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.
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# 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 )