optim in r :non finite finite difference error - r

Question

I have a simple likelihood function (from a normal dist with mean=0) that I want to maximize. optim keeps giving me this error:
Error in optim(par = phi, fn = loglike, estimates = estimates, NULL, hessian = TRUE, : non-finite finite-difference value [1]
Here is my data and likelihood function:
y = [ -0.01472 0.03942 0.03592 0.02776 -0.00090 ]
C = a varcov matrix:
1.66e-03 -0.000120 -6.780e-06 0.000102 -4.000e-05
-1.20e-04 0.001387 7.900e-05 -0.000140 -8.000e-05
-6.78e-06 0.000079 1.416e-03 -0.000070 8.761e-06
1.02e-04 -0.000140 -7.000e-05 0.001339 -6.000e-05
-4.00e-05 -0.000080 8.761e-06 -0.000060 1.291e-03
my log likelihood function is:
lglkl = -.5*(log(det(v)) + (t(y)%%vi%%y))` where v = phi*I + C and vi=inverse(v) and I= 5*5 Identity matrix.
I am trying to get the mle estimate for "phi". I thought this would be a simple optimization problem but am struggling. Would really appreciate any help. Thanks in advance. My code is below:
loglike <- function(phi,y) {
v = phi*I + C
vi = solve(v)
loglike = -.5*(log(det(v)) + (t(y)%*%vi%*%y))
return(-loglike)
}
phi = 0
parm <- optim(par=phi,fn=loglike,y=y,NULL,hessian = TRUE, method="L-BFGS-B",lower=0,upper=1000)

Answer 1

The error you ran into is because ϕ becomes negative beyond a certain number of iterations (which indicates that the constraints are not being applied correctly by the algorithm). Also, the solution does not converge to a single value but jumps between a few small values before reaching a situation where the updated covariance matrix is no-longer positive definite. At that stage you get det(v) < 0 and log[det(v)] is undefined. The optim algorithm bails out at that stage.
To see what's happening, play with the maxit and ndeps parameters in the code below.
require("matrixcalc")
#-------------------------------------------------
# Log-likelihood function
#-------------------------------------------------
loglike <- function(phi, y) {
# Shift the covariance matrix
print(paste("phi = ", phi))
#v = phi*I + (1 - phi)*C
v = phi*I + C
stopifnot(is.positive.definite(v))
# Invert shifted matrix
vi = solve(v)
# Compute log likelihood
loglike = -.5*(log(det(v)) + (t(y) %*% vi %*% y))
print(paste("L = ", loglike))
return(-loglike)
}
#-------------------------------------------------
# Data
#-------------------------------------------------
y = c(-0.01472, 0.03942, 0.03592, 0.02776, -9e-04)
C = structure(c(0.00166, -0.00012, -6.78e-06, 0.000102, -4e-05, -0.00012,
0.001387, 7.9e-05, -0.00014, -8e-05, -6.78e-06, 7.9e-05,
0.001416, -7e-05, 8.761e-06, 0.000102, -0.00014, -7e-05,
0.001339, -6e-05, -4e-05, -8e-05, 8.761e-06, -6e-05, 0.001291),
.Dim = c(5L, 5L ))
#--------
# Initial parameter
#--------
I = diag(5)
phi = 50
#--------
# Minimize
#--------
parm <- optim(par = phi, fn = loglike, y = y, NULL, hessian = TRUE,
method = "L-BFGS-B", lower = 0.0001, upper = 1000,
control = list(trace = 3,
maxit = 1000,
ndeps = 1e-4) )