ELI5: Why is population structure considered a fixed effect in mixed linear models?

Question

[Jeremy Leipzig]

MLMs are popular for controlling for confounding population structure effects in GWAS.

From what I can see the population is usually modeled as a fixed effect and the SNPs as a random effect. Why isn't it the other way around?

Asking for a 5-year old.

[Jeremy Leipzig]

cross-posted: http://stats.stackexchange.com/questions/233978/why-is-population-structure-considered-a-fixed-effect-in-mixed-linear-models

Answer 1

[theobroma22]

First, it's not the other way around because of the experimental design of the study of what you are trying to explain. Second, population structure could be a random effect if that is what you are taking observations on, or quantifying, like if one were to try explaining migration patterns based on population structure. Third, the random effects of the mixed model are those that, ahem, could arise from randomness, and it has been previously shown that population structure is controlled by variables like access to food and water, sex, birth and death rate, competition from enemies, help from benefactors and perhaps in your question, SNPs. Note that some, or all, of those listed are in fact mostly random. Mixed modelling is certainly a model to use when things aren't as linear as one would expect. So, in the case of whether you are going to have a boy or a girl is a 50:50 chance, it is still random, and now the outcome of sex may ultimately be explained by SNPs, and so sex won't be random after all. That is, one could determine or explain sexual outcomes between two parents before the sexual act is undertaken. 50:50 could become 0:100, like a family with say all 5 girls as children. Is this really random, or fixed and controlled by SNPs? Finally, now you should understand why population structure can be considered a fixed effect.