# example_3way: Simulated example of a 3 way interaction GxExz model In LEGIT: Latent Environmental & Genetic InTeraction (LEGIT) Model

## Description

Simulated example of a 3 way interaction GxExz model (where G and E are latent variables).

g_j \sim Binomial(n=1,p=.30)

j = 1, 2, 3, 4

e_l \sim Normal(μ=0,σ=1.5)

l = 1, 2, 3

z \sim Normal(μ=3,σ=1)

g = .2g_1 + .15g_2 - .3g_3 + .1g_4 + .05g_1g_3 + .2g_2g_3

e = -.45e_1 + .35e_2 + .2e_3

μ = -2 + 2g + 3e + z + 5ge - 1.5ez + 2gz + 2gez

 y \sim Normal(μ=μ,σ=\code{sigma}) if `logit`=FALSE y \sim Binomial(n=1,p=logit(μ)) if `logit`=TRUE

## Usage

 `1` ```example_3way(N, sigma = 2.5, logit = FALSE, seed = NULL) ```

## Arguments

 `N` Sample size. `sigma` Standard deviation of the gaussian noise (if `logit`=FALSE). `logit` If TRUE, the outcome is transformed to binary with a logit link. `seed` RNG seed.

## Value

Returns a list containing, in the following order: data.frame with the observed outcome (with noise), the true outcome (without noise) and z, data.frame of the genetic variants (G), data.frame of the environments (E), vector of the true genetic coefficients, vector of the true environmental coefficients, vector of the true main model coefficients

## Examples

 ```1 2``` ```example_3way(5,2.5,logit=FALSE) example_3way(5,0,logit=TRUE) ```

LEGIT documentation built on Aug. 30, 2019, 1:05 a.m.