# Likelihood Ratio test for Stochastic Frontier Models

### Description

Testing parameter restrictions in stochastic frontier models by a Likelihood Ratio test.

### Usage

1 2 | ```
## S3 method for class 'frontier'
lrtest( object, ... )
``` |

### Arguments

`object` |
a fitted model object of class |

`...` |
further fitted model objects of class |

### Details

If `lrtest.frontier`

is called with only one argument/object
(i.e. argument `...`

is not used),
it compares the fitted model to a corresponding model
without inefficiency (i.e. estimated by OLS).

If `lrtest.frontier`

is called with more than one argument/object
(i.e. argument `...`

is used),
it consecutively compares
the fitted model object `object`

with the models passed in `...`

.

The test statistic is
`2 * ( logLik( mu ) - logLik( mr ) )`

,
where `mu`

is the unrestricted model
and `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.

### Value

An object of class `anova`

,
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 `lrtest`

in package "lmtest".

### Author(s)

Arne Henningsen

### References

Coelli, T.J. (1995), Estimators and Hypothesis Tests for a Stochastic:
A Monte Carlo Analysis, *Journal of Productivity Analysis*,
6, 247-268.

### See Also

`sfa`

, `lrtest`

### Examples

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 <- plm.data( 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 )
``` |

Want to suggest features or report bugs for rdrr.io? Use the GitHub issue tracker. Vote for new features on Trello.