| Title: | Generation of Multivariate Ordinal Variates |
|---|---|
| Description: | A method for multivariate ordinal data generation given marginal distributions and correlation matrix based on the methodology proposed by Demirtas (2006) <DOI:10.1080/10629360600569246>. |
| Authors: | Anup Amatya, Hakan Demirtas, Ran Gao |
| Maintainer: | Ran Gao <[email protected]> |
| License: | GPL-2 |
| Version: | 2.4.3 |
| Built: | 2025-01-23 02:53:21 UTC |
| Source: | https://github.com/cran/MultiOrd |
A package for multivariate ordinal data generation given marginal distributions and correlation matrix based on the methodology proposed by Demirtas (2006).
| Package: | MultiOrd |
| Type: | Package |
| Version: | 2.4.3 |
| Date: | 2021-03-05 |
| License: | GPL-2 |
This package can be used to generate multivariate ordinal data. Two main input required are the matrix of marginal probabilities of each variable and the correlation matrix of the ordinal variables. Due to the limitation on the magnitude of the binary correlations which depends on the marginal probabilities, off-diagonal entries of ordinal correlation matrix are not free to vary between -1 and 1.
The main function in this package is genOrd which generates the multivariate ordinal data. Another important function is simBinCorr which calculates the intermediate binary correlation.
Anup Amatya, Hakan Demirtas, Ran Gao
Maintainer: Ran Gao <[email protected]>
Demirtas, H. (2006). A method for multivariate ordinal data generation given marginal distributions and correlations. Journal of Statistical Computation and Simulation, Volume 76, Issue 11, 1017-1025.
Emrich, L.J. and Piedmonte, M.R. (1991). A method for generating high-dimensional multivariate binary variates. The American Statistician, Volume 45, Issue 4, 302-304.
Converts multivariate binary data to multivariate ordinal data using original ordinal probabilities.
BinToOrd(prop.vec.bin, ordPmat, Mlocation, bin.data)BinToOrd(prop.vec.bin, ordPmat, Mlocation, bin.data)
prop.vec.bin |
Vector of marginal probabilities. It is usually a first component of the
list returned by |
ordPmat |
Input matrix of ordinal marginal probabilities |
Mlocation |
Vector of locations where dichotomization is done. It is usually a second component of the list
returned by |
bin.data |
Matrix of binary data generated using |
As a part of the multivariate ordinal data generation, intermediate multivariate binary data are generated.
This function converts multivariate binary data generated by generate.binary to the
multivariate ordinal data.
y |
Matrix of multivariate ordinal data |
Corr |
Correlation matrix of |
## Not run: nObs = 1000; no.rows = 100000 ## Not run: ordPmat1 = matrix( c(0.15,0.70,0.40, 0.55,0.10,0.25, 0.25,0.10,0.15, 0.05,0.10,0.20),4,3,byrow=TRUE) ## End(Not run) ## Not run: \ cmat1= matrix( c(1,0.2,0.2, 0.2,1,0.2, 0.2,0.2,1),3,3,byrow=TRUE) ## End(Not run) ## Not run: binObj = simBinCorr(ordPmat1, cmat1, no.rows) ## Not run: ep0 = generate.binary( nObs, binObj$pvec, binObj$del.next) ## Not run: Mydata= BinToOrd(binObj$pvec, ordPmat1, binObj$Mlocation, ep0)## Not run: nObs = 1000; no.rows = 100000 ## Not run: ordPmat1 = matrix( c(0.15,0.70,0.40, 0.55,0.10,0.25, 0.25,0.10,0.15, 0.05,0.10,0.20),4,3,byrow=TRUE) ## End(Not run) ## Not run: \ cmat1= matrix( c(1,0.2,0.2, 0.2,1,0.2, 0.2,0.2,1),3,3,byrow=TRUE) ## End(Not run) ## Not run: binObj = simBinCorr(ordPmat1, cmat1, no.rows) ## Not run: ep0 = generate.binary( nObs, binObj$pvec, binObj$del.next) ## Not run: Mydata= BinToOrd(binObj$pvec, ordPmat1, binObj$Mlocation, ep0)
It computes the tetrachoric correlation matrix using the algorithm described in Emrich and Piedmonte (1991). If the resulting matrix is non-positive definite, a nearest positive definite matrix is returned and the warning message will be printed.
compute.sigma.star(prop.vec.bin, corr.mat)compute.sigma.star(prop.vec.bin, corr.mat)
prop.vec.bin |
Vector of marginal probabilities |
corr.mat |
Correlation matrix of the binary data |
Tetrachoric correlation matrix
Checks whether the dimension of marginal probability matrix matches the dimension of correlation matrix.
conformity.Check(ordPmat, CorrMat)conformity.Check(ordPmat, CorrMat)
ordPmat |
Input matrix of ordinal marginal probabilities |
CorrMat |
Correlation matrix of the multivariate ordinal data. |
Collapses the ordinal categories to binary ones and counts the number of categories in each variable.
find.binary.prob(ordPmat)find.binary.prob(ordPmat)
ordPmat |
Input matrix of ordinal marginal probabilities. |
p |
Vector of binary probabilities |
Mlocation |
Vector of points where ordinal variables will be dichotomized |
## Not run: ordPmat1 = matrix( c(0.15,0.70,0.40, 0.55,0.10,0.25, 0.25,0.10,0.15, 0.05,0.10,0.20),4,3,byrow=TRUE) find.binary.prob(ordPmat1) ## End(Not run)## Not run: ordPmat1 = matrix( c(0.15,0.70,0.40, 0.55,0.10,0.25, 0.25,0.10,0.15, 0.05,0.10,0.20),4,3,byrow=TRUE) find.binary.prob(ordPmat1) ## End(Not run)
Generates multivariate binary data given marginal probabilities and correlation based on the algorithm described in Emrich and Piedmonte (1991).
generate.binary(nObs, prop.vec.bin, corr.mat)generate.binary(nObs, prop.vec.bin, corr.mat)
nObs |
Number of observations |
prop.vec.bin |
Vector of binary marginal probabilities |
corr.mat |
correlation matrix of the binary data |
It generates multivariate binary data from the marginal probabilities and correlation matrix. It uses the algorithm described in Emrich and Piedmonte (1991). In the process, if the tetrachoric correlation matrix is non-positive definite, a nearest positive definite matrix is used.
data |
Matrix of multivariate binary data |
## Not run: ordPmat1 = matrix( c(0.15,0.70,0.40, 0.55,0.10,0.25, 0.25,0.10,0.15, 0.05,0.10,0.20),4,3,byrow=TRUE) ## End(Not run) ## Not run: cmat1= matrix( c(1,0.2,0.2, 0.2,1,0.2, 0.2,0.2,1),3,3,byrow=TRUE) ## End(Not run) ## Not run: p=find.binary.prob(ordPmat1) ## Not run: finalCorr = simBinCorr(ordPmat1, cmat1, no.rows=100000) ## Not run: y=generate.binary( 1000, p$p, finalCorr$del.next)## Not run: ordPmat1 = matrix( c(0.15,0.70,0.40, 0.55,0.10,0.25, 0.25,0.10,0.15, 0.05,0.10,0.20),4,3,byrow=TRUE) ## End(Not run) ## Not run: cmat1= matrix( c(1,0.2,0.2, 0.2,1,0.2, 0.2,0.2,1),3,3,byrow=TRUE) ## End(Not run) ## Not run: p=find.binary.prob(ordPmat1) ## Not run: finalCorr = simBinCorr(ordPmat1, cmat1, no.rows=100000) ## Not run: y=generate.binary( 1000, p$p, finalCorr$del.next)
Generates multivariate ordinal data from the ordinal marginal probabilities and a list returned
by the simBinCorr function.
genOrd(no.rows, ordPmat, binObj)genOrd(no.rows, ordPmat, binObj)
no.rows |
Number of rows |
ordPmat |
Input matrix of ordinal marginal probabilities |
binObj |
A list returned by the |
It generates multivariate ordinal data. The argument binObj must be obtained using simBinCorr before executing this function.
Mydata |
A list with two components. Two components are a matrix of multivariate ordinal data (y) and its correlation matrix (Corr) |
simBinCorr, BinToOrd, generate.binary
## Not run: ordPmat1 = matrix( c(0.15,0.70,0.40, 0.55,0.10,0.25, 0.25,0.10,0.15, 0.05,0.10,0.20),4,3,byrow=TRUE) ## End(Not run) ## Not run: cmat1= matrix( c(1,0.2,0.2, 0.2,1,0.2, 0.2,0.2,1),3,3,byrow=TRUE) ## End(Not run) ## Not run: binObj=simBinCorr(ordPmat1, cmat1, no.rows=100000, steps=0.025) ## Not run: myData = genOrd( 1000, ordPmat1, binObj)## Not run: ordPmat1 = matrix( c(0.15,0.70,0.40, 0.55,0.10,0.25, 0.25,0.10,0.15, 0.05,0.10,0.20),4,3,byrow=TRUE) ## End(Not run) ## Not run: cmat1= matrix( c(1,0.2,0.2, 0.2,1,0.2, 0.2,0.2,1),3,3,byrow=TRUE) ## End(Not run) ## Not run: binObj=simBinCorr(ordPmat1, cmat1, no.rows=100000, steps=0.025) ## Not run: myData = genOrd( 1000, ordPmat1, binObj)
Calculates intermediate binary correlation matrix via simulation.
simBinCorr(ordPmat, CorrMat, no.rows, steps = 0.025)simBinCorr(ordPmat, CorrMat, no.rows, steps = 0.025)
ordPmat |
Input matrix of ordinal marginal probabilities |
CorrMat |
Correlation matrix of the multivariate ordinal data |
no.rows |
Number of rows to use to calculate intermediate binary correlation matrix |
steps |
Fraction of difference between the current and target matrix to be added in each iteration. |
del.next |
Calculated binary correlation matrix |
Mlocation |
Cutoff point for converting ordinal probabilities to binary ones. |
pvec |
Vector of binary probabilities |
## Not run: ordPmat1 = matrix( c(0.15,0.70,0.40, 0.55,0.10,0.25, 0.25,0.10,0.15, 0.05,0.10,0.20),4,3,byrow=TRUE) ## End(Not run) ## Not run: cmat1= matrix( c(1,0.2,0.2, 0.2,1,0.2, 0.2,0.2,1),3,3,byrow=TRUE) ## End(Not run) ## Not run: simBinCorr(ordPmat1, cmat1, no.rows=100000, steps = 0.025)## Not run: ordPmat1 = matrix( c(0.15,0.70,0.40, 0.55,0.10,0.25, 0.25,0.10,0.15, 0.05,0.10,0.20),4,3,byrow=TRUE) ## End(Not run) ## Not run: cmat1= matrix( c(1,0.2,0.2, 0.2,1,0.2, 0.2,0.2,1),3,3,byrow=TRUE) ## End(Not run) ## Not run: simBinCorr(ordPmat1, cmat1, no.rows=100000, steps = 0.025)
Checks symmetry, positive definiteness, conformity and range of the correlation matrix.
validation.CorrMat(prop.vec.bin, CorrMat)validation.CorrMat(prop.vec.bin, CorrMat)
prop.vec.bin |
Vector of binary (converted from ordinal) marginal probabilities |
CorrMat |
Correlation matrix to be validated |
This function checks the correlation matrix for basic properties of correlation matrix, such as symmetry and positive definiteness. In addition it verifies that all the correlations are in valid range for the calculated binary marginal probabilities. Range violation error message indicates that ordinal data with the specified correlations cannot be generated due to distributional constraints.
Validates the range of input matrix of marginal probabilities. It also counts the ordinal categories for each variable.
validation.ordPmat(ordPmat)validation.ordPmat(ordPmat)
ordPmat |
Matrix of marginal probabilities. |
Number of columns of input matrix is the number of variables and each column contains probability of each category within each variable. Any probability with 0 value must be entered at the end of corresponding column. For example if a column contains c(0.3,0.5,0.2,0), then it is assumed that particular variable has only 3 (1, 2 and 3) categories.
J |
Number of ordinal variables |
K |
Vector of number of categories for each variable |
## Not run: # 3 outcomes with 3, 4 and 4 categories. ordPmat1 = matrix( c(0.15,0.70,0.40, 0.55,0.10,0.25, 0.30,0.10,0.15, 0,0.10,0.20),4,3,byrow=TRUE) validation.ordPmat(ordPmat1) ## End(Not run)## Not run: # 3 outcomes with 3, 4 and 4 categories. ordPmat1 = matrix( c(0.15,0.70,0.40, 0.55,0.10,0.25, 0.30,0.10,0.15, 0,0.10,0.20),4,3,byrow=TRUE) validation.ordPmat(ordPmat1) ## End(Not run)