vcov.frontier: vcov method for class frontier

In frontier: Stochastic Frontier Analysis

Description

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

Usage

## S3 method for class '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.

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.

Value

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

Author(s)

Arne Henningsen

See Also

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

Examples

   # example included in FRONTIER 4.1
   data( front41Data )

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

Example output

Loading required package: micEcon

If you have questions, suggestions, or comments regarding one of the 'micEcon' packages, please use a forum or 'tracker' at micEcon's R-Forge site:
https://r-forge.r-project.org/projects/micecon/
Loading required package: lmtest
Loading required package: zoo

Attaching package: ‘zoo’

The following objects are masked from ‘package:base’:

    as.Date, as.Date.numeric


Please cite the 'frontier' package as:
Tim Coelli and Arne Henningsen (2013). frontier: Stochastic Frontier Analysis. R package version 1.1. http://CRAN.R-Project.org/package=frontier.

If you have questions, suggestions, or comments regarding the 'frontier' package, please use a forum or 'tracker' at frontier's R-Forge site:
https://r-forge.r-project.org/projects/frontier/
              (Intercept)  log(capital)   log(labour)       sigmaSq
(Intercept)   0.041053586 -3.144681e-03 -8.003034e-03  4.045661e-03
log(capital) -0.003144681  2.269891e-03  4.010768e-05 -2.953064e-05
log(labour)  -0.008003034  4.010768e-05  2.047703e-03 -4.719114e-05
sigmaSq       0.004045661 -2.953064e-05 -4.719114e-05  4.084369e-03
gamma         0.009251994 -9.155472e-05 -1.640503e-04  6.745093e-03
                     gamma
(Intercept)   9.251994e-03
log(capital) -9.155472e-05
log(labour)  -1.640503e-04
sigmaSq       6.745093e-03
gamma         1.861161e-02

frontier documentation built on April 19, 2020, 3:54 p.m.