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-ordinal, binary-binary, binary-ordinal, and ordinal-ordinal combinations.

Usage

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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.

See Also

validation.corr, correlation.bound.check

Examples

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## 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)