Variance Covariance Matrix of maxLik objects

Extract variance-covariance matrices from maxLik objects.

# S3 method for class 'maxLik'
vcov( object, eigentol=1e-12, ... )

Arguments

object

a ‘maxLik’ object.

eigentol

eigenvalue tolerance, controlling when the Hessian matrix is treated as numerically singular.

...

further arguments (currently ignored).

Value

the estimated variance covariance matrix of the coefficients. In case of the estimated Hessian is singular, it's values are Inf. The values corresponding to fixed parameters are zero.

Details

The standard errors are only calculated if the ratio of the smallest and largest eigenvalue of the Hessian matrix is less than “eigentol”. Otherwise the Hessian is treated as singular.

Author

Arne Henningsen, Ott Toomet

See also

vcov, maxLik.

Examples

## ML estimation of exponential random variables
t <- rexp(100, 2)
loglik <- function(theta) log(theta) - theta*t
gradlik <- function(theta) 1/theta - t
hesslik <- function(theta) -100/theta^2
## Estimate with numeric gradient and hessian
a <- maxLik(loglik, start=1, control=list(printLevel=2))
#> ----- Initial parameters: -----
#> fcn value: -50.81886 
#>      parameter initial gradient free
#> [1,]         1         49.18114    1
#> Condition number of the (active) hessian: 1 
#> -----Iteration 1 -----
#> -----Iteration 2 -----
#> -----Iteration 3 -----
#> -----Iteration 4 -----
#> -----Iteration 5 -----
#> --------------
#> gradient close to zero (gradtol) 
#> 5  iterations
#> estimate: 1.967773 
#> Function value: -32.30974 
vcov(a)
#>            [,1]
#> [1,] 0.03872798
## Estimate with analytic gradient and hessian
a <- maxLik(loglik, gradlik, hesslik, start=1)
vcov(a)
#>            [,1]
#> [1,] 0.03872132