imperfect.trivariateVineCopulaREMADA: Maximum likelihood estimation of trivariate 1-truncated...

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

Maximum likelihood estimation of trivariate 1-truncated D-vine copula mixed models for meta-analysis of diagnostic accuracy studies without a gold standard

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

imperfect.trivariateVineCopulaREMADA.norm.comprehensive(y11,
y10,y01,y00,gl,mgrid,qcond,tau2par,select.random,start)
                               
imperfect.trivariateVineCopulaREMADA.norm(y11,
y10,y01,y00,gl,mgrid,qcond1,tau2par1,qcond2,tau2par2,select.random,start)

imperfect.trivariateVineCopulaREMADA.beta.comprehensive(y11,
y10,y01,y00,gl,mgrid,qcond,tau2par,select.random,start)
                               
imperfect.trivariateVineCopulaREMADA.beta(y11,
y10,y01,y00,gl,mgrid,qcond1,tau2par1,qcond2,tau2par2,select.random,start)

Arguments

y11	the number of the test results where the index test outcome is positive and the reference test outcome is positive
y10	the number of the test results where the index test outcome is positive and the reference test outcome is negative
y01	the number of the test results where the index test outcome is negative and the reference test outcome is positive
y00	the number of the test results where the index test outcome is negative and the reference test outcome is negative
gl	a list containing the components of Gauss-Legendre nodes gl$nodes and weights gl$weights
mgrid	a list containing three-dimensional arrays. Replicates of the quadrature points that produce a 3-dimensional full grid
select.random	vector (t_{1},t_{2},t_3), where 1\leq t_1<t_2<t_3\leq 5, that indicates the random effects
qcond	function for the inverse of conditional copula cdf; choices are qconbvn and qcondfrk
tau2par	function for maping Kendall's tau to copula parameter; choices are tau2par.bvn and tau2par.frk
qcond1	function for the inverse of conditional copula cdf for the (t_{1},t_{2}) bivariate margin; choices are qcondcln and qcondcln180
tau2par1	function for maping Kendall's tau to copula parameter for the (t_{1},t_{2}) bivariate margin; choices are tau2par.cln and tau2par.cln180
qcond2	function for the inverse of conditional copula cdf for the (t_{2},t_{3}) bivariate margin; choices are qcondcln90 and qcondcln270
tau2par2	function for maping Kendall's tau to copula parameter for the (t_{2},t_{3}) bivariate margin; choices are tau2par.cln90 and tau2par.cln270
start	starting values for the parameters

Value

A list containing the following components:

LogLikelihood	the maximized log-likelihood
Estimates	the MLE
SE	the standard errors

References

Nikoloulopoulos, A.K. (2024) Vine copula mixed models for meta-analysis of diagnostic accuracy studies without a gold standard. Submitted.

Examples

data(Pap)
attach(Pap)

nq=30
gl=gauss.quad.prob(nq,"uniform")
mgrid<- meshgrid(gl$n,gl$n,gl$n,nargout=3)

tau2par=tau2par.bvn
qcond=qcondbvn

select.random=c(1,2,4)
start=c(rep(0.6,5),rep(0.5,3),c(0.01,-0.01))
est.norm=imperfect.trivariateVineCopulaREMADA.norm.comprehensive(y11,y10,
y01,y00,gl,mgrid,qcond,tau2par,select.random,start)

tau2par1=tau2par.cln180
qcond1=qcondcln180
tau2par2=tau2par.cln270
qcond2=qcondcln270
est.norm.cln=imperfect.trivariateVineCopulaREMADA.norm(y11,y10,y01,
y00,gl,mgrid,qcond1,tau2par1,qcond2,tau2par2,select.random,start)

start=c(rep(0.6,5),rep(0.05,3),c(0.1,-0.1))
est.beta=imperfect.trivariateVineCopulaREMADA.beta.comprehensive(y11,y10,y01,y00,
gl,mgrid,qcond,tau2par,select.random,start)

est.beta.cln=imperfect.trivariateVineCopulaREMADA.beta(y11,y10,y01,y00,
gl,mgrid,qcond1,tau2par1,qcond2,tau2par2,select.random,start)

detach(Pap)

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