FactorCopula (version 0.9.3)

rFactorTree: 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)

Value

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

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.

Author

Sayed H. Kadhem
Aristidis K. Nikoloulopoulos

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)