Vuong.Factor {FactorCopula}

Vuong's test for the comparison of factor copula models

Description

Vuong (1989)'s test for the comparison of non-nested factor copula models for mixed data. We compute the Vuong's test between the factor copula model with BVN copulas (that is the standard factor model) and a competing factor copula model to reveal if the latter provides better fit than the standard factor model.

Usage

vuong.1f(cpar.bvn, cpar, copF1, continuous, ordinal, count, gl, param)
vuong.2f(cpar.bvn, cpar, copF1, copF2, continuous, ordinal, count, gl, param)

Arguments

cpar.bvn

copula parameters of the factor copula model with BVN copulas.

cpar

copula parameters of the competing factor copula model.

copF1

copula names for the first factor of the competing factor copula model.

copF2

copula names for the second factor of the competing factor copula model.

continuous

matrix of continuous data.

ordinal

matrix of ordinal data.

count

matrix of count data.

gl

gauss-legendre quardature points.

param

parameterization of estimated copula parameters. If FALSE, then cpar are the actual copula parameters without any transformation/reparamterization.

Value

A vector containing the following components:

z

the test statistic.

p.value

the p-value.

CI.left

lower/left endpoint of 95% confidence interval.

CI.right

upper/right endpoint of 95% confidence interval.

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.

Vuong, Q.H. (1989). Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica, 57, 307–333.

Examples

#------------------------------------------------
# Setting quadreture points
nq <- 25  
gl <- gauss.quad.prob(nq) 
#------------------------------------------------
#                     PE Data
#------------------             -----------------
data(PE)
continuous.PE1 = -PE[,1]
continuous.PE2 = PE[,2]
continuous.PE <- cbind(continuous.PE1, continuous.PE2)
categorical.PE <- PE[, 3:5]
d <- ncol(PE)
#------------------------------------------------
#                   Estimation
#------------------             -----------------
# factor copula model with BVN copulas
cop1f.PE.bvn <- rep("bvn", d)
PE.bvn1f <- mle1factor(continuous.PE, categorical.PE, 
count=NULL, copF1=cop1f.PE.bvn, gl, hessian = TRUE)

# Selected factor copula model
cop1f.PE <- c("joe", "joe", "rjoe", "joe", "gum")
PE.selected1f <- mle1factor(continuous.PE, categorical.PE, 
count=NULL, copF1=cop1f.PE, gl, hessian = TRUE)
#------------------------------------------------
#                   Vuong's test
#------------------             -----------------
v1f.PE.selected <- vuong.1f(PE.bvn1f$cpar$f1,
PE.selected1f$cpar$f1,cop1f.PE, continuous.PE, 
categorical.PE, count=NULL, gl, param=FALSE)