Testing parameter restrictions in stochastic frontier models by a Likelihood Ratio test.
## S3 method for class 'frontier' lrtest( object, ... )
a fitted model object of class
further fitted model objects of class
lrtest.frontier is called with only one argument/object
... is not used),
it compares the fitted model to a corresponding model
without inefficiency (i.e. estimated by OLS).
lrtest.frontier is called with more than one argument/object
... is used),
it consecutively compares
the fitted model object
with the models passed in
The test statistic is
2 * ( logLik( mu ) - logLik( mr ) ),
mu is the unrestricted model
mr is the restricted model.
If a Frontier model (estimated by ML) is compared to a model without inefficiency (estimated by OLS), the test statistic asymptotically has a mixed χ^2 distribution under the null hypothesis (see Coelli, 1995).
If two Frontier models (estimated by ML) are compared, the test statistic asymptotically has a χ^2 distribution with j degrees of freedom under the null hypothesis, where j is the number of restrictions.
An object of class
which contains the log-likelihood value,
degrees of freedom, the difference in degrees of freedom,
likelihood ratio Chi-squared statistic and corresponding p value.
See documentation of
in package "lmtest".
Coelli, T.J. (1995), Estimators and Hypothesis Tests for a Stochastic: A Monte Carlo Analysis, Journal of Productivity Analysis, 6, 247-268.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
# rice producers in the Philippines (panel data) data( "riceProdPhil" ) library( "plm" ) riceProdPhil <- pdata.frame( riceProdPhil, c( "FMERCODE", "YEARDUM" ) ) # Error Components Frontier with truncated normal distribution # and time effects (unrestricted model) mu <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ), truncNorm = TRUE, timeEffect = TRUE, data = riceProdPhil ) # Error Components Frontier with half-normal distribution # without time effects (restricted model) mr <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ), data = riceProdPhil ) ## compare the two models by an LR-test lrtest( mu, mr ) ## compare each of the models to a corresponding model without inefficiency lrtest( mu ) lrtest( mr )
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/ Loading required package: Formula Likelihood ratio test Model 1: mu Model 2: mr #Df LogLik Df Chisq Pr(>Chisq) 1 8 -84.407 2 6 -86.430 -2 4.0473 0.1322 Likelihood ratio test Model 1: OLS (no inefficiency) Model 2: Error Components Frontier (ECF) #Df LogLik Df Chisq Pr(>Chisq) 1 5 -104.907 2 8 -84.407 3 41 2.298e-09 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Likelihood ratio test Model 1: OLS (no inefficiency) Model 2: Error Components Frontier (ECF) #Df LogLik Df Chisq Pr(>Chisq) 1 5 -104.91 2 6 -86.43 1 36.953 6.051e-10 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.