PoisBinOrdNonNor (version 1.5.3)

genPBONN: Engine (generation) function for the PoisBinOrdNonNor package

Description

This function generates a chosen number of Poisson, binary, ordinal, and continuous (via Fleishman polynomials) random variables, with specified correlations and marginal properties. The correlation matrix and the generated data follow the order of Poisson, binary, ordinal and continuous.

Usage

genPBONN(n, cmat.star, 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

n

The number of rows in the generated data matrix.

cmat.star

The intermediate 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. Each vector should have entries between 0 and 1 inclusive, and 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.

Value

A n by (no.pois+no.bin+no.ord+no.nonn) matrix. Each column corresponds to a variable, and each row is one random sample.

Details

After transformation and checking of parameters, a n by (no.pois+no.bin+no.ord+no.nonn) matrix of standard normal random data is generated, using cmat.star as the correlation matrix.

Then for each variable, the appropriate transformation is applied to each column of the data generated.

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

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

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

Examples

# NOT RUN {
cmat.star <- find.cor.mat.star(cor.mat = .8 * diag(8) + .2, no.pois = 2, no.ord = 4, 
    no.nonn = 2, pois.list = list(1, 2), ord.list = list(c(.2, .8), c(.5, .5),
    c(.1, .2, .3, .4), c(.8, 0, .1, .1)), nonn.list = list(c(-1, 1, 0, 1), c(0, 3, 0, 2)))
mydata <- genPBONN(1000, no.pois = 2, no.ord = 4, no.nonn = 2, 
    cmat.star = cmat.star, pois.list = list(1, 2), 
    ord.list = list(c(.2, .8), c(.5, .5),c(.1, .2, .3, .4),
    c(.8, 0, .1, .1)), nonn.list = list(c(-1, 1, 0, 1), c(0, 3, 0, 2)))

apply(mydata, 2, mean)
apply(mydata, 2, var)
library(moments)
apply(mydata, 2, skewness)
apply(mydata, 2, kurtosis) - 3
lapply(apply(mydata[, 1:6], 2, table), prop.table)
cor(mydata)
# }