# Computes lower and upper correlation bounds for each pair of variables

### Description

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

### Usage

1 2 | ```
correlation.limits(n.P, n.B, n.C, lambda.vec = NULL, prop.vec = NULL,
coef.mat = NULL)
``` |

### Arguments

`n.P` |
Number of Poisson variables. |

`n.B` |
Number of binary variables. |

`n.C` |
Number of continuous variables. |

`lambda.vec` |
Rate vector for Poisson variables. |

`prop.vec` |
Proportion vector for binary variables. |

`coef.mat` |
Matrix of coefficients produced from |

### 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-continuous, binary-continuous, and continuous-continuous variables through the method suggested by Demirtas and Hedeker (2011).

### Value

The function returns a matrix of size (n.P + n.B + n.C)*(n.P + n.B + n.C), 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.

### See Also

`validation.corr`

, `correlation.bound.check`

### Examples

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 41 42 43 | ```
## Not run:
n.P<-3
n.B<-2
n.C<-3
lambda.vec<-c(1,2,3)
prop.vec<-c(0.3,0.5)
coef.mat<-matrix(c(
-0.3137491, 0.0000000, 0.1004464,
0.8263239, 1.0857433, 1.1050196,
0.3137491, 0.0000000, -0.1004464,
0.0227066, -0.0294495, -0.0400078),4,3,byrow=F)
#Correlation limits among Poisson variables
correlation.limits(n.P,n.B=0,n.C=0,lambda.vec,prop.vec=NULL,coef.mat=NULL)
#See also Cor.PP.Limit in R package PoisNor
#Correlation limits among binary variables
correlation.limits(n.P=0,n.B,n.C=0,lambda.vec=NULL,prop.vec,coef.mat=NULL)
#See also correlation.limits in R package BinNonNor
#Correlation limits among continuous variables
correlation.limits(n.P=0,n.B=0,n.C,lambda.vec=NULL,prop.vec=NULL,coef.mat)
#Correlation limits among Poisson and binary variables and within themselves.
correlation.limits(n.P,n.B,n.C=0,lambda.vec,prop.vec,coef.mat=NULL)
#Correlation limits among Poisson and continuous variables and within themselves.
correlation.limits(n.P,n.B=0,n.C,lambda.vec,prop.vec=NULL,coef.mat)
#Correlation limits among binary and continuous variables and within themselves.
correlation.limits(n.P=0,n.B,n.C,lambda.vec=NULL,prop.vec,coef.mat)
#Correlation limits among Poisson, binary, and continuous variables and within themselves.
correlation.limits(n.P,n.B,n.C,lambda.vec,prop.vec,coef.mat)
n.P<-2
lambda.vec=c(-1,1)
correlation.limits(n.P,n.B=0,n.C=0,lambda.vec,prop.vec=NULL,coef.mat=NULL)
## End(Not run)
``` |