vuong {CopulaREMADA}

Vuong's test for the comparison of non-nested copula mixed models for diagnostic test accuaracy studies

Description

Vuong (1989)'s test for the comparison of non-nested copula mixed models for diagnostic test accuaracy studies. It shows if a copula mixed model provides better fit than the standard GLMM. We compute the Vuong's test with Model 1 being the copula mixed model with BVN copula and normal margins, i.e., the standard GLMM.

Usage

vuong.norm(qcond,tau2par,param1,param2,TP,FN,FP,TN,gl,mgrid)
vuong.beta(qcond,tau2par,param1,param2,TP,FN,FP,TN,gl,mgrid)
countermonotonicity.vuong(param1,param2,TP,FN,FP,TN,gl,mgrid)  

Arguments

qcond

function for conditional copula cdf for Model 2

tau2par

function for maping Kendall's tau to copula parameter for Model 2

param1

parameters for the Model 1. i.e., the GLMM

param2

parameters for the Model 2

TP

the number of true positives

FN

the number of false negatives

FP

the number of false positives

TN

the number of true negatives

gl

a list containing the components of Gauss-Legendre nodes gl$nodes and weights gl$weights

mgrid

a list containing two matrices with the rows of the output matrix X are copies of the vector gl$nodes; columns of the output matrix Y are copies of the vector gl$nodes. For more details see meshgrid

Value

A list containing the following components:

z

the test statistic

p-value

the p-value

References

Nikoloulopoulos, A.K. (2015) A mixed effect model for bivariate meta-analysis of diagnostic test accuracy studies using a copula representation of the random effects distribution. Statistics in Medicine, 34, 3842–3865. doi:10.1002/sim.6595.

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

See Also

CopulaREMADA

Examples

nq=15
gl=gauss.quad.prob(nq,"uniform")
mgrid<- meshgrid(gl$n,gl$n)

data(MRI)
attach(MRI)
c270est.b=CopulaREMADA.beta(TP,FN,FP,TN,gl,mgrid,qcondcln270,tau2par.cln270)
nest.n=CopulaREMADA.norm(TP,FN,FP,TN,gl,mgrid,qcondbvn,tau2par.bvn)
c90est.n=CopulaREMADA.norm(TP,FN,FP,TN,gl,mgrid,qcondcln90,tau2par.cln90)
vuong.beta(qcondcln270,tau2par.cln270,nest.n$e,c270est.b$e,TP,FN,FP,TN,gl,mgrid)
vuong.norm(qcondcln90,tau2par.cln90,nest.n$e,c90est.n$e,TP,FN,FP,TN,gl,mgrid)
detach(MRI)

data(CT)
attach(CT)
est.n=countermonotonicCopulaREMADA.norm(TP,FN,FP,TN,gl,mgrid)
est.b=countermonotonicCopulaREMADA.beta(TP,FN,FP,TN,gl,mgrid)
countermonotonicity.vuong(est.n$e,est.b$e,TP,FN,FP,TN,gl,mgrid)
detach(CT)