rfactor {FactorCopula}

Simulation of factor copula models for mixed continuous and discrete data

Description

Simulating standard uniform and ordinal response data from factor copula models.

Usage

r1factor(n, d1, d2, categ, theta, copF1)
r2factor(n, d1, d2, categ, theta, delta, copF1, copF2)

Arguments

n

Sample size.

d1

Number of standard uniform variables.

d2

Number of ordinal variables.

categ

A vector of categories for the ordinal variables.

theta

Copula parameters for the 1st factor.

delta

Copula parameters for the 2nd factor.

copF1

(d_1+d_2)-vector with the names of bivariate copulas that link the each of the oberved variabels with the 1st factor. Choices are “bvn” for BVN, “bvt\nu” with \nu = \{1, \ldots, 9\} degrees of freedom for t-copula, “frk” for Frank, “gum” for Gumbel, “rgum” for reflected Gumbel, “1rgum” for 1-reflected Gumbel, “2rgum” for 2-reflected Gumbel, “joe” for Joe, “rjoe” for reflected Joe, “1rjoe” for 1-reflected Joe, “2rjoe” for 2-reflected Joe, “BB1” for BB1, “rBB1” for reflected BB1, “BB7” for BB7, “rBB7” for reflected BB7, “BB8” for BB8, “rBB8” for reflected BB8, “BB10” for BB10, “rBB10” for reflected BB10.

copF2

(d_1+d_2)-vector with the names of bivariate copulas that link the each of the oberved variabels with the 2nd factor. Choices are “bvn” for BVN, “bvt[\nu]” with \nu = \{1, \ldots, 9\} degrees of freedom for t-copula, “frk” for Frank, “gum” for Gumbel, “rgum” for reflected Gumbel, “1rgum” for 1-reflected Gumbel, “2rgum” for 2-reflected Gumbel, “joe” for Joe, “rjoe” for reflected Joe, “1rjoe” for 1-reflected Joe, “2rjoe” for 2-reflected Joe, “BB1” for BB1, “rBB1” for reflected BB1, “BB7” for BB7, “rBB7” for reflected BB7, “BB8” for BB8, “rBB8” for reflected BB8, “BB10” for BB10, “rBB10” for reflected BB10.

Value

Data matrix of dimension n\times d, where n is the sample size, and d=d_1+d_2 is the total number of variables.

Author(s)

Sayed H. Kadhem [e-mail]
Aristidis K. Nikoloulopoulos [e-mail]

References

Kadhem, S.H. and Nikoloulopoulos, A.K. (2021) Factor copula models for mixed data. British Journal of Mathematical and Statistical Psychology, 74, 365–403. doi:10.1111/bmsp.12231.

Examples

# ---------------------------------------------------
# ---------------------------------------------------
#              One-factor copula model
# ---------------------------------------------------
# ---------------------------------------------------
#Sample size ----------------------------------------
n = 100

#Continuous Variables  ------------------------------
d1 = 5

#Ordinal Variables  ---------------------------------
d2 = 3

#Categories for ordinal  ----------------------------
categ = c(3,4,5)

#Copula parameters  ---------------------------------
theta = rep(2, d1+d2)

#Copula names  --------------------------------------
copnamesF1 = rep("gum", d1+d2)

#----------------- Simulating data ------------------
datF1 = r1factor(n, d1=d1, d2=d2, categ, theta, copnamesF1)

#------------  Plotting continuous data -------------
pairs(qnorm(datF1[, 1:d1]))

# ---------------------------------------------------
# ---------------------------------------------------
#              Two-factor copula model
# ---------------------------------------------------
# ---------------------------------------------------
#Sample size ----------------------------------------
n = 100

#Continuous Variables  ------------------------------
d1 = 5

#Ordinal Variables  ---------------------------------
d2 = 3

#Categories for ordinal  ----------------------------
categ = c(3,4,5)

#Copula parameters  ---------------------------------
theta = rep(2.5, d1+d2)
delta = rep(1.5, d1+d2)

#Copula names  --------------------------------------
copnamesF1 = rep("gum", d1+d2)
copnamesF2 = rep("gum", d1+d2)

#----------------- Simulating data ------------------
datF2 = r2factor(n, d1=d1, d2=d2, categ, theta, delta, 
                copnamesF1, copnamesF2)

#-----------------  Plotting  data ------------------
pairs(qnorm(datF2[,1:d1]))