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Last data update: 2014.03.03

R: Finds intermediate correlation matrix

find.cor.mat.star

R Documentation

Finds intermediate correlation matrix

Description

This function calculates an intermediate correlation matrix for a chosen number of Poisson, binary, ordinal, and continuous (via Fleishman polynomials) random variables, with specified target correlations and marginal properties.

The correlation matrix follows the order of Poisson, binary, ordinal, continuous.

Usage

find.cor.mat.star(cor.mat, no.pois = 0, no.bin = 0, no.ord = 0, 
    no.nonn = 0, pois.list = list(), bin.list = list(), ord.list = list(), 
    is.ord.list.cum = FALSE, nonn.list = list())

Arguments

`cor.mat`	The desired target correlation matrix.
`no.pois`	The number of Poisson random variables desired. Defaults to 0.
`no.bin`	The number of binary random variables desired. Defaults to 0.
`no.ord`	The number of ordinal random variables desired. Defaults to 0.
`no.nonn`	The number of continuous random variables desired, created using Fleishman polynomials. Defaults to 0.
`pois.list`	A list of the lambda values, which must be greater than 0. Length will be equal to no.pois, or an error will be thrown. Defaults to an empty list.
`bin.list`	A list of vectors containing the probabilities for each variable. Each vector should have 2 entries between 0 and 1 inclusive, and sum to 1. Length must be equal to no.bin. Defaults to an empty list.
`ord.list`	A list of vectors containing the probabilities for each variable. If is.ord.list.cum is TRUE, each vector should have entries between 0 and 1, in increasing order. Otherwise, each vector should have entries between 0 and 1 inclusive that sum to 1. Length must be equal to no.ord. Defaults to an empty list.
`is.ord.list.cum`	Flag for whether the ordinal list supplied contains cumulative probabilities. Defaults to FALSE.
`nonn.list`	A list of vectors containing the first four moments of each variable, in order. If only two parameters are supplied, they will be assumed to be skew and excess kurtosis, with mean = 0 and variance = 1. If only three parameters are supplied, they will be assumed to be variance, skew and excess kurtosis, with mean = 0. If less than two parameters or more than four parameters are supplied for any variable, an error will be raised. Variance must be positive, and excess kurtosis must be greater than or equal to skew^2-2. Length must be equal to no.nonn. Defaults to an empty list.

Details

First, the target correlation matrix and input parameters are checked using validate.cor.mat.

Second, the input lists are transformed and combined.

Third, each entry is tranformed in order.

Poisson-Poisson entries follow Amatya and Demirtas (2016).
Ordinal/Binary-Ordinal/Binary entries are transformed using a call to ordcont in GenOrd package.
Continuous-Continuous entries use the correlation matrix for the underlying Fleishman polynomials.
All mixed entries use the approximation from Demirtas and Hedeker 2016: corr(X, Z) = cor(X, Y) * cor(Y, Z) where Y is a standard normal variable. In other words, the association between X and Z is assumed to be fully explained by the association between X and Y and the association between Y and Z.

Fourth, the resulting matrix is checked for validity. If it is not a valid correlation matrix, a warning message is printed and the nearest valid matrix is returned instead. (nearPD from Matrix)

Value

A (no.pois+no.bin+no.ord+no.nonn) by (no.pois+no.bin+no.ord+no.nonn) square matrix, containing the intermediate correlation values.

References

Amatya, A. & Demirtas, H. (2015) Simultaneous generation of multivariate mixed data with Poisson and normal marginals. Journal of Statistical Computation and Simulation 85:15, 3129–3139.

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

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

Demirtas, H. (2014). Joint generation of binary and nonnormal continuous data. Journal of Biometrics and Biostatistics 5:3:1000199, 1–9.

Demirtas, H. & Hedeker, D. (2016). Computing the point-biserial correlation under any underlying continuous distribution. Forthcoming in Communications in Statistics– Simulation and Computation.

Examples

validate.cor.mat(cor.mat = .3 * diag(3) + .7, no.pois = 3, 
    pois.list = list(.25, .5, 1))
find.cor.mat.star(cor.mat = .3 * diag(3) + .7, no.pois = 3, 
    pois.list = list(.25, .5, 1))

validate.cor.mat(cor.mat = .8 * diag(3) + .2, no.ord = 3, 
    ord.list = list(c(.2, .8), c(.1, .2, .3, .4), c(.8, 0, .1, .1)))
find.cor.mat.star(cor.mat = .8 * diag(3) + .2, no.ord = 3, 
    ord.list = list(c(.2, .8), c(.1, .2, .3, .4), c(.8, 0, .1, .1)))

validate.cor.mat(cor.mat = .5 * diag(3) + .5, no.pois = 1, no.nonn = 1,
    no.ord = 1, pois.list = list(.5), ord.list = list(c(.8, 0, .1, .1)),
    nonn.list = list(c(0, 1, 0, 1)))
find.cor.mat.star(cor.mat = .5 * diag(3) + .5, no.pois = 1, no.nonn = 1,
    no.ord = 1, pois.list = list(.5), ord.list = list(c(.8, 0, .1, .1)),
    nonn.list = list(c(0, 1, 0, 1)))

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(PoisBinOrdNonNor)
Loading required package: Matrix
Loading required package: corpcor
Loading required package: MASS
Loading required package: GenOrd
Loading required package: mvtnorm
Loading required package: BB
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/PoisBinOrdNonNor/find.cor.mat.star.Rd_%03d_medium.png", width=480, height=480)
> ### Name: find.cor.mat.star
> ### Title: Finds intermediate correlation matrix
> ### Aliases: find.cor.mat.star
> 
> ### ** Examples
> 
> validate.cor.mat(cor.mat = .3 * diag(3) + .7, no.pois = 3, 
+     pois.list = list(.25, .5, 1))
[1] TRUE
> find.cor.mat.star(cor.mat = .3 * diag(3) + .7, no.pois = 3, 
+     pois.list = list(.25, .5, 1))
          [,1]      [,2]      [,3]
[1,] 1.0000000 0.9113454 0.8776507
[2,] 0.9113454 1.0000000 0.8214920
[3,] 0.8776507 0.8214920 1.0000000
> 
> validate.cor.mat(cor.mat = .8 * diag(3) + .2, no.ord = 3, 
+     ord.list = list(c(.2, .8), c(.1, .2, .3, .4), c(.8, 0, .1, .1)))
[1] TRUE
> find.cor.mat.star(cor.mat = .8 * diag(3) + .2, no.ord = 3, 
+     ord.list = list(c(.2, .8), c(.1, .2, .3, .4), c(.8, 0, .1, .1)))
          [,1]      [,2]      [,3]
[1,] 1.0000000 0.3001883 0.5139426
[2,] 0.3001883 1.0000000 0.3235655
[3,] 0.5139426 0.3235655 1.0000000
> 
> validate.cor.mat(cor.mat = .5 * diag(3) + .5, no.pois = 1, no.nonn = 1,
+     no.ord = 1, pois.list = list(.5), ord.list = list(c(.8, 0, .1, .1)),
+     nonn.list = list(c(0, 1, 0, 1)))
[1] TRUE
> find.cor.mat.star(cor.mat = .5 * diag(3) + .5, no.pois = 1, no.nonn = 1,
+     no.ord = 1, pois.list = list(.5), ord.list = list(c(.8, 0, .1, .1)),
+     nonn.list = list(c(0, 1, 0, 1)))
          [,1]      [,2]      [,3]
[1,] 1.0000000 0.8353501 0.5985016
[2,] 0.8353501 1.0000000 0.6940252
[3,] 0.5985016 0.6940252 1.0000000
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>