internal-tests/fim-cmp.R

In lotze/COMPoissonReg: Conway-Maxwell Poisson (COM-Poisson) Regression

library(COMPoissonReg)
library(Matrix)

x = 1.25
X = model.matrix(~ x)
S = model.matrix(~ x)
W = model.matrix(~ x)
beta = rep(1.5, 2)
gamma = rep(1.25, 2)
zeta = rep(0, 2)

lambda = exp(X %*% beta)
nu = exp(S %*% gamma)
p = plogis(W %*% zeta)

FIM = fim.zicmp.reg(X, S, W = matrix(1,1,1), beta, gamma, zeta = 0, max = 100)
qq = ncol(W) + ncol(S)
FIM[1:qq, 1:qq]

# This transformation should also yield the correct FIM for (Beta, Gamma, Zeta)
FIM.noreg = fim.zicmp(lambda, nu, p = p, max = 200)
qq = ncol(W) + ncol(S) + ncol(X)
J = bdiag(
	as.numeric(exp(X %*% beta)) * X,
	as.numeric(exp(S %*% gamma)) * S,
	as.numeric(dlogis(W %*% zeta)) * W	
)

FIM.outer = t(J) %*% FIM.noreg %*% J
FIM.outer[-c(5,6), -c(5,6)]