centred around zero with standard deviation one. We also assume that the data has been corrected for any confounding factors, either by regressing out known covariates and/or by estimating hidden factors [@stegle2012using].

Genetics of gene expression {#sec:genet-gene-expr}
===========================

A first step towards identifying molecular networks affected by DNA variants is to identify variants that underpin variations in eQTLs of transcripts [@cookson2009mapping], proteins [@foss2007] or metabolites [@nicholson2011genome] across individuals. When studying a single trait, as in GWAS, it is possible to consider multiple statistical models to explicitly account for additive and/or dominant genetic effects [@laird2011]. However, when the possible effects of a million or more SNPs on tens of thousands of molecular abundance traits need to be tested, as is common in modern genetics of gene expression studies, the computational cost of testing SNP-trait associations one-by-one becomes prohibitive. To address this problem, new methods have been developed to calculate the test statistics for the parametric linear regression and analysis of variance (ANOVA) models [@shabalin2012matrix] and the non-parametric ANOVA model (or Kruskal-Wallis test) [@qi2014] using fast matrix multiplication algorithms, implemented in the softwares **matrix-eQTL** (<http://www.bios.unc.edu/research/genomic_software/Matrix_eQTL/>) [@shabalin2012matrix] and **kruX** (<https://github.com/tmichoel/krux>) [@qi2014].

In both softwares, genotype values of $s$ genetic markers and expression levels 