Select.Factor {FactorCopula}

Model selection of the factor copula models for mixed data

Description

A heuristic algorithm that automatically selects the bivariate parametric copula families that link the observed to the latent variables.

Usage

select1F(continuous, ordinal, count, copnamesF1, gl)
select2F(continuous, ordinal, count, copnamesF1, copnamesF2, gl)

Arguments

continuous

n \times d_1 matrix with the continuous reponse data, where n and d_1 is the number of observations and continous variables, respectively.

ordinal

n \times d_2 matrix with the ordinal reponse data, where n and d_2 is the number of observations and ordinal variables, respectively.

count

n \times d_3 matrix with the count reponse data, where n and d_3 is the number of observations and count variables, respectively.

copnamesF1

A vector with the names of possible candidates 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.

copnamesF2

A list with the names of possible candidates of bivariate copulas that link the each of the oberved variabels with the 1st and 2nd factors. 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.

gl

Gauss legendre quardrature nodes and weights.

Details

The linking copulas at each factor are selected with a sequential algorithm under the initial assumption that linking copulas are Frank, and then sequentially copulas with non-tail quadrant independence are assigned to any of pairs where necessary to account for tail asymmetry (discrete data) or tail dependence (continuous data).

Value

A list containing the following components:

``1st factor''

The selected bivariate linking copulas for the 1st factor.

``2nd factor''

The selected bivariate linking copulas for the 2nd factor.

AIC

Akaike information criterion.

taus

The estimated copula parameters in Kendall's tau scale.

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

#------------------------------------------------
#                   Estimation
#------------------             -----------------
# Setting quadreture points
nq<-25  
gl<-gauss.quad.prob(nq) 
#------------------------------------------------
#                     PE Data
#------------------             -----------------
data(PE)
continuous.PE1 = -PE[,1]
continuous.PE <- cbind(continuous.PE1, PE[,2])
categorical.PE <- PE[, 3:5]

#------------------ One-factor  -----------------
# listing the possible copula candidates:
d <- ncol(PE)
copulasF1 <- rep(list(c("bvn", "bvt3", "bvt5", "frk", "gum", 
"rgum", "rjoe","joe", "1rjoe","2rjoe", "1rgum","2rgum")), d)
out1F.PE <- select1F(continuous.PE, categorical.PE, 
count=NULL, copulasF1, gl)