Computes lower and upper correlation bounds for each pair of variables

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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

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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 fleishman.coef.

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

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## 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)