`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.

To install `gemma2`

, use the `devtools`

R package from CRAN. If you
haven’t installed `devtools`

, please run this line of code:

```
install.packages("devtools")
```

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

:

```
devtools::install_github("fboehm/gemma2")
```

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

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