Disequilibrium (version 1.1)

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

Description

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

Usage

DllhoodDatanhrho(Y, mu, logsigma11, logsigma22, atanhrho, lhood)

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 of the inverse hyperbolic tangent of the correlation of equations 1 and 2.

lhood

A vector of length \(N\) of likelihood values.

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)])
lhood = exp(-nLLikelihoodDE(theta, Y, X, transformR3toPD = TRUE, summed = FALSE))

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

# }