# contord

From GenOrd v1.0.1
by Alessandro Barbiero

##### Correlations of discretized variables

The function computes the correlation matrix of the $k$ variables, with given marginal distributions, derived discretizing a $k$-variate standard normal variable with given correlation matrix

- Keywords
- models, distribution, htest, datagen

##### Usage

`contord(marginal, Sigma, support = list(), Spearman = FALSE)`

##### Arguments

- 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 correlation matrix of the standard multivariate normal variable
- 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 provide
`support`

), if FALSE (default) Pearson's correlations

##### Value

- the correlation matrix among the discretized variables

##### See Also

##### Examples

```
# consider 4 discrete variables
k<-4
# with these marginal distributions
marginal<-list(0.4,c(0.3,0.6),c(0.25,0.5,0.75),c(0.1,0.2,0.8,0.9))
# generated discretizing a multivariate standard normal variable
# with correlation matrix
Sigma<-matrix(0.6,4,4)
diag(Sigma)<-1
# the resulting correlation matrix for the discrete variables is
contord(marginal,Sigma)
# note all the correlations are smaller than the original 0.6
# change Sigma, adding a negative correlation
Sigma[1,2]<--0.2
Sigma[2,1]<-Sigma[1,2]
Sigma
contord(marginal, Sigma)
```

*Documentation reproduced from package GenOrd, version 1.0.1, License: GPL*

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