gausstrvineGAlg: Gaussian truncated d-dimensional vines based on minimum...

In vincenzocoia/CopulaModel: CopulaModel: Dependence Modeling with Copulas

Description

Gaussian truncated d-dimensional vines based on a genetic algorithm and spanning trees with weights of one minus squared partial correlation

Usage

gausstrvine.galg(cormat,target=0.99,nneigh=10,nbmst=10,
  selectcrit="prop",selectfact=0.1,elite=0.05,method="nfi",n=0,iprint=T)

Arguments

cormat	dxd correlation matrix
target	target fit value (near but less than 1; 1-alpha in publication)
nneigh	number of nearest neighbors of minimum spanning tree
nbmst	number of best minimum spanning trees
selectcrit	selection criterion ("prop" for proportional or "rank")
selectfact	selection factor with default 0.1 (total fraction of solutions retained after elitism and random selection)
elite	percentage for elitism (default 0.05)
method	fit index ("nfi", "cfi" or "ifi"); NFI=normed fit index, CFI=comparative fit index, IFI=incremental fit index
n	sample size for the correlation matrix, default 0 if unknown
ntrunc	specified upper bound in truncation level to consider
iprint	print flag for intermediate results

Details

This function depends on the minimum spanning tree algorithm in the library igraph.

Value

RVM	object with $RVM$VineA = d-dimensional vine array, $RVM$pc = partial correlations by tree, $RVM$Matrix = vine array in VineCopula format [d:1,d:1], $RVM$Cor = partial correlations in VineCopula format [d:1,d:1]
mst	spanning trees 1,2,...d-1: $mst[[1]], $mst[[2]], ...
treeweight	vector of length d-1 with sum_edge log(1-rho[edge]^2) for trees 1,...d-1
trunclevel	same as inputted ntrunc
truncval	sum treeweight[1:trunclevel] / sum treeweight[1:(d-1)]

References

Brechmann and Joe (2015), Truncation of vine copulas using fit indices. J Multivariate Analysis, v 138, 19-33.

See Also

gausstrvine gausstrvineMST

Examples

## Not run: 
library(igraph) # version 0.7.1 and 1.0.0 work
rrvec=c(
-0.04,-0.08, 0.47,-0.07, 0.67, 0.50,-0.02, 0.52, 0.61, 0.46, 0.00,-0.06,
-0.08,-0.07,-0.10, 0.15,-0.03,-0.14,-0.15,-0.06, 0.19, 0.03,-0.01,-0.04,
-0.03,-0.03, 0.10, 0.22, 0.19, 0.10,-0.09,-0.11, 0.02,-0.02, 0.62, 0.18, 
 0.10, 0.04, 0.02,-0.03, 0.05, 0.07, 0.20, 0.27, 0.16, 0.10, 0.18,-0.09,
-0.10, 0.01, 0.00, 0.32, 0.04, 0.53, 0.05,-0.16, 0.03, 0.12, 0.15, 0.06,
-0.25,-0.83,-0.24,-0.52,-0.23,-0.26,-0.11,-0.49, 0.05, 0.01,-0.14,-0.03,
-0.38,-0.11,-0.57,-0.18,-0.43, 0.35, 0.15,-0.02,-0.14,-0.13,-0.05, 0.17, 
 0.95, 0.21, 0.63, 0.18, 0.33,-0.81,-0.38,-0.05, 0.07, 0.13, 0.10, 0.08,
-0.33,-0.32,-0.15,-0.13,-0.21,-0.06, 0.42, 0.13,-0.31, 0.40,-0.03,-0.11,
-0.08,-0.05,-0.07, 0.13, 0.01, 0.25, 0.06, 0.22,-0.12,-0.17, 0.15, 0.02,
 0.66, 0.00,-0.11,-0.06,-0.02,-0.02, 0.18, 0.04, 0.26, 0.11, 0.16,-0.18,
-0.18, 0.19,-0.03, 0.52, 0.29,-0.01,-0.02,-0.04,-0.01,-0.02, 0.05, 0.01,
 0.09, 0.07, 0.04,-0.05,-0.05, 0.05, 0.02, 0.15, 0.30, 0.35,-0.22,-0.12,
-0.17,-0.09,-0.07, 0.10,-0.02, 0.15, 0.03, 0.14,-0.10, 0.01, 0.12, 0.02,
 0.80, 0.50, 0.19)

rmat=corvec2mat(rrvec)
nn=1187; d=ncol(rmat)
mxtrunc=10
bestmst=gausstrvine.mst(rmat,ntrunc=mxtrunc,iprint=F)
set.seed(123)
kbmst=gausstrvine.galg(rmat,selectcrit="prop",method="nfi",n=nn,iprint=F)
# there is a random component in the genetic algorithm
# so different seeds can lead to different suboptimal truncated vines
set.seed(12345)
kbmst2=gausstrvine.galg(rmat,selectcrit="prop",method="nfi",n=nn,iprint=F)
# Use the different vine arrays for further analysis such as
#  replace bivariate Gaussian copulas on edges with tail asymmetric copulas

# greedy algorithm : sequential MST
cat("\nsequential MST\n")
perm=diag(kbmst$RVM$VineA)
Aori=kbmst$RVM$VineA
iperm=order(perm)
AA=varrayperm(Aori,iperm)
pcmat=kbmst$RVM$pc
rperm=rmat[perm,perm]
npar=0
for(ell in 1:mxtrunc)
{ Rtrun=pcor2cor.truncvine(pcmat,AA,ntrunc=ell)
  npar=npar+(d-ell)
  if(ell>1) Rtrun=Rtrun$rmat
  cat("\nMST",ell,"-truncated R-vine with npar=", npar,"\n")
  cat("max abs difference =", max(abs(rperm-Rtrun)),"\n")
  cat("avg abs difference =", sum(abs(rperm-Rtrun))/d/(d-1),"\n")
  outtr=corDis(Rtrun,rperm,nn,npar=npar)
  cat("corDis:Dfit, 2*nllk, AIC, BIC=", outtr,"\n")
}
cat("\n============================================================\n")

# non-greedy MST with genetic algorithm
cat("\nnon-greedy, seed=123\n")
perm=diag(kbmst$RVM$VineA)
Aori=kbmst$RVM$VineA
iperm=order(perm)
AA=varrayperm(Aori,iperm)
pcmat=kbmst$RVM$pc
rperm=rmat[perm,perm]
npar=0
for(ell in 1:mxtrunc)
{ Rtrun=pcor2cor.truncvine(pcmat,AA,ntrunc=ell)
  npar=npar+(d-ell)
  if(ell>1) Rtrun=Rtrun$rmat
  cat("\nGenetic-alg with MST",ell,"-truncated R-vine with npar=", npar,"\n")
  cat("max abs difference =", max(abs(rperm-Rtrun)),"\n")
  cat("avg abs difference =", sum(abs(rperm-Rtrun))/d/(d-1),"\n")
  outtr=corDis(Rtrun,rperm,nn,npar=npar)
  cat("corDis:Dfit, 2*nllk, AIC, BIC=", outtr,"\n")
}

## End(Not run)

vincenzocoia/CopulaModel documentation built on Oct. 27, 2021, 6:41 a.m.