The Mat ́ern correlation function provides great flexibility for modeling spatially correlated random processes in two dimensions, in particular via a smoothness parameter, whose estimation allows data to determine the degree of smoothness of a spatial process. The extension to include anisotropy provides a very general and flexible class of spatial covariance functions that can be used in a mod...

Estimation of heritability is fundamental in genetic studies. Recently, heritability estimation using linear mixed models (LMMs) has gained popularity because these estimates can be obtained from unrelated individuals collected in genome-wide association studies. Typically, heritability estimation under LMMs uses the restricted maximum likelihood (REML) approach. Existing methods for the constr...

The objective of this study was to remove bottlenecks generally found in a computer program for average-information REML. The refinements included improvements to setting-up mixed-model equations on a hash table with a faster hash function as sparse matrix storage, changing sparse structures in calculation of traces, and replacing a sparse matrix package using traditional methods (FSPAK) with a...

Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixedand random-effects terms. The formula and data together determine a numerical repr...

Heritability is a central element in quantitative genetics. New molecular markers to assess genetic variance and heritability are continually under development. The availability of molecular single nucleotide polymorphism (SNP) markers can be applied for estimation of variance components and heritability on population, where relationship information is unknown. In this study, we evaluated the c...

The authors explore likelihood-based methods for making inferences about the components of variance in a general normal mixed linear model. In particular, they use local asymptotic approximations to construct confidence intervals for the components of variance when the components are close to the boundary of the parameter space. In the process, they explore the question of how to profile the re...

The widespread use of the set of multiple-trait derivative-free REML programs for prediction of breeding values and estimation of variance components has led to significant improvement in traits of economic importance. The initial version of this software package, however, was generally limited to pedigree-based relationships. With continued advances in genomic research and the increased availa...

In order to ascertain changes in bitterness as beer aged naturally, time±intensity (TI) measurements were made by a professional sensory panel using a squeezer transducer system. TI parameters were ®tted by variance components models using Restricted Maximum Likelihood (REML). It was shown that bitterness decreased with age, although this age-induced di€erence was smaller than the original di€e...

Six packages for solving mixed model equations and estimating variance components by REML are compared. Each has a unique strength. Meticulously finished DFREML is the only one that implements hypothesis testing for variance component estimates. MTDFREML is a comprehensive, relatively easy to install and simple to use package for analyses of experimental data. PEST, the only semi-commercial pro...

With the recent advances in graph neural networks, there is a rising number of studies on graph-based multi-label classification with consideration object dependencies within visual data. Nevertheless, representations can become indistinguishable due to complex nature label relationships. We propose image framework based transformer networks fully exploit inter-label interactions. The paper pre...