example_3way

Simulated example of a 3 way interaction GxExz model (where G and E are latent variables). 
$$g_j \sim Binomial(n=1,p=.30)$$
$$j = 1, 2, 3, 4$$
$$e_l \sim Normal(\mu=0,\sigma=1.5)$$
$$l = 1, 2, 3$$
$$z \sim Normal(\mu=3,\sigma=1)$$
$$g = .2g_1 + .15g_2 - .3g_3 + .1g_4 + .05g_1g_3 + .2g_2g_3$$
$$e = -.45e_1 + .35e_2 + .2e_3$$
$$\mu = -2 + 2g + 3e + z + 5ge - 1.5ez + 2gz + 2gez$$<table class="table">
<tr><td>$y \sim Normal(\mu=\mu,\sigma=\code{sigma})$ if <code>logit</code>=FALSE</td><td>$y \sim Binomial(n=1,p=logit(\mu))$ if <code>logit</code>=TRUE</td></tr>
</table>

Constructs genotype x environment interaction (GxE) models where
G is a weighted sum of genetic variants (genetic score) and E is a weighted
sum of environments (environmental score) using the alternating optimization algorithm
by Jolicoeur-Martineau et al. (2017) <arXiv:1703.08111>. This approach has greatly
enhanced predictive power over traditional GxE models which include only a single
genetic variant and a single environmental exposure. Although this approach was
originally made for GxE modelling, it is flexible and does not require the use of
genetic and environmental variables. It can also handle more than 2 latent variables
(rather than just G and E) and 3-way interactions or more. The LEGIT model produces
highly interpretable results and is very parameter-efficient thus it can even be
used with small sample sizes (n < 250). Tools to determine the type of interaction
(vantage sensitivity, diathesis-stress or differential susceptibility), with any
number of genetic variants or environments, are available <arXiv:1712.04058>. The
software can now produce mixed-effects LEGIT models through the lme4 package.

Alexia Jolicoeur-Martineau

LEGIT

Latent Environmental & Genetic InTeraction (LEGIT) Model

example_3way function

<dl><dt>N</dt>
<dd>Sample size.</dd>
<dt>sigma</dt>
<dd>Standard deviation of the gaussian noise (if <code>logit</code>=FALSE).</dd>
<dt>logit</dt>
<dd>If TRUE, the outcome is transformed to binary with a logit link.</dd>
<dt>seed</dt>
<dd>RNG seed.</dd></dl>

Arguments

Simulated example of a 3 way interaction GxExz model (where G and E are latent variables). 
$$g_j \sim Binomial(n=1,p=.30)$$
$$j = 1, 2, 3, 4$$
$$e_l \sim Normal(\mu=0,\sigma=1.5)$$
$$l = 1, 2, 3$$
$$z \sim Normal(\mu=3,\sigma=1)$$
$$g = .2g_1 + .15g_2 - .3g_3 + .1g_4 + .05g_1g_3 + .2g_2g_3$$
$$e = -.45e_1 + .35e_2 + .2e_3$$
$$\mu = -2 + 2g + 3e + z + 5ge - 1.5ez + 2gz + 2gez$$<table class='table'>
<tr><td>$y \sim Normal(\mu=\mu,\sigma=\code{sigma})$ if <code>logit</code>=FALSE</td><td>$y \sim Binomial(n=1,p=logit(\mu))$ if <code>logit</code>=TRUE</td></tr>
</table>

Simulated example of a 3 way interaction GxExz model — example_3way

<dl>

<dt>N</dt>
<dd>Sample size.</dd>


<dt>sigma</dt>
<dd>Standard deviation of the gaussian noise (if <code>logit</code>=FALSE).</dd>


<dt>logit</dt>
<dd>If TRUE, the outcome is transformed to binary with a logit link.</dd>


<dt>seed</dt>
<dd>RNG seed.</dd>

</dl>

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example_3way: Simulated example of a 3 way interaction GxExz model

Description

Usage

Value

Arguments

Examples