example_3way_3latent {LEGIT}

Simulated example of a 3 way interaction GxExZ model

Description

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

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

j = 1, 2, 3, 4

e_k \sim Normal(\mu=0,\sigma=1.5)

k = 1, 2, 3

z_l \sim Normal(\mu=3,\sigma=1)

l = 1, 2, 3

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

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

z = .15z_1 + .60z_2 + .25z_3

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

y \sim Normal(\mu=\mu,\sigma=\code{sigma}) if logit=FALSE

y \sim Binomial(n=1,p=logit(\mu)) if logit=TRUE

Usage

example_3way_3latent(N, sigma = 1, 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) and the true outcome (without noise), list containing the data.frame of the genetic variants (G), the data.frame of the e environments (E) and the data.frame of the z environments (Z), vector of the true genetic coefficients, vector of the true e environmental coefficients, vector of the true z environmental coefficients, vector of the true main model coefficients

Examples

example_3way_3latent(5,1,logit=FALSE)
example_3way_3latent(5,0,logit=TRUE)