Asymptotic Optimality of Restricted Maximum Likelihood Estimates for the Mixed Model

1979 ◽  
Vol 28 (1-4) ◽  
pp. 125-142 ◽  
Author(s):  
Kalyan Das
Keyword(s):  
Maximum Likelihood ◽  
Conceptual Design ◽  
Analysis Of Variance ◽  
Variance Components ◽  
Mixed Model ◽  
Asymptotic Optimality ◽  
Restricted Maximum Likelihood ◽  
Maximum Likelihood Estimates ◽  
Asymptotically Normal ◽  
Reasonable Sense

In this paper we study the asymptotic optimality of the restricted maximum likelihood estimates of variance components in the mixed model of analysis of variance. Using conceptual design sequences of Miller (1977), under slightly stronger conditions, we show that the restricted maximum likelihood estimates are not only asymptotically normal, but also asymptotically equivalent to the maximum likelihood estimates in a reasonable sense.

An Alternative Method for Estimating Variance Components in Generalizability Theory

1990 ◽  
Vol 66 (2) ◽  
pp. 379-386 ◽  
Author(s):  
George A. Marcoulides
Keyword(s):  
Maximum Likelihood ◽  
Analysis Of Variance ◽  
Variance Components ◽  
Generalizability Theory ◽  
Simulated Data ◽  
Restricted Maximum Likelihood ◽  
Alternative Method ◽  
Sample Data

This study compares, using simulated data, two methods for estimating variance components in generalizability (G) studies. Traditionally variance components are estimated from an analysis of variance of sample data. The alternative method for estimating variance components is restricted maximum likelihood (REML). The results indicate that REML provides estimates for the components in the various designs that are closer to the true parameters than the estimates from analysis of variance.

Animal x testing environment interaction on postweaning liveweight gains of young bulls

1998 ◽  
Vol 49 (4) ◽  
pp. 607 ◽  
Author(s):  
S. J. Schoeman ◽  
G. G. Jordaan
Keyword(s):  
Maximum Likelihood ◽  
Genetic Correlation ◽  
Variance Components ◽  
Restricted Maximum Likelihood ◽  
Animal Breeding ◽  
Environment Interaction ◽  
Maximum Likelihood Analysis ◽  
Breeding Values ◽  
Testing Environment ◽  
Likelihood Analysis

Postweaning liveweight gain records of 1610 young bulls obtained both in feedlot and under pasture were used to estimate (co)variance components using a multivariate restricted maximum likelihood analysis. The pedigree file included 3477 animals. Heritability estimates for liveweights and gain in both environments correspond to most previously reported estimates. The genetic correlation of gain between the 2 environments was -0·12, suggesting a large genotype testing environment interaction and re-ranking of animal breeding values across environments. Results of this analysis suggest the need for environment-specific breeding values for postweaning gain.

scholarly journals Hybrid of Restricted and Penalized Maximum Likelihood Method for Efficient Genome-Wide Association Study

Genes ◽  
2020 ◽  
Vol 11 (11) ◽  
pp. 1286
Author(s):  
Wenlong Ren ◽  
Zhikai Liang ◽  
Shu He ◽  
Jing Xiao
Keyword(s):  
Maximum Likelihood ◽  
Variance Components ◽  
Statistical Power ◽  
Mixed Model ◽  
Single Locus ◽  
Genome Wide Association ◽  
Likelihood Method ◽  
Penalized Maximum Likelihood ◽  
Genome Wide ◽  
Estimation Of Variance

In genome-wide association studies, linear mixed models (LMMs) have been widely used to explore the molecular mechanism of complex traits. However, typical association approaches suffer from several important drawbacks: estimation of variance components in LMMs with large scale individuals is computationally slow; single-locus model is unsatisfactory to handle complex confounding and causes loss of statistical power. To address these issues, we propose an efficient two-stage method based on hybrid of restricted and penalized maximum likelihood, named HRePML. Firstly, we performed restricted maximum likelihood (REML) on single-locus LMM to remove unrelated markers, where spectral decomposition on covariance matrix was used to fast estimate variance components. Secondly, we carried out penalized maximum likelihood (PML) on multi-locus LMM for markers with reasonably large effects. To validate the effectiveness of HRePML, we conducted a series of simulation studies and real data analyses. As a result, our method always had the highest average statistical power compared with multi-locus mixed-model (MLMM), fixed and random model circulating probability unification (FarmCPU), and genome-wide efficient mixed model association (GEMMA). More importantly, HRePML can provide higher accuracy estimation of marker effects. HRePML also identifies 41 previous reported genes associated with development traits in Arabidopsis, which is more than was detected by the other methods.

Sign in / Sign up

Export Citation Format

Share Document