simulate_data: Simulate 3 levels data

In Redha-ALLICHE/clusterwiselmm: Apply geometrical clusterwise to linear multi-level models (lmm)

Description

Generate univariate (for now) linear 3 level data with n3 groups, n2 subgroups per group and n1 individuals per subgroups.

Usage

simulate_data(
  n1,
  n2,
  n3,
  fixed_slope,
  fixed_intercept,
  lvl2_corr_mat,
  lvl3_corr_mat,
  sigma2,
  separable_in_x = TRUE,
  distance_factor = 2
)

Arguments

n1	number of individuals at level 1. Must be strictly positive.
n2	number of subgroups at level 2. Must be strictly positive.
n3	number of groups at level 3. Must be strictly positive.
fixed_slope	Fixed effect slope. Must be finite.
fixed_intercept	Fixed effect intercept. Must be finite.
lvl2_corr_mat	Level 2 random effect correlation matrix. Must be of type matrix with size of 2x2
lvl3_corr_mat	Level 3 random effect correlation matrix. Must be of type matrix with size of 2x2
sigma2	variance of the residuals. Must be strictly positive.
separable_in_x	logical; if TRUE, the data will be separable in x axis.
distance_factor	numeric; When separable_in_x == TRUE, indicates the distances in x between level 3 groups. Must be strictly positive.

Details

The generated data follows the 3 levels lmm equations given below :

Y_{ijk} = β_{0jk} + β_{1jk} X_{ijk} + ε_{ijk}

Level 2 :

β_{0jk} = γ_{00k} + u_{0jk}

β_{1jk} = γ_{10k} + u_{1jk}

Level 3 :

γ_{00k} = δ_{000} + u_{00k}

γ_{10k} = δ_{100} + u_{10k}

With :

• δ_{000} and δ_{100} : fixed effects intercept and slope.
  

• u_{00k} and u_{10k} : level 3 random effects intercept and slope for each level 3 group.
  

• u_{0jk} and u_{0jk} : level 2 random effects intercept and slope for each level 2 group within level 3 group.
  

• ε_{ijk} : residual noise.

Value

data frame containing the generated data containing the following list of columns :

• x : explicative variable
  

• y : target variable
  

• lvl2 : factors indicating level 2 groups
  

• lvl3 : factors indicating level 3 groups
  

• lvl3_intercepts : numeric indicating level 3 random intercepts
  

• lvl3_slopes : numeric indicating level 3 random slopes
  

• lvl2_intercepts : numeric indicating level 2 random intercepts
  

• lvl2_slopes : numeric indicating level 2 random slopes
  

Examples

## define correlation matrices for random effects slopes and intercepts
lvl2_corr_mat = matrix(c(1, 0,
                         0, 1), 2, 2)
lvl3_corr_mat = matrix(c(10, 0,
                         0, 10), 2, 2)

## to generate 3 levels data with 3 groups that contains each 10 subgroups,
## and each subgroup contains 30 individuals
data = simulate_data(n1 = 30,
                     n2 = 10,
                     n3 = 3,
                     fixed_slope = -2,
                     fixed_intercept = 2,
                     lvl2_corr_mat = lvl2_corr_mat,
                     lvl3_corr_mat = lvl3_corr_mat,
                     sigma2 = 1
                     )

Redha-ALLICHE/clusterwiselmm documentation built on Aug. 3, 2020, 1:10 a.m.