MRVCModels
MRVCModels.jl is a package for fitting and testing multivariate response variance components linear mixed models of form
\[\text{vec}\ \boldsymbol{Y} \sim \mathcal{N}(\text{vec}(\boldsymbol{X} \boldsymbol{B}), \sum_{i=1}^m \boldsymbol{\Gamma}_i \otimes \boldsymbol{V}_i),\]
where $\boldsymbol{Y}$ and $\boldsymbol{X}$ are $n \times d$ response and $n \times p$ predictor matrices, respectively, and $\boldsymbol{V}_1, \ldots, \boldsymbol{V}_m$ are $m$ known $n \times n$ positive semidefinite matrices. $\text{vec}\ \boldsymbol{Y}$ creates an $nd \times 1$ vector from $\boldsymbol{Y}$ by stacking its columns and $\otimes$ denotes the Kronecker product. The parameters of the model include $p \times d$ mean effects $\boldsymbol{B}$ and $d \times d$ variance components ($\boldsymbol{\Gamma}_1, \dots, \boldsymbol{\Gamma}_m$), which MRVCModels.jl estimates through either minorization-maximization (MM) or expectation–maximization (EM) algorithms.
MRVCModels.jl can also handle data with missing response, which destroys the symmetry of the log-likelihood and complicates maximum likelihood estimation. MM algorithm easily adapts to this challenge.
MRVCModels.jl is not suitable for biobank-scale data, except in the setting of $m = 2$. For $m > 2$, we recommend using this package for datasets of size up to $n \cdot d \approx 60000$. Further note that large $m$ can affect memory needed when calculating standard errors, since it will require $m(nd)^2$ storage space.
Installation
To use MRVCModels.jl, type:
using Pkg
Pkg.add(url = "https://github.com/Hua-Zhou/MultiResponseVarianceComponentModels.jl.git")This documentation was built using Documenter.jl.
Documentation built 2024-06-27T04:00:45.930 with Julia 1.10.4