The function sample.multinom generates a random sample of n observations,
composed of p predictors, collected in the n x p matrix X, and a binary
response, in a vector Y of length n, thanks to a logistic model, where the
response Y is generated as a Bernoulli random variable of parameter
logit^{-1}(XB), the coefficients B are sparse. In addition, the covariate
matrix X is composed of correlated blocks of predictors.
sample.multinom(
n,
p,
nb.class = 2,
kstar,
lstar,
beta.min,
beta.max,
mean.H = 0,
sigma.H = 1,
sigma.F = 1,
seed = NULL
)An object with the following attributes:
the (n x p) covariate matrix, containing the n observations
for each of the p predictors.
the (n) vector of Y observations.
the n vector of Bernoulli parameters used to generate the
response, in particular logit^{-1}(X %*% B).
the index in (1:p) of covariates with non null coefficients
in B.
the index in (1:p) of covariates with null coefficients
in B.
the (n) vector of coefficients.
a (p) vector indicating the block of each predictors in (1:kstar).
the number of covariates in the sample.
the number of underlying latent variables used to generates
the covariate matrix X, kstar <= p. kstar is also
the number of blocks in the covariate matrix (see details).
the number of blocks in the covariate matrix X that
are used to generates the response Y, i.e. with non null
coefficients in vector B, lstar <= kstar.
the number of predictors with non null coefficients in B.
a (lstar) vector indicating the index in (1:kstar) of
blocks with predictors having non null coefficient in B.
the inf bound for non null coefficients (see details).
the sup bound for non null coefficients (see details).
the mean of latent variables used to generates X.
the standard deviation of latent variables used to
generates X.
the standard deviation of the noise added to latent
variables used to generates X.
an positive integer, if non NULL it fix the seed
(with the command set.seed) used for random number generation.
the number of observations in the sample.
the number of covariates in the sample.
the number of groups in the data.
the number of underlying latent variables used to generates
the covariate matrix X, kstar <= p. kstar is also the
number of blocks in the covariate matrix (see details).
the number of blocks in the covariate matrix X that are
used to generates the response Y, i.e. with non null coefficients
in vector B, lstar <= kstar.
the inf bound for non null coefficients (see details).
the sup bound for non null coefficients (see details).
the mean of latent variables used to generates X.
the standard deviation of latent variables used to
generates X.
the standard deviation of the noise added to latent
variables used to generates X.
an positive integer, if non NULL it fix the seed (with the
command set.seed) used for random number generation.
Ghislain Durif (https://gdurif.perso.math.cnrs.fr/).
The set (1:p) of predictors is partitioned into kstar block. Each block k (k=1,...,kstar) depends on a latent variable H.k which are independent and identically distributed following a Gaussian distribution N(mean.H, sigma.H^2). Each columns X.j of the matrix X is generated as H.k + F.j for j in the block k, where F.j is independent and identically distributed gaussian noise N(0,sigma.F^2).
The coefficients B are generated as random between beta.min and beta.max on lstar blocks, randomly chosen, and null otherwise. The variables with non null coefficients are then relevant to explain the response, whereas the ones with null coefficients are not.
The response is generated as by drawing one observation of n different Bernoulli random variables of parameters logit^{-1}(XB).
The details of the procedure are developped by Durif et al. (2018).
Durif, G., Modolo, L., Michaelsson, J., Mold, J.E., Lambert-Lacroix, S., Picard, F., 2018. High dimensional classification with combined adaptive sparse PLS and logistic regression. Bioinformatics 34, 485--493. tools:::Rd_expr_doi("10.1093/bioinformatics/btx571"). Available at http://arxiv.org/abs/1502.05933.
sample.cont
### load plsgenomics library
library(plsgenomics)
### generating data
n <- 100
p <- 1000
nclass <- 3
sample1 <- sample.multinom(n=n, p=p, nb.class=nclass,
kstar=20, lstar=2, beta.min=0.25,
beta.max=0.75, mean.H=0.2,
sigma.H=10, sigma.F=5)
str(sample1)
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