VarianceComponentModels.jl

Utilities for fitting and testing variance component models

VarianceComponentModels.jl implements computation routines for fitting and testing variance component model of form

\[\text{vec}(Y) \sim \text{Normal}(X B, \Sigma_1 \otimes V_1 + \cdots + \Sigma_m \otimes V_m),\]

where $\otimes$ is the Kronecker product.

In this model, data is represented by

• Y: n x d response matrix
• X: n x p covariate matrix
• V=(V1,...,Vm): a tuple m n x n covariance matrices

and parameters are

• B: p x d mean parameter matrix
• Σ=(Σ1,...,Σm): a tuple of m d x d variance components

Package Features

• Maximum likelihood estimation (MLE) and restricted maximum likelihood estimation (REML) of mean parameters B and variance component parameters Σ
• Allow constrains in the mean parameters B
• Choice of optimization algorithms: Fisher scoring and minorization-maximization algorithm
• Heritability analysis in genetics

Installation

This package requires Julia v0.7.0 or later, which can be obtained from https://julialang.org/downloads/ or by building Julia from the sources in the https://github.com/JuliaLang/julia repository.

The package has not yet been registered and must be installed using the repository location. Start julia and use the ] key to switch to the package manager REPL

(v1.2) pkg> add https://github.com/OpenMendel/VarianceComponentModels.jl.git

Use the backspace key to return to the Julia REPL.

Manual Outline

• MLE and REML
• • Demo data
  • Maximum likelihood estimation (MLE)
  • Restricted maximum likelihood estimation (REML)
  • Optimization algorithms
  • Starting point
  • Constrained estimation of B
• Heritability Analysis
• • Read in binary SNP data
  • Summary statistics of SNP data
  • Empirical kinship matrix
  • Phenotypes
  • Pre-processing data for heritability analysis
  • Save intermediate results
  • Heritability of single traits
  • Pairwise traits
  • 3-trait analysis
  • 13-trait joint analysis
  • Save analysis results