mutinom6dVineCopulaREMADA {CopulaREMADA}

Maximum likelhood estimation for multinomial six-variate 1-truncated D-vine copula mixed models for meta-analysis of two diagnostic tests accounting for within and between studies dependence

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

multinom6dVineCopulaREMADA.norm(y001,y011,y101,y111,y000,y010,y100,y110,
          gl,mgrid,qcond1,qcond2,qcond3,qcond4,qcond5,
          tau2par1,tau2par2,tau2par3,tau2par4,tau2par5,
          sel1,sel2,sel3)
multinom6dVineCopulaREMADA.beta(y001,y011,y101,y111,y000,y010,y100,y110,
          gl,mgrid,qcond1,qcond2,qcond3,qcond4,qcond5,
          tau2par1,tau2par2,tau2par3,tau2par4,tau2par5,
          sel1,sel2,sel3)

Arguments

y001

the number of the test results in the diseased where the test 1 outcome is negative and the test 2 outcome is negative

y011

the number of the test results in the diseased where the test 1 outcome is negative and the test 2 outcome is positive

y101

the number of the test results in the diseased where the test 1 outcome is positive and the test 2 outcome is negative

y111

the number of the test results in the diseased where the test 1 outcome is positive and the test 2 outcome is positive

y000

the number of the test results in the non-diseased where the test 1 outcome is negative and the test 2 outcome is negative

y010

the number of the test results in the non-diseased where the test 1 outcome is negative and the test 2 outcome is positive

y100

the number of the test results in the non-diseased where the test 1 outcome is positive and the test 2 outcome is negative

y110

the number of the test results in the non-diseased where the test 1 outcome is positive and the test 2 outcome is positive

gl

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

mgrid

a list containing 6-dimensional arrays.

qcond1

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

qcond2

function for the inverse conditional copula cdf at the (2,3) bivariate margin

qcond3

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

qcond4

function for the inverse conditional copula cdf at the (4,5) bivariate margin

qcond5

function for the inverse conditional copula cdf at the (5,6) bivariate margin

tau2par1

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

tau2par2

function for maping Kendall's tau at the (2,3) bivariate margin to copula parameter

tau2par3

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

tau2par4

function for maping Kendall's tau at the (4,5) bivariate margin to copula parameter

tau2par5

function for maping Kendall's tau at the (5,6) bivariate margin to copula parameter

sel1

Indicates the position of bivariate copulas with positive dependence only such as the Clayton and the Clayton rotated by 180 degrees

sel2

Indicates the position of bivariate copulas with negative dependence only such as the Clayton rotated by 90 degrees and the Clayton rotated by 270 degrees

sel3

Indicates the position of bivariate copulas with comprehensive dependence such as the BVN and Frank copulas

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. (2024) Joint meta-analysis of two diagnostic tests accounting for within and between studies dependence. Submitted.

See Also

rmultinom6dVineCopulaREMADA

Examples

data(Down)
attach(Down)
y111=down_n_11 
y110=nodown_n_11
y101=down_n_10
y100=nodown_n_10 
y001=down_n_00 
y000=nodown_n_00 
y010=nodown_n_01
y011=down_n_01

nq=15
gl=gauss.quad.prob(nq,"uniform")
data(mgrid6d)

tau2par1=tau2par.cln90
qcond1=qcondcln90
tau2par3=tau2par4=tau2par5=tau2par.cln
qcond3=qcond4=qcond5=qcondcln
tau2par2=tau2par.bvn
qcond2=qcondbvn

sel1=3:5; sel2=1; sel3=2

est=multinom6dVineCopulaREMADA.norm(y001,y011,y101,y111,
y000,y010,y100,y110,gl,mgrid,qcond1,qcond2,qcond3,qcond4,qcond5,
tau2par1,tau2par2,tau2par3,tau2par4,tau2par5,sel1,sel2,sel3)

detach(Down)