# Calculation of Intermediate Correlation Matrix This function calculates an intermediate correlation matrix for Poisson, ordinal, and continuous random variables, with specified target correlations and marginal properties. ```r 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. ## Returns 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 ```r 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) ```

MVN.corr function