Consider a transformed linear mixed model (TLMM) obtained pre-multiplying (LMM) M : y = Zα + Rγ e by given matrix. This work concerns the problem of equalities predictors under considered two LMMs general assumptions. We characterize between best unbiased (BLUPs) LMM and its TLMM using various rank formulas block matrices elementary matrix operations.

Genome-wide association studies have been successful in uncovering novel genetic variants that are associated with disease status or cross-sectional phenotypic traits. Researchers are beginning to investigate how genes play a role in the development of a trait over time. Linear mixed effects models (LMM) are commonly used to model longitudinal data; however, it is unclear if the failure to meet...

Linear mixed model (LMM) analysis has been recently used extensively for estimating additive genetic variances and narrow-sense heritability in many genomic studies. While the LMM analysis is computationally less intensive than the Bayesian algorithms, it remains infeasible for large-scale genomic data sets. In this paper, we advocate the use of a statistical procedure known as symmetric differ...

Bivariate clustered (correlated) data often encountered in epidemiological and clinical research are routinely analyzed under a linear mixed model (LMM) framework with underlying normality assumptions of the random effects and within-subject errors. However, such normality assumptions might be questionable if the data set particularly exhibits skewness and heavy tails. Using a Bayesian paradigm...

The Intraclass Correlation Coefficient (ICC) is commonly used to estimate the similarity between quantitative measures obtained from different sources. Overdispersed data is traditionally transformed so that linear mixed model (LMM) based ICC can be estimated. A common transformation used is the natural logarithm. The reliability of environmental sampling of fecal slurry on freestall pens has b...

Mixed linear models can be used to improve the informational value of milk yield forecasts. For this purpose two different functional approaches for modelling lactation curves are as well compared as three linear mixed models with varying random effects of individual animals and lactation numbers. It can be shown that more complex random regression models fit significantly better than fixed reg...

 Spatial generalized linear mixed models are used commonly for modelling non-Gaussian discrete spatial responses. We present an algorithm for parameter estimation of the models using Laplace approximation of likelihood function. In these models, the spatial correlation structure of data is carried out by random effects or latent variables. In most spatial analysis, it is assumed that rando...

The complexity of eye-movement control during reading allows measurement of many dependent variables, the most prominent ones being fixation durations and their locations in words. In current practice, either variable may serve as dependent variable or covariate for the other in linear mixed models (LMMs) featuring also psycholinguistic covariates of word recognition and sentence comprehension....

A linear mixed model ($\LMM$) $\M :\yy = \mxX\BETA + \mxZ\uu \EPS $ with general assumptions and its transformed $\T:\mxT\yy \mxT\mxX\BETA \mxT\mxZ\uu \mxT\EPS are considered. This work concerns the comparison problem of predictors under $\M$ $\T$. Our aim is to establish equality relations between best unbiased ($\BLUP$s) unknown vectors two $\LMM$s $\T$ through their covariance matrices by us...