GenOrd (version 1.0.1)

ordsample: Drawing a sample of ordinal/discrete data

Description

The function draws a sample of given size from a multivariate ordinal/discrete variable with correlation matrix Sigma and pre-specified marginals marginal

Usage

ordsample(n, marginal, Sigma, support=list(), Spearman=FALSE, cormat="ordinal")

Arguments

n

the sample size

marginal

a list of $k$ elements, where $k$ is the number of variables. The $i$-th element of marginal is the vector of the cumulative probabilities defining the marginal distribution of the $i$-th component of the multivariate variable. If the $i$-th component h

Sigma

the target correlation matrix of the ordinal/discrete variables

support

a list of k elements, where k is the number of variables. The i-th element of support contains the ordered values of the support of the i-th variable. By default, the support of the $i$-th variable is $1,2,...,k_i$

Spearman

if TRUE, the function finds Spearman's correlations (and it is not necessary to prvide support), if FALSE (default) Pearson's correlations

cormat

"ordinal" if the Sigma in input is the target correlation matrix of ordinal/discrete variables; "continuous" if the Sigma in input is the intermediate correlation matrix of the multivariate standard normal to be discretized

Value

• a $n\times k$ matrix of discrete/ordinal data drawn from the k-variate discrete/ordinal r.v. with the desired marginal distributions and correlation matrix

See Also

contord, ordcont, corrcheck

Examples

# Example 1

# draw a sample from a bivariate ordinal variable
# with 4 of categories and asymmetrical marginal distributions
# and correlation coefficient 0.6 (to be checked)
k<-2
marginal<-list(c(0.1,0.3,0.6),c(0.4,0.7,0.9))
corrcheck(marginal) # check ok
Sigma<-matrix(c(1,0.6,0.6,1),2,2)
# sample size 100
n<-500
# generate a sample of size n
m<-ordsample(n, marginal, Sigma)
head(m)
# sample correlation matrix
cor(m) # compare it with Sigma
table(m[,1])/sum(table(m[,1]))
table(m[,2])/sum(table(m[,2])) # compare it with the two marginal distributions

# Example 2

# draw a sample from a 4-dimensional ordinal variable
# with different number of categories
# and uniform marginal distributions, and different correlation coefficients
k<-4
marginal<-list(0.5,c(1/3,2/3),c(1/4,2/4,3/4),c(1/5,2/5,3/5,4/5))
corrcheck(marginal)
# select a feasible correlation matrix
Sigma<-matrix(c(1,0.5,0.4,0.3,0.5,1,0.5,0.4,0.4,0.5,1,0.5,0.3,0.4,0.5,1),4,4,byrow=TRUE)
Sigma
# sample size 100
n<-100
# generate a sample of size n
set.seed(1)
m<-ordsample(n, marginal, Sigma)
# sample correlation matrix
cor(m) # compare it with Sigma
table(m[,4]) # compare it with the fourth marginal
head(m)
# or equivalently...
set.seed(1)
res<-ordcont(marginal, Sigma)
res[[1]] # the intermediate correlation matrix of the multivariate normal
m<-ordsample(n, marginal, res[[1]], cormat="continuous")
head(m)
# increasing n, the sample correlations get close to
# the theoretical correlations
# and the empirical marginal distributions get closer to
# the theoretical marginal distribution