frontier (version 1.1-8)

vcov.frontier: vcov method for class frontier

Description

Extract the covariance matrix of the maximum likelihood coefficients of a stochastic frontier model returned by frontier.

Usage

# S3 method for frontier
vcov( object, extraPar = FALSE, … )

Arguments

object

an object of class frontier (returned by the function frontier).

extraPar

logical. If TRUE, the variances and covariances of additional parameters are returned: sigmaSqU = sigmaSq * gamma (with \(u\) ~ \(N^+\)( mu, sigmaSqU )), sigmaSqV = sigmaSq * ( 1 - gamma ) (with \(v\) ~ N( 0, sigmaSqV )), sigma = sigmaSq^0.5, sigmaU = sigmaSqU^0.5, sigmaV = sigmaSqV^0.5, lambdaSq = sigmaSqU / sigmaSqV, and lambda = sigmaU / sigmaV. Please note that sigmaSqU and sigmaU are not the variance and standard error, respectively, of \(u\).

…

currently unused.

Value

vcov.frontier returns the covariance matrix of the maximum likelihood coefficients.

Details

The variance-covariance matrix of the estimated parameters is taken from the direction matrix that is used in the final iteration of the Davidon-Fletcher-Powell procedure that is used for maximising the (log) likelihood function.

If argument extraPar is TRUE, the variances and covariances of the additional parameters are obtained by the delta method. Please note that the delta method might provide poor approximations of the ‘true’ variances and covariances, because parameter \(\sigma^2\) is left-censored and parameter \(\gamma\) is both left-censored and right-censored so that these parameters cannot be normally distributed.

Please note further that it might not be appropriate to use standard statistical tests (e.g. t-tests or other Wald tests) that are based on the variances and covariances of \(\sigma^2\), \(\gamma\), and the ‘additional parameters’, because these parameters are censored and cannot follow normal distributions.

See Also

coef.frontier, coef.summary.frontier, summary.frontier, and sfa.

Examples

# NOT RUN {
   # example included in FRONTIER 4.1
   data( front41Data )

   sfaResult <- sfa( log( output ) ~ log( capital ) + log( labour ),
      data = front41Data )
   vcov( sfaResult )
# }