# [R] How can I pick a matrix from a function? (Out Product of Gradient)

yanghaowang yanghaowang at utk.edu
Wed Nov 30 18:38:10 CET 2011

```Hi all,

I would like to use optim() to estimate the equation by the log-likelihood
function and gradient function which I had written. I try to use OPG(Out
Product of Gradient) to calculate the Hessian matrix since sometime Hessian
matrix is difficult to calculate. Thus I want to pick the Gradient matrix

Moreover, could R show the process of calculation on gradient function I
written by using "optim( )" or other commands?

Thanks,

Yanghao

============================================================

X <- cbind(rep(1,n),sex,age,yrmarry,children,rating)
dy <- (mydata\$y>0)*1

# *********************************************
# Probit model: log-likelihood
# *********************************************
fprobit <- function(beta,y,X) {
n  <- length(y)
k  <- ncol(X)
b  <- beta[1:k]
kk <- 2*y-1
z  <- X %*% b
L  <- log(pnorm(kk*z))
L  <- sum(L)
return(-L)
}

# *********************************************
# *********************************************
gprobit <- function(b,y,X) {
kappa=2*y-1
z <- kappa*(X %*% b)
imr <- kappa*dnorm(z)/pnorm(z)
G<-matrix(ncol=ncol(X),nrow=nrow(X))
for(i in 1:nrow(imr)){
G[i,]<-imr[i,]*X[i,]
}
g <- apply(G,2,sum)
return(-g)
}

############For initial value#####################
xx   <- cbind(sex,age,yrmarry,children,rating)
reg1 <- lm(dy~xx)
(b0  <- reg1\$coef)
##################################################

(mle  <- optim(b0,fprobit,gr=gprobit,
method="BFGS",hessian=T,y=dy,X=X,control=list(trace=T)))

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```