# contord: Correlations of discretized variables In GenOrd: Simulation of Discrete Random Variables with Given Correlation Matrix and Marginal Distributions

## Description

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

## Usage

 `1` ```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 can take k_i values, the i-th element of `marginal` will contain k_i-1 probabilities (the k_i-th is obviously 1 and shall not be included). `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` is the vector containing 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 of the discretized variables

## Author(s)

Alessandro Barbiero, Pier Alda Ferrari

`ordcont`, `ordsample`, `corrcheck`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```# 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(0.5,4,4) 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] <- -0.15 Sigma[2,1] <- Sigma[1,2] Sigma # checking whether Sigma is still positive definite eigen(Sigma)\$values # all >0, OK contord(marginal, Sigma) ```

### Example output

```Loading required package: mvtnorm
[,1]      [,2]      [,3]      [,4]
[1,] 1.0000000 0.3638969 0.3758811 0.3569778
[2,] 0.3638969 1.0000000 0.4197643 0.4004595
[3,] 0.3758811 0.4197643 1.0000000 0.4198205
[4,] 0.3569778 0.4004595 0.4198205 1.0000000
[,1]  [,2] [,3] [,4]
[1,]  1.00 -0.15  0.5  0.5
[2,] -0.15  1.00  0.5  0.5
[3,]  0.50  0.50  1.0  0.5
[4,]  0.50  0.50  0.5  1.0
 2.226487 1.150000 0.500000 0.123513
[,1]       [,2]      [,3]      [,4]
[1,]  1.0000000 -0.1046097 0.3758811 0.3569778
[2,] -0.1046097  1.0000000 0.4197643 0.4004595
[3,]  0.3758811  0.4197643 1.0000000 0.4198205
[4,]  0.3569778  0.4004595 0.4198205 1.0000000
```

GenOrd documentation built on May 2, 2019, 8:16 a.m.