Why would GREML in GCTA treat SNP effects as random effects?

Question

I've read many papers, but none of them gave clear answer to my question.

For example, https://www.nature.com/articles/s41576-019-0137-z#Sec5

The univariate GREML approach can model multiple random effects and hence estimate multiple genetic variances using multiple GRMs, each built with SNPs selected on different annotations.

https://www.nature.com/articles/ng.608

The effects of the SNPs are treated statistically as random, and the variance explained by all the SNPs together is estimated.

I've also read that random effect refers to random grouping (site) effects. Why should SNP be considered groups?

Answer 1

Linear mixed models are used in genetic association studies because if you try and fit SNP effects using a straight forward fixed effects linear model and ordinary least squares, there is a tendency to overfit the $p$ (where $p$ is a large number of SNP densely located SNPS in some kind of LD) model parameters, as SNPs are often in strong linkage disequilibrium with one another (i.e. the SNPs effects are non-independent). Instead, if you treat SNP effects as random effects, you can restrict the SNP effect parameter values to a joint 'variance parameter' which is estimated from the data. In other words, we want to estimate a single 'shared' variance parameter value rather than many parameters for all $p$ SNPs to avoid overfitting the model.