fmdepmeas: Spearman rho matrix for 1-factor, 2-factor, nested factor...

In YafeiXu/CopulaModel: CopulaModel: Dependence Modeling with Copulas

Description

Spearman rho matrix for 1-factor, 2-factor, nested factor copulas and multivariate Gaussian factor model

Usage

srho1fact(param1,pcondcop,nq)
srho2fact(param1,param2,pcondcop1,pcondcop2,nq)
rho2nestfact(param1,param2,dcop1,pcondcop2,nq)
rhomvn(fct,param) # matrix of Spearman rho for MVN factor model
cop2srho(param,pcop,nq) # Spearman rho via Gauss-Legendre quadrature

Arguments

param1	vector/matrix of copula parameters for linking copulas to factor 1 or global latent variable
param2	vector of copula parameters for linking copulas to factor 2 or group latent variable
fct	number of factors
param	dxfct matrix of partial correlation parameters for multivariate normal/Gaussian factor model with fct factors
pcondcop	function for conditional cdf of copula family for factor 1
pcondcop1	function for conditional cdf of copula family for factor 1
pcondcop2	function for conditional cdf of copula family for factor 2 or group latent variable
dcop1	function for bivariate copula pdf for global latent variable
pcop	function for bivariate copula cdf
nq	number of quadrature points for Gauss-Legendre quadrature

Details

2-dimensional Gauss-Legendre quadrature for 1-factor model, 4-dimensional Gauss-Legendre quadrature for 2-factor model.

Value

dxd matrix for srho1fact, srho2fact, rhomvn

single number for rho2nestfact, cop2srho

See Also

factorcopsim structcop

Examples

n=40000  
cpar=frk.b2cpar(seq(.7,.8,.02)); cpar2=frk.b2cpar(seq(.5,.6,.02))
set.seed(123)
frk1dat=sim1fact(n,cpar,qcondfrk,"frank")
set.seed(123)
frk2dat=sim2fact(n,cpar,cpar2,qcond1=qcondfrk,qcond2=qcondfrk,"frank","frank")
# 1-factor
r1=cor(frk1dat)
print(r1)
r1t=srho1fact(cpar,pcondfrk,nq=15)
print(r1t)
print(max(abs(r1-r1t)))
# 2-factor
r2=cor(frk2dat)
print(r2)
r2t=srho2fact(cpar,cpar2,pcondfrk,pcondfrk,nq=15)
print(r2t)
print(max(abs(r2-r2t)))
# nested-factor
grsize=c(4,4)
set.seed(123)
parne=c(c(4,3),rep(6,4),rep(6.5,4))
udatne=simnestfact(n=600, grsize, cop=5, parne) # Frank pair-copulas
parwglobal=c(4,3)
parwgrp=c(6,6.5)
srh=rho2nestfact(parwglobal,parwgrp,dfrk,pcondfrk,21)
print(srh)
print(cor(udatne[,1],udatne[,5:8]))  # should be round same as above
# Spearman's rho for bivariate copula (which could be margin of factor copula)
cop2srho(c(2.5,2.8), pfact1gum, 35)  # Gauss-Legendre
rhoS(c(2.5,2.8),pfact1gum)  # cubature
cop2srho(matrix(c(2.5,2.8,1.5,1.6),2,2), pfact2gum, 35) 

YafeiXu/CopulaModel documentation built on May 9, 2019, 11:07 p.m.