Disequilibrium (version 1.1)

DlhoodDatanhrho: Derivative of likelihood with respect to the inverse hyperbolic tangent of correlation

Description

Derivative of likelihood with respect to the inverse hyperbolic tangent of correlation

Usage

DlhoodDatanhrho(Y, mu, logsigma11, logsigma22, atanhrho)

Arguments

Y

A vector of observed responses.

mu

A \(N \times 2\) matrix of means for equations 1 and 2.

logsigma11

A scalar log of the variance of the equation 1.

logsigma22

A scalar log of the variance of the equation 2.

atanhrho

A scalar log of inverse hyperbolic tangent of the correlation of equations 1 and 2.

Value

A vector of derivatives for each observation.

Examples

# NOT RUN {
set.seed(1775)
library(MASS)
beta01 = c(1,1)
beta02 = c(-1,-1)
N = 10000
SigmaEps = diag(2)
SigmaX = diag(2)
MuX = c(0,0)
par0 = c(beta01, beta02, SigmaX[1, 1], SigmaX[1, 2], SigmaX[2, 2])

Xgen = mvrnorm(N,MuX,SigmaX)
X1 = cbind(1,Xgen[,1])
X2 = cbind(1,Xgen[,2])
X = list(X1 = X1,X2 = X2)
eps = mvrnorm(N,c(0,0),SigmaEps)
eps1 = eps[,1]
eps2 = eps[,2]
Y1 = X1 %*% beta01 + eps1
Y2 = X2 %*% beta02 + eps2
Y = pmin(Y1,Y2)

p1 = 2
p2 = 2
theta = c(beta01, beta02, log(SigmaX[1, 1]), atanh(SigmaX[1, 2]), log(SigmaX[2, 2]))
mu = cbind(X[[1]] %*% theta[1:p1], X[[2]] %*% theta[(p1 + 1):(p1 + p2)])

d = DlhoodDatanhrho(Y = Y, mu = mu, logsigma11 = theta[p1 + p2 + 1],
   logsigma22 = theta[p1 + p2 + 3], atanhrho = theta[p1 + p2 + 2])
head(d)

# }