# R/loglik_cragg_AC.R In jackiemauro/hurdleIV:

#### Defines functions loglik_AC

```### This function returns the negative log-likelihood (so that it can be minimized)
### The math follows Alex C's derivation.
### Not done--don't understand how to get the integral. y0 is in the conditioning
### statement, so I can't figure out how to tell R to integrate over it.

loglik_AC = function(params){
sig_v = params[1]
sig_u = params[2]
tau1 = params[3]
tau0 = params[4]
rho = params[5]
beta11 = params[6]
beta12 = params[7]
beta2 = params[8]
gamma11 = params[9]
gamma12 = params[10]
gamma2 = params[11]
pi11 = params[12]
pi12 = params[13]
pi2 = params[14]

censored = y1<=0

#Check for invalid parameters
# Sig_err= matrix( c(1, rho,    tau0,
#                    rho,     sig_u^2,    tau1,
#                    tau0,  tau1, sig_v^2),
#                  ncol = 3, byrow = T)

pre = matrix( c(1, rho,    tau0,
0,     sig_u^2,    tau1,
0,  0, sig_v^2),
ncol = 3, byrow = T)
Sig_err = t(pre)%*%pre / ((t(pre)%*%pre)[1,1])
if(min(eigen(Sig_err)\$values)<=0){return(Inf)}
if((sig_u<=0)|(sig_v<=0)){return(Inf)}

#Transformation matrix from (eta, u, v) to (y0*, log y1*, x2) (without the mean)
A = rbind(
c(1,0,gamma2),
c(0,1,beta2),
c(0,0,1)
)
#Covariance of (y0*, log y1*, x2)
Sig = A%*%Sig_err%*%t(A)
if(min(eigen(Sig)\$values)<=0){return(Inf)}

#Means for (y0^*, y1*, x2).
mu_y0 = gamma11 + gamma12*x1 + gamma2*(pi11 + pi12*x1 + pi2*z)
mu_y1 = beta11 + beta12*x1 + beta2*(pi11 + pi12*x1 + pi2*z)
mu_x2 = pi11 + x1*pi12 + z*pi2

#Parameters for x2
sig2_x2 = Sig[3,3]

#Parameters for y0star given x2
mu_y0_x2 = mu_y0 + Sig[1,3]/Sig[3,3]*(x2-mu_x2)
sig2_y0_x2 = Sig[1,1] - Sig[1,3]^2/Sig[3,3]

#Parameters for log(y1star) given x2
mu_y1_x2 = mu_y1 + Sig[2,3]/Sig[3,3]*(x2-mu_x2)
sig2_y1_x2 = Sig[2,2] - Sig[2,3]^2/Sig[3,3]

#Parameters for y0star given y1star and x2
tempSig = Sig[-2,-2]
mu_y0_y1x2 = mu_y0 + Sig[2,c(1,3),drop=FALSE]%*%solve(tempSig)%*%rbind(y0-mu_y0,x2-mu_x2)
sig2_y0_y1x2 = Sig[2,2] - Sig[2,c(1,3),drop=FALSE]%*%solve(tempSig)%*%Sig[c(1,3),2,drop=FALSE]

#Parameters for y1star given y0star and x2
mu_y1_y0x2 = mu_y1 + Sig[1,2:3,drop=FALSE]%*%solve(Sig[2:3,2:3])%*%rbind(y1-mu_y1,x2-mu_x2)
sig2_y1_y0x2 = Sig[1,1] - Sig[1,2:3,drop=FALSE]%*%solve(Sig[2:3,2:3])%*%Sig[2:3,1,drop=FALSE]

#Parameters for y0star and y1star given x2
mu_y1y0_x2 = t(cbind(mu_y0,mu_y1)) + Sig[1:2,3]%*%solve(sig2_x2)%*%t(x2-mu_x2)
sig2_y1y0_x2 = Sig[1:2,1:2] - Sig[1:2,3]%*%solve(sig2_x2)%*%Sig[3,1:2]
sig2_y1y0_x2[upper.tri(sig2_y1y0_x2)] <- sig2_y1y0_x2[lower.tri(sig2_y1y0_x2)]
if(any(eigen(sig2_y1y0_x2)\$value<0)){return(-Inf)}

#ll1 integral -- don't know how to get integral over y0 in conditioning
# don't know how to divide by it either within the integral
l = c(0,0); u = c(Inf,Inf)
f <- function(x){pmvnorm(lower = l, upper = u, mean = x, sigma = sig2_y1_y0x2)}
ll0_int <- tryCatch({
apply(mu_y1_y0x2,2,f)
}, error = function(e){
print(paste("Error message from pmvnorm: ",e))
print(sig2_y1_y0x2)
return(Inf)
}, warning = function(w){
print(paste("Warning message from pmvnorm: ",w))
}
)

###Calculate the contributions to the log likelihood.
#When y1=0:
ll0 = pnorm(0,mean=mu_y0_x2,sd=sqrt(sig2_y0_x2),log.p = TRUE) + dnorm(x2,mean=mu_x2,sd=sqrt(sig2_x2),log = TRUE)

#When y1>0:
ll1 = dnorm(y1,mean = mu_y1_y0x2,sd=sqrt(sig2_y1_y0x2),log=T)-ll1_int

#Combine them, based on y1
ll = ifelse(censored,ll0,ll1)
print(-sum(ll))

#Return the negative log-likelihood, since I will be using optim (which minimizes instead of maximizing)
-sum(ll)
}
```
jackiemauro/hurdleIV documentation built on April 2, 2018, 8:28 p.m.