This package provides functions for estimating matrix linear models which are bilinear models of the form $$Y = X B Z^\prime + E,$$ where $Y$ is the response matrix, $X$ and $Z$ are design matrices contributing information on the rows and columns of the response matrix, $B$ is a matrix of coefficients to be estimated and $E$ is random errors. The core functions obtain closed-form least squares estimates for matrix linear models, and a sandwich estimator for the variance. Variance shrinkage is adapted from Ledoit & Wolf (2003)¹.

The package is intended for high-dimensional applications such as high-throughput biological data. The core functions are very fast as they use matrix operations. The package provides flexibility in modeling via the use of model formulas for both row covariates ($X$) and column covariates ($Z$).

The first application of MatrixLM was for high-throughput genetic screens; some additional specialized functions are available in the package GeneticScreens package. See the associated paper, "Matrix linear models for high-throughput chemical genetic screens", and its reproducible code for more details.

A second application is metabolomics. See the associated paper, "Matrix Linear Models for connecting metabolite composition to individual characteristics" and its associated reproducible code for more details.

MatrixLMnet is a related package that provides sparse estimates of $B$ using L$_1$ and L$_2$-penalized estimates. See the associated paper, "Sparse matrix linear models for structured high-throughput data", and its reproducible code for more details.

The MatrixLM package can be installed by running:

using Pkg
Pkg.add("MatrixLM")

or from the julia REPL, press ] to enter pkg mode, and execute the following command:

add MatrixLM

For the most recent (development) version, use:

using Pkg
Pkg.add(url = "https://github.com/senresearch/MatrixLM.jl", rev="main")

We appreciate contributions from users including reporting bugs, fixing issues, improving performance and adding new features.

If you have questions about contributing or using MatrixLM package, please communicate with the authors via GitHub.

If you use MatrixLM in a scientific publication, please consider citing the following paper:

Jane W Liang, Robert J Nichols, Śaunak Sen, Matrix Linear Models for High-Throughput Chemical Genetic Screens, Genetics, Volume 212, Issue 4, 1 August 2019, Pages 1063–1073, https://doi.org/10.1534/genetics.119.302299

@article{10.1534/genetics.119.302299,
    author = {Liang, Jane W and Nichols, Robert J and Sen, Śaunak},
    title = "{Matrix Linear Models for High-Throughput Chemical Genetic Screens}",
    journal = {Genetics},
    volume = {212},
    number = {4},
    pages = {1063-1073},
    year = {2019},
    month = {06},
    issn = {1943-2631},
    doi = {10.1534/genetics.119.302299},
    url = {https://doi.org/10.1534/genetics.119.302299},
    eprint = {https://academic.oup.com/genetics/article-pdf/212/4/1063/42105135/genetics1063.pdf},
}