# correlation.limits: Computes lower and upper correlation bounds for each pair of... In PoisBinOrd: Data Generation with Poisson, Binary and Ordinal Components

## Description

This function computes lower and upper limits for pairwise correlations of Poisson-Poisson, Poisson-binary, Poisson-ordinal, binary-binary, binary-ordinal, and ordinal-ordinal combinations.

## Usage

 ```1 2``` ```correlation.limits(n.P, n.B, n.O, lambda.vec = NULL, prop.vec = NULL, prop.list = NULL) ```

## Arguments

 `n.P` Number of Poisson variables. `n.B` Number of binary variables. `n.O` Number of ordinal variables. `lambda.vec` Rate vector for Poisson variables `prop.vec` Probability vector for binary variables. `prop.list` A list of probability vectors for ordinal variables.

## Details

While the function computes the exact lower and upper bounds for pairwise correlations among binary-binary variables as formulated in Demirtas et al. (2012), it computes approximate lower and upper bounds for pairwise correlations among Poisson-Poisson, Poisson-binary, Poisson-ordinal, binary-ordinal, and ordinal-ordinal variables through the method suggested by Demirtas and Hedeker (2011).

## Value

The function returns a matrix of size (n.P + n.B + n.O)*(n.P + n.B + n.O), where the lower triangular part of the matrix contains the lower bounds and the upper triangular part of the matrix contains the upper bounds of the feasible correlations.

## References

Demirtas, H. and Hedeker, D. (2011). A practical way for computing approximate lower and upper correlation bounds. The American Statistician, 65(2), 104-109.

Demirtas, H., Hedeker, D., and Mermelstein, R.J. (2012). Simulation of massive public health data by power polynomials. Statistics in Medicine, 31(27), 3337-3346.

`validation.corr`, `correlation.bound.check`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40``` ```## Not run: n.P<-3 n.B<-2 n.O<-3 lambda.vec<-c(1,2,3) prop.vec<-c(0.3,0.5) prop.list<-list(c(0.3,0.6),c(0.25,0.5,0.75),c(0.1,0.2,0.8,0.9)) #Correlation limits among Poisson variables correlation.limits(n.P,n.B=0,n.O=0,lambda.vec,prop.vec=NULL,prop.list=NULL) #See also Cor.PP.Limit in R package PoisNor #Correlation limits among binary variables correlation.limits(n.P=0,n.B,n.O=0,lambda.vec=NULL,prop.vec,prop.list=NULL) #See also correlation.limits in R package BinNonNor #Correlation limits among ordinal variables correlation.limits(n.P=0,n.B=0,n.O,lambda.vec=NULL,prop.vec=NULL,prop.list) #See also Limit_forOO in R package OrdNor #Correlation limits among Poisson and binary variables and within themselves. correlation.limits(n.P,n.B,n.O=0,lambda.vec,prop.vec,prop.list=NULL) #Correlation limits among Poisson and ordinal variables and within themselves. correlation.limits(n.P,n.B=0,n.O,lambda.vec,prop.vec=NULL,prop.list) #Correlation limits among binary and ordinal variables and within themselves. correlation.limits(n.P=0,n.B,n.O,lambda.vec=NULL,prop.vec,prop.list) #Correlation limits among Poisson, binary, and ordinal variables and within themselves. correlation.limits(n.P,n.B,n.O,lambda.vec,prop.vec,prop.list) n.P<-2 lambda.vec=c(-1,1) correlation.limits(n.P,n.B=0,n.O=0,lambda.vec,prop.vec=NULL,prop.list=NULL) ## End(Not run) ```