MVN.corr {MultiVarMI}

Calculation of Intermediate Correlation Matrix

Description

This function calculates an intermediate correlation matrix for Poisson, ordinal, and continuous random variables, with specified target correlations and marginal properties.

Usage

MVN.corr(indat, var.types, ord.mps=NULL, nct.sum=NULL, count.rate=NULL)

Arguments

indat

A data frame containing multivariate data. Continuous variables should be standardized.

var.types

The variable type corresponding to each column in dat, taking values of "NCT" for continuous data, "O" for ordinal or binary data, or "C" for count data.

ord.mps

A list containing marginal probabilities for binary and ordinal variables as packaged from output in ordmps. Default is NULL.

nct.sum

A matrix containing summary statistics for continuous variables as packaged from output in nctsum. Default is NULL.

count.rate

A vector containing rates for count variables as packaged from output in countrate. Default is NULL.

Value

The intermediate correlation matrix.

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.

Demirtas, H. (2016). A note on the relationship between the phi coefficient and the tetrachoric correlation under nonnormal underlying distributions. The American Statistician, 70(2), 143-148.

Demirtas, H. and Hedeker, D. (2016). Computing the point-biserial correlation under any underlying continuous distribution. Communications in Statistics-Simulation and Computation, 45(8), 2744-2751.

Demirtas, H., Ahmadian, R., Atis, S., Can, F.E., and Ercan, I. (2016). A nonnormal look at polychoric correlations: modeling the change in correlations before and after discretization. Computational Statistics, 31(4), 1385-1401.

Ferrari, P.A. and Barbiero, A. (2012). Simulating ordinal data. Multivariate Behavioral Research, 47(4), 566-589.

Fleishman A.I. (1978). A method for simulating non-normal distributions. Psychometrika, 43(4), 521-532.

Vale, C.D. and Maurelli, V.A. (1983). Simulating multivariate nonnormal distributions. Psychometrika, 48(3), 465-471.

See Also

MI, MVN.dat, ordmps, nctsum, countrate

Examples

library(PoisBinOrdNonNor)
n<-1e4
lambdas<-list(1, 3)
mps<-list(c(.2, .8), c(.6, 0, .3, .1))
moms<-list(c(-1, 1, 0, 1), c(0, 3, 0, 2))
  
#generate Poisson, ordinal, and continuous data
cmat.star <- find.cor.mat.star(cor.mat = .8 * diag(6) + .2, 
                               no.pois = length(lambdas), 
                               no.ord = length(mps),
                               no.nonn = length(moms), 
                               pois.list = lambdas, 
                               ord.list = mps, 
                               nonn.list = moms)

mydata <- genPBONN(n, 
                   no.pois = length(lambdas), 
                   no.ord = length(mps), 
                   no.nonn = length(moms),
                   cmat.star = cmat.star, 
                   pois.list = lambdas,
                   ord.list = mps, 
                   nonn.list = moms)

#set a sample of each variable to missing
mydata<-apply(mydata, 2, function(x) {
  x[sample(1:n, size=n/10)]<-NA
  return(x)
})

mydata<-data.frame(mydata)

#get information for use in function
ord.info<-ordmps(ord.dat=mydata[,c('X3', 'X4')])
nct.info<-nctsum(nct.dat=mydata[,c('X5', 'X6')])
count.info<-countrate(count.dat=mydata[,c('X1', 'X2')])

#extract marginal probabilites, continuous properties, and count rates
mps<-sapply(ord.info, "[[", 2)
nctsum<-sapply(nct.info, "[[", 2)
rates<-sapply(count.info, "[[", 2)

#replace continuous with standardized forms
mydata[,c('X5', 'X6')]<-sapply(nct.info, "[[", 1)[,c('X5', 'X6')] 

var.types<-c('C', 'C', 'O', 'O', 'NCT', 'NCT')
mvn.cmat<-MVN.corr(indat=mydata,
                   var.types=var.types,
                   ord.mps=mps,
                   nct.sum=nctsum,
                   count.rate=rates)