This tutorial demonstrates how to use the `SEAGLE`

package when the user inputs ${\bf y}$, ${\bf X}$, ${\bf E}$, and ${\bf G}$ from .txt files. We'll begin by loading the `SEAGLE`

package.

knitr::opts_chunk$set( collapse = TRUE, comment = "#>" )

```
library(SEAGLE)
```

If you have your own files ready to read in for ${\bf y}$, ${\bf X}$, ${\bf E}$, and ${\bf G}$, you can read them into R using the `read.csv()`

command.

As an example, we've included `y.txt`

, `X.txt`

, `E.txt`

, and `G.txt`

files in the `extdata`

folder of this package. The following code loads those files into R so we can use them in this tutorial.

y_loc <- system.file("extdata", "y.txt", package = "SEAGLE") y <- as.numeric(unlist(read.csv(y_loc))) X_loc <- system.file("extdata", "X.txt", package = "SEAGLE") X <- as.matrix(read.csv(X_loc)) E_loc <- system.file("extdata", "E.txt", package = "SEAGLE") E <- as.numeric(unlist(read.csv(E_loc))) G_loc <- system.file("extdata", "G.txt", package = "SEAGLE") G <- as.matrix(read.csv(G_loc))

Now we can input ${\bf y}$, ${\bf X}$, ${\bf E}$, and ${\bf G}$ into the `prep.SEAGLE`

function. The `intercept = 1`

parameter indicates that the first column of ${\bf X}$ is the all ones vector for the intercept.

This preparation procedure formats the input data for the `SEAGLE`

function by checking the dimensions of the input data. It also pre-computes a QR decomposition for $\widetilde{\bf X} = \begin{pmatrix} {\bf 1}*{n} & {\bf X} & {\bf E} \end{pmatrix}$, where ${\bf 1}*{n}$ denotes the all ones vector of length $n$.

objSEAGLE <- prep.SEAGLE(y=as.matrix(y), X=X, intercept=1, E=E, G=G)

Finally, we'll input the prepared data into the `SEAGLE`

function to compute the score-like test statistic $T$ and its corresponding p-value. The `init.tau`

and `init.sigma`

parameters are the initial values for $\tau$ and $\sigma$ employed in the REML EM algorithm.

res <- SEAGLE(objSEAGLE, init.tau=0.5, init.sigma=0.5) res$T res$pv

The score-like test statistic $T$ for the G$\times$E effect and its corresponding p-value can be found in `res$T`

and `res$pv`

, respectively.

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