Disequilibrium (version 1.1)

DlhoodDbeta1: Derivative of likelihood with respect to the coefficients of equation 1

Description

Derivative of likelihood with respect to the coefficients of equation 1

Usage

DlhoodDbeta1(Y, mu, logsigma11, logsigma22, atanhrho, X1)

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.

X1

A \(N \times k_1\) design matrix for equation 1.

Value

A matrix of derivatives for each observation and parameter.

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 = DlhoodDbeta1(Y = Y, mu = mu, logsigma11 = theta[p1 + p2 + 1],
   logsigma22 = theta[p1 + p2 + 3], atanhrho = theta[p1 + p2 + 2], X1 = X1)
head(d)

# }