Genetic analysis in structured populations used mixed linear models where the variance matrix of the error term is a linear combination of an identity matrix and a positive definite matrix.
The linear model is of the familiar form: 𝑦 = 𝑋 β + ϵ.
- 𝑦: phenotype
- 𝑋: covariates
- β: fixed effects
- ϵ: error term
Further, V(ϵ) = τ²𝐾+ σ²𝐼, where τ² is the genetic variance, σ² is the environmental variance, 𝐾 is the kinship matrix, and 𝐼 is the identity matrix.
The key idea in speeding up computations here is that by rotating the phenotypes by the eigenvectors of 𝐾 we can transform estimation to a weighted least squares problem.
This code is under development.
Guide to the directories:
src: Julia source codedata: Example data for development and testingtest: Code for testingdocs: Notes on comparisons with other implementations