sim_normal {clusteval} | R Documentation |
We generate n_m observations (m = 1, …, M) from each of M multivariate normal distributions such that the Euclidean distance between each of the means and the origin is equal and scaled by Δ ≥ 0.
sim_normal(n = rep(25, 5), p = 50, rho = rep(0.9, 5), delta = 0, sigma2 = 1, seed = NULL)
n |
a vector (of length M) of the sample sizes for each population |
p |
the dimension of the multivariate normal populations |
rho |
a vector (of length M) of the intraclass constants for each population |
delta |
the fixed distance between each population and the origin |
sigma2 |
the coefficient of each intraclass covariance matrix |
seed |
seed for random number generation (If NULL, does not set seed) |
Let Π_m denote the mth population with a p-dimensional multivariate normal distribution, N_p(μ_m, Σ_m) with mean vector μ_m and covariance matrix Σ_m. Also, let e_m be the mth standard basis vector (i.e., the mth element is 1 and the remaining values are 0). Then, we define
μ_m = Δ ∑_{j=1}^{p/M} e_{(p/M)(m-1) + j}.
Note that p
must be divisible
by M
. By default, the first 10 dimensions of
μ_1 are set to delta
with all remaining
dimensions set to 0, the second 10 dimensions of
μ_2 are set to delta
with all remaining
dimensions set to 0, and so on.
Also, we consider intraclass covariance (correlation) matrices such that Σ_m = σ^2 (1 - ρ_m) J_p + ρ_m I_p, where -(p-1)^{-1} < ρ_m < 1, I_p is the p \times p identity matrix, and J_p denotes the p \times p matrix of ones.
By default, we let M = 5, Δ = 0, and σ^2 = 1. Furthermore, we generate 25 observations from each population by default.
For Δ = 0 and ρ_m = ρ, m = 1, …, M, the M populations are equal.
named list containing:
A matrix
whose rows are the observations generated and whose
columns are the p
features (variables)
A vector denoting the population from which the observation in each row was generated.
data_generated <- sim_normal(n = 10 * seq_len(5), seed = 42) dim(data_generated$x) table(data_generated$y) data_generated2 <- sim_normal(p = 10, delta = 2, rho = rep(0.1, 5)) table(data_generated2$y) sample_means <- with(data_generated2, tapply(seq_along(y), y, function(i) { colMeans(x[i,]) })) (sample_means <- do.call(rbind, sample_means))