README.Rmd

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## Statuses

[![Travis-CI Build Status](https://travis-ci.org/fboehm/gemma2.svg?branch=master)](https://travis-ci.org/fboehm/gemma2)

[![codecov](https://codecov.io/gh/fboehm/gemma2/branch/master/graph/badge.svg)](https://codecov.io/gh/fboehm/gemma2)

[![CRAN RStudio mirror downloads](https://cranlogs.r-pkg.org/badges/grand-total/gemma2?color=blue)](https://r-pkg.org/pkg/gemma2)


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## Overview

`gemma2` is an implementation in R of the GEMMA v 0.97 EM algorithm that is part of the GEMMA algorithm for REML estimation of multivariate linear mixed effects models of the form:

$$vec(Y) = X vec(B) + vec(G) + vec(E)$$ 

where $E$ is a n by 2 matrix of random effects that follows the matrix-variate normal distribution

$$G \sim MN(0, K, V_g)$$ 

where $K$ is a relatedness matrix and $V_g$ is a 2 by 2 covariance matrix for the two traits of interest.

Additionally, the random errors matrix $E$ follows the distribution:

$$E \sim MN(0, I_n, V_e)$$

and $G$ and $E$ are independent.





## Installation

To install `gemma2`, use the `devtools` R package from CRAN. If you haven't installed `devtools`, please run this line of code:

```{r, eval = FALSE}
install.packages("devtools")
```

Then, run this line of code to install `gemma2`:

```{r, eval = FALSE}
devtools::install_github("fboehm/gemma2")
```

## References

X. Zhou & M. Stephens. Efficient multivariate linear mixed model algorithms for genome-wide association studies. *Nature Methods* volume 11, pages 407–409 (2014). https://www.nature.com/articles/nmeth.2848

https://github.com/genetics-statistics/GEMMA