Extract Gradients Evaluated at each Observation

Extract the gradients of the log-likelihood function evaluated at each observation (‘Empirical Estimating Function’, see estfun).

# S3 method for class 'maxLik'
estfun(x, ...)
# S3 method for class 'maxim'
gradient(x, ...)

Arguments

x

an object inheriting from class maxim (for gradient) or maxLik. (for estfun.)

...

further arguments (currently ignored).

Value

gradient

vector, objective function gradient at estimated maximum (or the last calculated value if the estimation did not converge.)

estfun

matrix, observation-wise log-likelihood gradients at the estimated parameter value evaluated at each observation. Observations in rows, parameters in columns.

Warnings

The sandwich package must be loaded in order to use estfun.

estfun only works if the observaton-specific gradient information was available for the estimation. This is the case of the observation-specific gradient was supplied (see the grad argument for maxLik), or the log-likelihood function returns a vector of observation-specific values.

Author

Arne Henningsen, Ott Toomet

See also

hessian, estfun, maxLik.

Examples

## ML estimation of exponential duration model:
t <- rexp(10, 2)
loglik <- function(theta) log(theta) - theta*t

## Estimate with numeric gradient and hessian
a <- maxLik(loglik, start=1 )

gradient(a)
#> [1] 1.04361e-08
# Extract the gradients evaluated at each observation
library( sandwich )
estfun( a )
#>             [,1]
#>  [1,]  0.1673213
#>  [2,] -0.1980411
#>  [3,]  0.3334365
#>  [4,] -0.2093178
#>  [5,] -0.2763933
#>  [6,] -0.2160405
#>  [7,]  0.2114339
#>  [8,]  0.2603026
#>  [9,]  0.1273366
#> [10,] -0.2000382

## Estimate with analytic gradient.
## Note: it returns a vector
gradlik <- function(theta) 1/theta - t
b <- maxLik(loglik, gradlik, start=1)
gradient(a)
#> [1] 1.04361e-08
estfun( b )
#>             [,1]
#>  [1,]  0.1673213
#>  [2,] -0.1980411
#>  [3,]  0.3334365
#>  [4,] -0.2093178
#>  [5,] -0.2763933
#>  [6,] -0.2160405
#>  [7,]  0.2114339
#>  [8,]  0.2603026
#>  [9,]  0.1273366
#> [10,] -0.2000382