# ordsample

0th

Percentile

##### Drawing a sample of ordinal/discrete data

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

Keywords
models, distribution, htest, datagen
##### 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
##### 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

contord, ordcont, corrcheck

• ordsample
##### 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 1000
n<-1000
# generate a sample of size n
m<-ordsample(n, marginal, Sigma)
# sample correlation matrix
cor(m) # compare it with Sigma
cumsum(table(m[,1]))/n
cumsum(table(m[,2]))/n # compare it with the two marginal distributions

# Example 1bis

# draw a sample from a bivariate ordinal variable
# with 4 of categories and asymmetrical marginal distributions
# and Spearman 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, Spearman=TRUE) # check ok
Sigma<-matrix(c(1,0.6,0.6,1),2,2)
# sample size 1000
n<-1000
# generate a sample of size n
m<-ordsample(n, marginal, Sigma, Spearman=TRUE)
# sample correlation matrix
cor(rank(m[,1]),rank(m[,2])) # compare it with Sigma
cumsum(table(m[,1]))/n
cumsum(table(m[,2]))/n # 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
cumsum(table(m[,4]))/n # compare it with the fourth marginal
head(m)