quadVineCopulaREMADA {CopulaREMADA} | R Documentation |
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 |
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)