Vuong: Vuong's test for the comparison of non-nested copula mixed...

In CopulaREMADA: Copula Mixed Models for Multivariate Meta-Analysis of Diagnostic Test Accuracy Studies

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

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. \Sexpr[results=rd]{tools:::Rd_expr_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)

CopulaREMADA documentation built on Oct. 18, 2024, 1:08 a.m.