quadVineCopulaREMADA {CopulaREMADA}

Maximum likelihood estimation of quadrivariate D-vine copula mixed models for joint meta-analysis and comparison of two diagnostic tests

Description

The estimated parameters can be obtained by using a quasi-Newton method applied to the logarithm of the joint likelihood. This numerical method requires only the objective function, i.e., the logarithm of the joint likelihood, while the gradients are computed numerically and the Hessian matrix of the second order derivatives is updated in each iteration. The standard errors (SE) of the ML estimates can be also obtained via the gradients and the Hessian computed numerically during the maximization process.

Usage

quadVineCopulaREMADA.norm(TP1,FN1,FP1,TN1,TP2,FN2,FP2,TN2,
                               gl,mgrid,qcond1,pcond1,tau2par1,
                               qcond2,pcond2,tau2par2)
                               
quadVineCopulaREMADA.beta(TP1,FN1,FP1,TN1,TP2,FN2,FP2,TN2,
                               gl,mgrid,qcond1,pcond1,tau2par1,
                               qcond2,pcond2,tau2par2) 
quadVineCopulaREMADA.norm.beta(TP1,FN1,FP1,TN1,TP2,FN2,FP2,TN2,
                               gl,mgrid,qcond1,pcond1,tau2par1,
                               qcond2,pcond2,tau2par2)              

Arguments

TP1

the number of true positives for test 1

FN1

the number of false negatives for test 1

FP1

the number of false positives for test 1

TN1

the number of true negatives for test 1

TP2

the number of true positives for test 2

FN2

the number of false negatives for test 2

FP2

the number of false positives for test 2

TN2

the number of true negatives for test 2

gl

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

mgrid

a list containing 4-dimensional arrays.

qcond1

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

pcond1

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

tau2par1

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

qcond2

function for the inverse conditional copula cdf at the (3,4) bivariate margin

pcond2

function for the conditional copula cdf at the (3,4) bivariate margin

tau2par2

function for maping Kendall's tau at the (3,4) bivariate margin to copula parameter

Value

A list containing the following components:

minimum

the value of the estimated minimum of the negative log-likelihood

estimate

the MLE

gradient

the gradient at the estimated minimum of of the negative log-likelihood

hessian

the hessian at the estimated minimum of the negative log-likelihood

code

an integer indicating why the optimization process terminated

iterations

the number of iterations performed

For more details see nlm

References

Nikoloulopoulos, A.K. (2019) A D-vine copula mixed model for joint meta-analysis and comparison of diagnostic tests. Statistical Methods in Medical Research, 28(10-11):3286–3300. doi:10.1177/0962280218796685.

Examples

nq=15
gl=gauss.quad.prob(nq,"uniform")
data(mgrid15)

data(arthritis)
attach(arthritis)

qcond1=qcondcln270
pcond1=pcondcln270
tau2par1=tau2par.cln270

qcond2=qcondfrk
pcond2=pcondfrk
tau2par2=tau2par.frk

out<-quadVineCopulaREMADA.norm(TP1,FN1,FP1,TN1,TP2,FN2,FP2,TN2,
gl,mgrid15,qcond1,pcond1,tau2par1,qcond2,pcond2,tau2par2)

detach(arthritis)