Keep in mind this is a highly idealized schematic of how GWAS analyses are actually done. If you want to do GWAS for real, you should take a look at GEMMA (http: //www.xzlab.org/software.html) or TASSEL (https://www.maizegenetics.net/tassel), or GenABEL (). One important way in which what I’ve presented is a simplification is that in a real GWAS analysis, you’d estimate the effects of every locus simultaneously, which raises an interesting problem. In a typical GWAS analysis, you will have measured the phenotype of a few thousand individuals, but you will have genotyped those individuals at several hundred thousand loci. Lango Allen et al. [3] report results from a large analysis of height variation in humans, 183,727 individuals genotyped at 2,834,208 loci. What’s the problem here? There are more predictors (loci) than observations (individual phenotypes). If you remember some basic algebra, you’ll remember that you can’t solve a set of linear equations unless you have the same number of equations as unknowns. For example, you can’t solve a set of three equations that has five unknowns. There’s a similar phenomenon in statistics when we’re fitting a linear regression. In statistics we don’t “solve” an equation. We find the best fit in a regression, and we can do so in a reasonable way so long as the number
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