FactorCopulaModel (version 0.1.1)

gauss1f1t: Compute correlation matrix according to 1-factor + 1-truncated vine (residual dependence) model

Description

Compute correlation matrix according to a 1-factor + 1-truncated vine (for residual dependence) model

Usage

gauss1f1t(cormat, start_loading, iter=10, est="mle", plots=TRUE, trace=TRUE)

Value

components:loading = final estimate for loading vector; R = correlation matrix (from MLE for 1F1T structure); Psi = vector of residual variances; loadings = matrix where ith row has the ith iteration; Rmats = list of correlation matrices; Rmats[[i]] has the ith iteration; Rstart = starting value of R based on starting values; dists = vector of distance measures as GOF criterion, ith entry for ith iteration; incls = iter x d*(d-1)/2 matrix, ith row for ith iteration columns are whether edge 12, 13, 23, 14, .... (d-1,d) are in residual tree; partcor = dxd matrix of partial correlations given latent variable; loglik = vector of loglik values, ith entry for ith iteration.

Arguments

cormat

dxd correlation matrix

start_loading

dx1 loading vector (for latent factor)

iter

number of iterations for modified EM

est

"mle" or "mom"

plots

flag that is TRUE to show plots of EM steps

trace

flag that is TRUE to print every 100th integer for iter

Details

A modified EM algorithm is used -- first step of the M-step performed either by MLE or by method of moments -- the second step assumes the moment estimator has been used

References

Brechmann EC and Joe H (2014). Parsimonious parameterization of correlation matrices using truncated vines and factor analysis. Computational Statistics and Data Analysis, 77, 233-251.

Examples

# \donttest{
library(igraph)
data(DJ20142016gf)
zdat = dj1416gf$zscore # GARCH-filtered returns that have been transformed to N(0,1)
rzmat = cor(zdat)
d = ncol(zdat)
cat("\n1-factor start for 1f1t\n")
fa = factanal(factors=1,covmat=rzmat)
start = c(fa$loading)
# fitting 1Factor 1Truncated vine residual dependence structure
out1f1t = gauss1f1t(rzmat,start_loading=start,iter=20,plots=FALSE)
print(out1f1t$loading)
cat("\nedges for tree of residual dependence\n")
i = 1:d
nn = i*(i-1)/2
niter = 21  # above iteration bound +1
incls = out1f1t$incls[niter,]
for(j in 2:d)
{ for(k in 1:(j-1)) 
  { if(incls[nn[j-1]+k]) 
    { cat("edge ", k,j," "); cat(out1f1t$partcor[k,j],"\n") } 
  }
}
# extract three columns of this output to use with factor1trvine_nllk
# See example in cop1f1t()
# }