Browse
Submit Data
Databases
API
Help

Dataset Information

18 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Fisher Scoring for crossed factor linear mixed models

ABSTRACT: The analysis of longitudinal, heterogeneous or unbalanced clustered data is of primary importance to a wide range of applications. The linear mixed model (LMM) is a popular and flexible extension of the linear model specifically designed for such purposes. Historically, a large proportion of material published on the LMM concerns the application of popular numerical optimization algorithms, such as Newton–Raphson, Fisher Scoring and expectation maximization to single-factor LMMs (i.e. LMMs that only contain one “factor” by which observations are grouped). However, in recent years, the focus of the LMM literature has moved towards the development of estimation and inference methods for more complex, multi-factored designs. In this paper, we present and derive new expressions for the extension of an algorithm classically used for single-factor LMM parameter estimation, Fisher Scoring, to multiple, crossed-factor designs. Through simulation and real data examples, we compare five variants of the Fisher Scoring algorithm with one another, as well as against a baseline established by the R package lme4, and find evidence of correctness and strong computational efficiency for four of the five proposed approaches. Additionally, we provide a new method for LMM Satterthwaite degrees of freedom estimation based on analytical results, which does not require iterative gradient estimation. Via simulation, we find that this approach produces estimates with both lower bias and lower variance than the existing methods.

Supplementary Information

The online version supplementary material available at 10.1007/s11222-021-10026-6.

SUBMITTER: Maullin-Sapey T

PROVIDER: S-EPMC8550113 | biostudies-literature |

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Similar Datasets

VARIABLE SELECTION IN LINEAR MIXED EFFECTS MODELS.

Project description:This paper is concerned with the selection and estimation of fixed and random effects in linear mixed effects models. We propose a class of nonconcave penalized profile likelihood methods for selecting and estimating important fixed effects. To overcome the difficulty of unknown covariance matrix of random effects, we propose to use a proxy matrix in the penalized profile likelihood. We establish conditions on the choice of the proxy matrix and show that the proposed procedure enjoys the model selection consistency where the number of fixed effects is allowed to grow exponentially with the sample size. We further propose a group variable selection strategy to simultaneously select and estimate important random effects, where the unknown covariance matrix of random effects is replaced with a proxy matrix. We prove that, with the proxy matrix appropriately chosen, the proposed procedure can identify all true random effects with asymptotic probability one, where the dimension of random effects vector is allowed to increase exponentially with the sample size. Monte Carlo simulation studies are conducted to examine the finite-sample performance of the proposed procedures. We further illustrate the proposed procedures via a real data example.

| S-EPMC4026175 | biostudies-other

Multiple testing correction in linear mixed models.

Project description:BACKGROUND:Multiple hypothesis testing is a major issue in genome-wide association studies (GWAS), which often analyze millions of markers. The permutation test is considered to be the gold standard in multiple testing correction as it accurately takes into account the correlation structure of the genome. Recently, the linear mixed model (LMM) has become the standard practice in GWAS, addressing issues of population structure and insufficient power. However, none of the current multiple testing approaches are applicable to LMM. RESULTS:We were able to estimate per-marker thresholds as accurately as the gold standard approach in real and simulated datasets, while reducing the time required from months to hours. We applied our approach to mouse, yeast, and human datasets to demonstrate the accuracy and efficiency of our approach. CONCLUSIONS:We provide an efficient and accurate multiple testing correction approach for linear mixed models. We further provide an intuition about the relationships between per-marker threshold, genetic relatedness, and heritability, based on our observations in real data.

| S-EPMC4818520 | biostudies-literature

Bayesian inference for generalized linear mixed models.

Project description:Generalized linear mixed models (GLMMs) continue to grow in popularity due to their ability to directly acknowledge multiple levels of dependency and model different data types. For small sample sizes especially, likelihood-based inference can be unreliable with variance components being particularly difficult to estimate. A Bayesian approach is appealing but has been hampered by the lack of a fast implementation, and the difficulty in specifying prior distributions with variance components again being particularly problematic. Here, we briefly review previous approaches to computation in Bayesian implementations of GLMMs and illustrate in detail, the use of integrated nested Laplace approximations in this context. We consider a number of examples, carefully specifying prior distributions on meaningful quantities in each case. The examples cover a wide range of data types including those requiring smoothing over time and a relatively complicated spline model for which we examine our prior specification in terms of the implied degrees of freedom. We conclude that Bayesian inference is now practically feasible for GLMMs and provides an attractive alternative to likelihood-based approaches such as penalized quasi-likelihood. As with likelihood-based approaches, great care is required in the analysis of clustered binary data since approximation strategies may be less accurate for such data.

| S-EPMC2883299 | biostudies-literature

Plant Variety Selection Using Interaction Classes Derived From Factor Analytic Linear Mixed Models: Models With Independent Variety Effects.

Project description:A major challenge in the analysis of plant breeding multi-environment datasets is the provision of meaningful and concise information for variety selection in the presence of variety by environment interaction (VEI). This is addressed in the current paper by fitting a factor analytic linear mixed model (FALMM) then using the fundamental factor analytic parameters to define groups of environments in the dataset within which there is minimal crossover VEI, but between which there may be substantial crossover VEI. These groups are consequently called interaction classes (iClasses). Given that the environments within an iClass exhibit minimal crossover VEI, it is then valid to obtain predictions of overall variety performance (across environments) for each iClass. These predictions can then be used not only to select the best varieties within each iClass but also to match varieties in terms of their patterns of VEI across iClasses. The latter is aided with the use of a new graphical tool called an iClass Interaction Plot. The ideas are introduced in this paper within the framework of FALMMs in which the genetic effects for different varieties are assumed independent. The application to FALMMs which include information on genetic relatedness is the subject of a subsequent paper.

| S-EPMC8460066 | biostudies-literature

Polygenic modeling with bayesian sparse linear mixed models.

Project description:Both linear mixed models (LMMs) and sparse regression models are widely used in genetics applications, including, recently, polygenic modeling in genome-wide association studies. These two approaches make very different assumptions, so are expected to perform well in different situations. However, in practice, for a given dataset one typically does not know which assumptions will be more accurate. Motivated by this, we consider a hybrid of the two, which we refer to as a "Bayesian sparse linear mixed model" (BSLMM) that includes both these models as special cases. We address several key computational and statistical issues that arise when applying BSLMM, including appropriate prior specification for the hyper-parameters and a novel Markov chain Monte Carlo algorithm for posterior inference. We apply BSLMM and compare it with other methods for two polygenic modeling applications: estimating the proportion of variance in phenotypes explained (PVE) by available genotypes, and phenotype (or breeding value) prediction. For PVE estimation, we demonstrate that BSLMM combines the advantages of both standard LMMs and sparse regression modeling. For phenotype prediction it considerably outperforms either of the other two methods, as well as several other large-scale regression methods previously suggested for this problem. Software implementing our method is freely available from http://stephenslab.uchicago.edu/software.html.

| S-EPMC3567190 | biostudies-literature

Confidence, prediction, and tolerance in linear mixed models.

Project description:The literature about Prediction Interval (PI) and Tolerance Interval (TI) in linear mixed models is usually developed for specific designs, which is a main limitation to their use. This paper proposes to reformulate the two-sided PI to be generalizable under a wide variety of designs (one random factor, nested and crossed designs for multiple random factors, and balanced or unbalanced designs). This new methodology is based on the Hessian matrix, namely, the inverse of (observed) Fisher Information matrix, and is built with a cell mean model. The degrees of freedom for the total variance are calculated with the generalized Satterthwaite method and compared to the Kenward-Roger's degrees of freedom for fixed effects. Construction of two-sided TIs are also detailed with one random factor, and two nested and two crossed random variables. An extensive simulation study is carried out to compare the widths and coverage probabilities of Confidence Intervals (CI), PIs, and TIs to their nominal levels. It shows excellent coverage whatever the design and the sample size are. Finally, these CIs, PIs, and TIs are applied to two real data sets: one from orthopedic surgery study (intralesional resection risk) and the other from assay validation study during vaccine development.

| S-EPMC6916346 | biostudies-literature

Goodness of Fit Tests for Linear Mixed Models.

Project description:Linear mixed models (LMMs) are widely used for regression analysis of data that are assumed to be clustered or correlated. Assessing model fit is important for valid inference but to date no confirmatory tests are available to assess the adequacy of the fixed effects part of LMMs against general alternatives. We therefore propose a class of goodness-of-fit tests for the mean structure of LMMs. Our test statistic is a quadratic form of the difference between observed values and the values expected under the estimated model in cells defined by a partition of the covariate space. We show that this test statistic has an asymptotic chi-squared distribution when model parameters are estimated by maximum likelihood or by least squares and method of moments, and study its power under local alternatives both analytically and in simulations. Data on repeated measurements of thyroglobulin from individuals exposed to the accident at the Chernobyl power plant in 1986 are used to illustrate the proposed test.

| S-EPMC5426279 | biostudies-literature

Linear mixed effects models under inequality constraints with applications.

Project description:Constraints arise naturally in many scientific experiments/studies such as in, epidemiology, biology, toxicology, etc. and often researchers ignore such information when analyzing their data and use standard methods such as the analysis of variance (ANOVA). Such methods may not only result in a loss of power and efficiency in costs of experimentation but also may result poor interpretation of the data. In this paper we discuss constrained statistical inference in the context of linear mixed effects models that arise naturally in many applications, such as in repeated measurements designs, familial studies and others. We introduce a novel methodology that is broadly applicable for a variety of constraints on the parameters. Since in many applications sample sizes are small and/or the data are not necessarily normally distributed and furthermore error variances need not be homoscedastic (i.e. heterogeneity in the data) we use an empirical best linear unbiased predictor (EBLUP) type residual based bootstrap methodology for deriving critical values of the proposed test. Our simulation studies suggest that the proposed procedure maintains the desired nominal Type I error while competing well with other tests in terms of power. We illustrate the proposed methodology by re-analyzing a clinical trial data on blood mercury level. The methodology introduced in this paper can be easily extended to other settings such as nonlinear and generalized regression models.

| S-EPMC3897384 | biostudies-literature

Meta-analysis of Proportions Using Generalized Linear Mixed Models.

Project description:Epidemiologic research often involves meta-analyses of proportions. Conventional two-step methods first transform each study's proportion and subsequently perform a meta-analysis on the transformed scale. They suffer from several important limitations: the log and logit transformations impractically treat within-study variances as fixed, known values and require ad hoc corrections for zero counts; the results from arcsine-based transformations may lack interpretability. Generalized linear mixed models (GLMMs) have been recommended in meta-analyses as a one-step approach to fully accounting for within-study uncertainties. However, they are seldom used in current practice to synthesize proportions. This article summarizes various methods for meta-analyses of proportions, illustrates their implementations, and explores their performance using real and simulated datasets. In general, GLMMs led to smaller biases and mean squared errors and higher coverage probabilities than two-step methods. Many software programs are readily available to implement these methods.

| S-EPMC7398826 | biostudies-literature

REHE: Fast variance components estimation for linear mixed models.

Project description:Linear mixed models are widely used in ecological and biological applications, especially in genetic studies. Reliable estimation of variance components is crucial for using linear mixed models. However, standard methods, such as the restricted maximum likelihood (REML), are computationally inefficient in large samples and may be unstable with small samples. Other commonly used methods, such as the Haseman-Elston (HE) regression, may yield negative estimates of variances. Utilizing regularized estimation strategies, we propose the restricted Haseman-Elston (REHE) regression and REHE with resampling (reREHE) estimators, along with an inference framework for REHE, as fast and robust alternatives that provide nonnegative estimates with comparable accuracy to REML. The merits of REHE are illustrated using real data and benchmark simulation studies.

| S-EPMC8604792 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

Tweets

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data