mutinom6dVineCopulaREMADA: Maximum likelhood estimation for multinomial six-variate...

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

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 six-dimensional arrays. Replicates of the quadrature points that produce a 6-dimensional full grid
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. Statistical Methods in Medical Research. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/09622802241269645")}

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)

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