vine.vuong {CopulaREMADA}

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

Description

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

Usage

vine.vuong.beta(qcondcop12,qcondcop13,qcondcop23,
tau2par12,tau2par13,tau2par23,param1,param2,TP,FN,FP,TN,gl,mgrid,NEP,NEN)
vine.vuong.norm(qcondcop12,qcondcop13,qcondcop23,
tau2par12,tau2par13,tau2par23,param1,param2,TP,FN,FP,TN,gl,mgrid,NEP,NEN) 
tvine.vuong.beta(qcondcop12,qcondcop13,
tau2par12,tau2par13,param1,param2,TP,FN,FP,TN,gl,mgrid,NEP,NEN)
tvine.vuong.norm(qcondcop12,qcondcop13,
tau2par12,tau2par13,param1,param2,TP,FN,FP,TN,gl,mgrid,NEP,NEN) 
tvine2.vuong.beta(qcondcop12,qcondcop13,
tau2par12,tau2par13,param1,param2,TP,FN,FP,TN,gl,mgrid,NEP,NEN)
tvine2.vuong.norm(qcondcop12,qcondcop13,
tau2par12,tau2par13,param1,param2,TP,FN,FP,TN,gl,mgrid,NEP,NEN) 

Arguments

qcondcop12

function for the inverse of conditional copula cdf at the (1,2) bivariate margin for Model 2

qcondcop13

function for the inverse of conditional copula cdf at the (1,3) bivariate margin for Model 2

qcondcop23

function for the inverse of conditional copula cdf at the (2,3|1) bivariate margin for Model 2

tau2par12

function for maping Kendall's tau at the (1,2) bivariate margin to copula parameter for Model 2

tau2par13

function for maping Kendall's tau at the (1,3) bivariate margin to copula parameter for Model 2

tau2par23

function for maping Kendall's tau at the (2,3|1) bivariate margin to the conditional 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 three-dimensional arrays. For more details see meshgrid

NEP

the number of non-evaluable positives in the presence of non-evaluable subjects

NEN

the number of non-evaluable negatives in the presence of non-evaluable subjects

Value

A list containing the following components:

z

the test statistic

p-value

the p-value

References

Nikoloulopoulos, A.K. (2017) A vine copula mixed effect model for trivariate meta-analysis of diagnostic test accuracy studies accounting for disease prevalence. Statistical Methods in Medical Research, 26, 2270–2286. doi:10.1177/0962280215596769.

Nikoloulopoulos, A.K. (2020) An extended trivariate vine copula mixed model for meta-analysis of diagnostic studies in the presence of non-evaluable outcomes. The International Journal of Biostatistics, 16(2). doi:10.1515/ijb-2019-0107.

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,gl$n,nargout=3)

data(betaDG)
attach(betaDG)
#nest.n2=VineCopulaREMADA.norm(TP,FN,FP,TN,gl,mgrid,
#qcondbvn,qcondbvn,qcondbvn,
#tau2par.bvn,tau2par.bvn,tau2par.bvn)
nest.n2.est= #nest.n2$e
c(0.87186926,  0.13696066,  0.70614956,  0.69152133,  
0.51780203,  0.70883558, -0.41354870,0.07701287, -0.12111253)
#c090est.b2=VineCopulaREMADA.beta(TP,FN,FP,TN,gl,mgrid,
#qcondcln90,qcondcln,qcondcln90,tau2par.cln90,tau2par.cln,tau2par.cln90)
c090est.b2.est= #c090est.b2$e
c(0.85528463,  0.14667571,  0.68321231,  0.04897466,
0.02776290,  0.08561436, -0.34639172, 0.04621924, -0.21627977)
c090vuong.b2=vine.vuong.beta(qcondcln90,qcondcln,qcondcln90,
tau2par.cln90,tau2par.cln,tau2par.cln90,
nest.n2.est,c090est.b2.est,TP,FN,FP,TN,gl,mgrid)
c090vuong.b2
detach(betaDG)