Simulate data to test mr.mash.

Function to simulate data from \(MN_{nxr}(XB, I, V)\), where \(X \sim N_p(0, Gamma)\), \(B \sim \sum_k w_k N_r(0, Sigma_k)\), with \(Gamma\), \(w_k\), \(Sigma_k\), and \(V\) defined by the user.

simulate_mr_mash_data(
  n,
  p,
  p_causal,
  r,
  r_causal = list(1:r),
  intercepts = rep(1, r),
  pve = 0.2,
  B_cor = 1,
  B_scale = 1,
  w = 1,
  X_cor = 0,
  X_scale = 1,
  V_cor = 0
)

Arguments

n

scalar indicating the number of samples.

p

scalar indicating the number of variables.

p_causal

scalar indicating the number of causal variables.

r

scalar indicating the number of responses.

r_causal

a list of numeric vectors (one element for each mixture component) indicating in which responses the causal variables have an effect.

intercepts

numeric vector of intercept for each response.

pve

per-response proportion of variance explained by the causal variables.

B_cor

scalar or numeric vector (one element for each mixture component) with positive correlation [0, 1] between causal effects.

B_scale

scalar or numeric vector (one element for each mixture component) with the diagonal value for Sigma_k;

w

scalar or numeric vector (one element for each mixture component) with mixture proportions associated to each mixture component.

X_cor

scalar indicating the positive correlation [0, 1] between variables.

X_scale

scalar indicating the diagonal value for Gamma.

V_cor

scalar indicating the positive correlation [0, 1] between residuals

Value

A list with some or all of the following elements:

X

n x p matrix of variables.

Y

n x r matrix of responses.

B

p x r matrix of effects.

V

r x r residual covariance matrix among responses.

Sigma

list of r x r covariance matrices among the effects.

Gamma

p x p covariance matrix among the variables.

intercepts

r-vector of intercept for each response.

causal_responses

a list of numeric vectors of indexes indicating which responses have causal effects for each mixture component.

causal_variables

p_causal-vector of indexes indicating which variables are causal.

causal_vars_to_mixture_comps

p_causal-vector of indexes indicating from which mixture components each causal effect comes.

Examples

set.seed(1)
dat <- simulate_mr_mash_data(n=50, p=40, p_causal=20, r=5,
                             r_causal=list(1:2, 3:4), intercepts=rep(1, 5),
                             pve=0.2, B_cor=c(0, 1), B_scale=c(0.5, 1),
                             w=c(0.5, 0.5), X_cor=0.5, X_scale=1, 
                             V_cor=0)