rFactorTree {FactorCopula}

Simulation of 1- and 2-factor tree copula models for item response data

Description

Simulating item response data from the 1- and 2-factor tree copula models.

Usage

r1factortree(n, d, A, copname1, copnametree, theta1, delta,K)
r2factortree(n, d, A, copname1, copname2, copnametree,theta1, theta2, delta,K)

Arguments

n

Sample size.

d

Number of observed variables/items.

A

d \times d vine array with 1,...,d on diagonal, note only the first row and diagnoal values are used for the 1-truncated vine model

theta1

copula parameter vector of size d for items with the first factor.

theta2

copula parameter vector of size d for items with the second factor.

delta

copula parameter vector of size d-1 for the 1-truncated vine tree (conditional dependence).

copname1

A name of a bivariate copula that link each of the oberved variabels with the first factor (note only a single copula family for all items with the 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.

copname2

A name of a bivariate copula that link each of the oberved variabels with the second factor (note only a single copula family for all items with the 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.

copnametree

A name of a bivariate copula that link each of the oberved variabels with one another given the factors in the 1-truncated vine (note only a single copula family for all tree). 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.

K

Number of categories for the observed variables/items.

Value

Data matrix of dimension n \times d, where n is the sample size, and d is the total number of observed variables/items.

Author(s)

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

References

Joe, H. (2014). Dependence Modelling with Copulas. Chapman & Hall, London.

Kadhem, S.H. and Nikoloulopoulos, A.K. (2022b) Factor tree copula models for item response data. Arxiv e-prints, <arXiv: 2201.00339>. https://arxiv.org/abs/2201.00339.

Examples

# ---------------------------------------------------
# ---------------------------------------------------
#Sample size
n = 500

#Ordinal Variables  ---------------------------------
d = 5

#Categories for ordinal  ----------------------------
K = 5
# ---------------------------------------------------
#              1-2-factor tree copula model
# ---------------------------------------------------
#Copula parameters
theta1 = rep(3, d)
theta2 = rep(2, d)
delta = rep(1.5, d-1)

#Copula names
copulaname_1f = "gum"
copulaname_2f = "gum"
copulaname_vine = "gum"

#vine array
#Dvine
d=5
A=matrix(0,d,d)
A[1,]=c(1,c(1:(d-1)))
diag(A)=1:d



#----------------- Simulating data ------------------
#1-factor tree copula
data_1ft = r1factortree(n, d, A, copulaname_1f, copulaname_vine, 
theta1, delta,K)
#2-factor tree copula
data_2ft = r2factortree(n, d, A, copulaname_1f, copulaname_2f, 
copulaname_vine, theta1,theta2, delta,K)