mutinomVineCopulaREMADA: Maximum likelhood estimation for multinomial quadrivariate...

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

Maximum likelhood estimation for multinomial quadrivariate (truncated) D-vine copula mixed models for diagnostic test accurracy studies accounting for non-evaluable outcomes

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

multinomVineCopulaREMADA.norm(TP,FN,FP,TN,NEP,NEN,
                                 gl,mgrid,qcond1,pcond1,tau2par1,
                                 qcond2,pcond2,tau2par2)
multinomVineCopulaREMADA.beta(TP,FN,FP,TN,NEP,NEN,
                                 gl,mgrid,qcond1,pcond1,tau2par1,
                                 qcond2,pcond2,tau2par2)
tmultinomVineCopulaREMADA.norm(TP,FN,FP,TN,NEP,NEN,
                                 gl,mgrid,
                                 qcond1,pcond1,tau2par1,
                                 qcond2,pcond2,tau2par2)
tmultinomVineCopulaREMADA.beta(TP,FN,FP,TN,NEP,NEN,
                                 gl,mgrid,
                                 qcond1,pcond1,tau2par1,
                                 qcond2,pcond2,tau2par2)

Arguments

TP	the number of true positives
FN	the number of false negatives
FP	the number of false positives
TN	the number of true negatives
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
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) and (3,4) bivariate margin
pcond1	function for the conditional copula cdf at the (1,2) and (3,4) bivariate margin
tau2par1	function for maping Kendall's tau at the (1,2) and (3,4) bivariate margin to copula parameter
qcond2	function for the inverse conditional copula cdf at the (2,3) bivariate margin
pcond2	function for the conditional copula cdf at the (2,3) bivariate margin
tau2par2	function for maping Kendall's tau at the (2,3) 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. (2020) A multinomial quadrivariate D-vine copula mixed model for diagnostic studies meta-analysis in the presence of non-evaluable subjects. Statistical Methods in Medical Research, 29 (10), 2988–3005. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/0962280220913898")}.

See Also

rmultinomVineCopulaREMADA

Examples

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

data(MK2016)
attach(MK2016)

out=tmultinomVineCopulaREMADA.beta(TP,FN,FP,TN,NEP,NEN,
gl,mgrid15,qcondcln180,pcondcln180,tau2par.cln180,
qcondcln90,pcondcln90,tau2par.cln90)

detach(MK2016)

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