disability. A number of important factors may have played a significant role in minimizing therapist effects in our study. These are: specialist setting, single centre, patients with the same primary diagnosis, therapists of the same orientation and training, shared environment and supervision. Future studies may stress the importance of these factors in the investigation of the therapist effect in psychotherapy.

Extended Bayesian Model Averaging in Generalized Linear Mixed Models Applied to Schizophrenia Family Data

The study of disease etiology and the search for susceptible genes of schizophrenia have attracted scientists' attention for decades. Many findings however are inconsistent, possibly due to the higher order interactions involving multi-dimensional genetic and environmental factors or due to the commingling of different ethnic groups. Several studies applied generalized linear mixed models (GLMMs) with family data to identify the genetic contribution to, and environmental influence on, schizophrenia, and to clarify the existence and sources of familial aggregation. Based on an extended Bayesian model averaging (EBMA) procedure, here we estimate the gene-gene (GG) and gene-environment (GE) interactions, and heritability of schizophrenia via variance components of random-effects in GLMMs. Our proposal takes into account the uncertainty in covariates and in genetic model structures, where each competing model includes environmental and genetic covariates, and GE and GG interactions. Simulation studies are conducted to compare the performance of the EBMA approach, permutation test procedure and GEE method. We also illustrate this approach with data from singleton and multiplex schizophrenia families. The results indicate that EBMA is a flexible and stable tool in exploring true candidate genes, and GE and GG interactions, after adjusting for explanatory variables and correlation structures within family members.

Comparison of Weights for Meta-Analysis of r and d Under Realistic Conditions

We compared unit, sample size, and inverse variance weighting procedures for estimating the overall mean and random-effects variance component (REVC) in random-effects meta-analysis under realistic conditions for both r and d. Root mean square error and average absolute error of estimation were used to compare weighting schemes via Monte-Carlo simulation. For r, unit weights worked surprisingly well, and sample size weights worked best overall. For d, unit weights worked poorly, and inverse variance weights worked best overall. Discussion focuses on the meta-analyst’s choice of weights, possible explanations for the differences across types of effect size, and implications for meta-analytic inferences in organizational research.

Extended Bayesian model averaging for heritability in twin studies

Family studies are often conducted to examine the existence of familial aggregation. Particularly, twin studies can model separately the genetic and environmental contribution. Here we estimate the heritability of quantitative traits via variance components of random-effects in linear mixed models (LMMs). The motivating example was a myopia twin study containing complex nesting data structures: twins and siblings in the same family and observations on both eyes for each individual. Three models are considered for this nesting structure. Our proposal takes into account the model uncertainty in both covariates and model structures via an extended Bayesian model averaging (EBMA) procedure. We estimate the heritability using EBMA under three suggested model structures. When compared with the results under the model with the highest posterior model probability, the EBMA estimate has smaller variation and is slightly conservative. Simulation studies are conducted to evaluate the performance of variance-components estimates, as well as the selections of risk factors, under the correct or incorrect structure. The results indicate that EBMA, with consideration of uncertainties in both covariates and model structures, is robust in model misspecification than the usual Bayesian model averaging (BMA) that considers only uncertainty in covariates selection.

How Many Studies Do You Need?

In this article, the authors outline methods for using fixed and random effects power analysis in the context of meta-analysis. Like statistical power analysis for primary studies, power analysis for meta-analysis can be done either prospectively or retrospectively and requires assumptions about parameters that are unknown. The authors provide some suggestions for thinking about these parameters, in particular for the random effects variance component. The authors also show how the typically uninformative retrospective power analysis can be made more informative. The authors then discuss the value of confidence intervals, show how they could be used in addition to or instead of retrospective power analysis, and also demonstrate that confidence intervals can convey information more effectively in some situations than power analyses alone. Finally, the authors take up the question “How many studies do you need to do a meta-analysis?” and show that, given the need for a conclusion, the answer is “two studies,” because all other synthesis techniques are less transparent and/or are less likely to be valid. For systematic reviewers who choose not to conduct a quantitative synthesis, the authors provide suggestions for both highlighting the current limitations in the research base and for displaying the characteristics and results of studies that were found to meet inclusion criteria.

PROTOCOL: Dropout Prevention and Intervention Programs: Effects on School Completion and Dropout Among School‐aged Children and Youth

PROTOCOL: Dropout Prevention and Intervention Programs: Effects on School Completion and Dropout Among School‐aged Children and Youth

Meta-analysis of Planetarium Efficacy Research

In this study, the instructional effectiveness of the planetarium in astronomy education was explored through a meta-analysis of 19 studies. This analysis resulted in a heterogeneous distribution of 24 effect sizes with a mean of +0.28, p .05. The variability in this distribution was not fully explained under a fixed effect model. As a result, a random effects model was applied. However, a large random effect variance component indicated that study differences were indeed systematic. The findings of this meta-analysis showed that the planetarium has been an effective astronomical teaching tool.

Regression modelling of correlated data in ecology: subject‐specific and population averaged response patterns

Summary 1. Statistical methods that assume independence among observations result in optimistic estimates of uncertainty when applied to correlated data, which are ubiquitous in applied ecological research. Mixed effects models offer a potential solution and rely on the assumption that latent or unobserved characteristics of individuals (i.e. random effects) induce correlation among repeated measurements. However, careful consideration must be given to the interpretation of parameters when using a nonlinear link function (e.g. logit). Mixed model regression parameters reflect the change in the expected response within an individual associated with a change in that individual’s covariates [i.e. a subject‐specific (SS) interpretation], which may not address a relevant scientific question. In particular, a SS interpretation is not natural for covariates that do not vary within individuals (e.g. gender). 2. An alternative approach combines the solution to an unbiased estimating equation with robust measures of uncertainty to make inferences regarding predictor–outcome relationships. Regression parameters describe changes in the average response among groups of individuals differing in their covariates [i.e. a population‐averaged (PA) interpretation]. 3. We compare these two approaches [mixed models and generalized estimating equations (GEE)] with illustrative examples from a 3‐year study of mallard (Anas platyrhynchos) nest structures. We observe that PA and SS responses differ when modelling binary data, with PA parameters behaving like attenuated versions of SS parameters. Differences between SS and PA parameters increase with the size of among‐subject heterogeneity captured by the random effects variance component. Lastly, we illustrate how PA inferences can be derived (post hoc) from fitted generalized and nonlinear‐mixed models. 4. Synthesis and applications. Mixed effects models and GEE offer two viable approaches to modelling correlated data. The preferred method should depend primarily on the research question (i.e. desired parameter interpretation), although operating characteristics of the associated estimation procedures should also be considered. Many applied questions in ecology, wildlife management and conservation biology (including the current illustrative examples) focus on population performance measures (e.g. mean survival or nest success rates) as a function of general landscape features, for which the PA model interpretation, not the more commonly used SS model interpretation may be more natural.

Bootstrap tests for variance components in generalized linear mixed models

AbstractIn many applications of generalized linear mixed models to clustered correlated or longitudinal data, often we are interested in testing whether a random effects variance component is zero. The usual asymptotic mixture of chi‐square distributions of the score statistic for testing constrained variance components does not necessarily hold. In this article, the author proposes and explores a parametric bootstrap test that appears to be valid based on its estimated level of significance under the null hypothesis. Results from a simulation study indicate that the bootstrap test has a level much closer to the nominal one while the asymptotic test is conservative, and is more powerful than the usual asymptotic score test based on a mixture of chi‐squares. The proposed bootstrap test is illustrated using two sets of real‐life data obtained from clinical trials. The Canadian Journal of Statistics © 2009 Statistical Society of Canada