# Gradient function return when using Optim and colSums functions

## Question:

I can't understand why when using the `gradlik` function as an argument to the `Optim` function I get the following error:

``````Error in optim(beta, loglik, gradlik, method = "BFGS", hessian = T, control = list(fnscale = -1)) :
gradiente em optim retorna um objeto de comprimento 9000 ao invés de 9
``````

However, when I call the `gradlik(beta)` function it returns the gradient vector as expected!

Does anyone have any suggestions for fixing this code?

``````loglik <- function(beta) {
NXS <- dim(model.matrix(~XS))[2]#Número de colunas de XS+1
NXO <- dim(model.matrix(~XO))[2]#Número de colunas de XO+1
## parameter indices
ibetaS <- 1:NXS
ibetaO <- seq(tail(ibetaS, 1)+1, length=NXO)
isigma <- tail(ibetaO, 1) + 1
irho <- tail(isigma, 1) + 1
g <- beta[ibetaS]
b <- beta[ibetaO]
sigma <- beta[isigma]
if(sigma < 0) return(NA)
rho <- beta[irho]
if( ( rho < -1) || ( rho > 1)) return(NA)

XS.g <- model.matrix(~XS) %*% g
XO.b <- model.matrix(~XO) %*% b
u2 <- YO - XO.b
r <- sqrt( 1 - rho^2)
B <- (XS.g + rho/sigma*u2)/r
ll <- ifelse(YS == 0,
(pnorm(-XS.g, log.p=TRUE)),
dnorm(u2/sigma, log = TRUE) - log(sigma) +
(pnorm(B, log.p=TRUE))
)
sum(ll)
}

NXS <- dim(model.matrix(~XS))[2]#Número de colunas de XS+1
NXO <- dim(model.matrix(~XO))[2]#Número de colunas de XO+1
nObs <- length(YS)
NO <- length(YS[YS > 0])
nParam <- NXS + NXO + 2 #Total of parameters

XS0 <- XS[YS==0,,drop=FALSE]
XS1 <- XS[YS==1,,drop=FALSE]
YO[is.na(YO)] <- 0
YO1 <- YO[YS==1]
XO1 <- XO[YS==1,,drop=FALSE]
N0 <- sum(YS==0)
N1 <- sum(YS==1)

w  <- rep(1,N0+N1 )
w0 <- rep(1,N0)
w1 <- rep(1,N1)
NXS <- dim(model.matrix(~XS))[2]#Número de colunas de XS+1
NXO <- dim(model.matrix(~XO))[2]#Número de colunas de XO+1
## parameter indices
ibetaS <- 1:NXS
ibetaO <- seq(tail(ibetaS, 1)+1, length=NXO)
isigma <- tail(ibetaO, 1) + 1
irho <- tail(isigma, 1) + 1

g <- beta[ibetaS]
b <- beta[ibetaO]
sigma <- beta[isigma]
if(sigma < 0) return(matrix(NA, nObs, nParam))
rho <- beta[irho]
if( ( rho < -1) || ( rho > 1)) return(matrix(NA, nObs, nParam))
XS0.g <- as.numeric(model.matrix(~XS0) %*% g)
XS1.g <- as.numeric(model.matrix(~XS1) %*% g)
XO1.b <- as.numeric(model.matrix(~XO1) %*% b)
#      u2 <- YO1 - XO1.b
u2 <- YO1 - XO1.b
r <- sqrt( 1 - rho^2)
#      B <- (XS1.g + rho/sigma*u2)/r
B <- (XS1.g + rho/sigma*u2)/r
lambdaB <- exp( dnorm( B, log = TRUE ) - pnorm( B, log.p = TRUE ) )
gradient[YS == 0, ibetaS] <- - w0 * model.matrix(~XS0) *
exp( dnorm( -XS0.g, log = TRUE ) - pnorm( -XS0.g, log.p = TRUE ) )
gradient[YS == 1, ibetaS] <- w1 * model.matrix(~XS1) * lambdaB/r
gradient[YS == 1, ibetaO] <- w1 * model.matrix(~XO1) * (u2/sigma^2 - lambdaB*rho/sigma/r)
gradient[YS == 1, isigma] <- w1 * ( (u2^2/sigma^3 - lambdaB*rho*u2/sigma^2/r) - 1/sigma )
gradient[YS == 1, irho] <- w1 * (lambdaB*(u2/sigma + rho*XS1.g))/r^3
}

n=1000
X1 <- runif(n)
X2 <- runif(n)
XO <- cbind(X1,X2)
X3 <- runif(n)
XS <- cbind(X1,X2,X3)
YS <- sample(c(0,1),n,replace = TRUE)
YO <- sample(100:400,n,replace = TRUE)*YS
beta <- c(1,1,1,1,1,1,1,1,0.5)
#Note que a função abaixo compila normalmente:
#Porém a função Optim não compila:
theta <-optim(beta,loglik, gradlik, method = "BFGS",hessian = T,control=list(fnscale=-1))
theta\$par
``````

The gradient function needs to return a vector with the same size as the number of parameters.

In his role, there are two occasions when this does not happen.

When `sigma <0` you return the following value in your function:

``````if(sigma < 0) return(matrix(NA, nObs, nParam))
``````

This is going to be a 9000 x 9 matrix that the error `optim()` gives you. You have to change this piece of code to something that returns only 9 elements and not an array.

Likewise, when `( rho < -1) || ( rho > 1)` your function returns:

``````if( ( rho < -1) || ( rho > 1)) return(matrix(NA, nObs, nParam))
``````

What is a 9000 x 9 matrix in your example causing the error.

Scroll to Top
AllEscort