Likelihood Ratio test for Equation Systems
Testing linear hypothesis on the coefficients of a system of equations by a Likelihood Ratio test.
## S3 method for class 'systemfit' lrtest( object, ... )
object |
a fitted model object of class |
... |
further fitted model objects of class |
lrtest.systemfit consecutively compares
the fitted model object object
with the models passed in ....
The LR-statistic for sytems of equations is
LR = T \cdot ≤ft( log ≤ft| \hat{ \hat{ Σ } }_r \right| - log ≤ft| \hat{ \hat{ Σ } }_u \right| \right)
where T is the number of observations per equation, and
\hat{\hat{Σ}}_r and \hat{\hat{Σ}}_u are
the residual covariance matrices calculated by formula "0"
(see systemfit)
of the restricted and unrestricted estimation, respectively.
Asymptotically, LR has a χ^2
distribution with j degrees of freedom
under the null hypothesis
(Green, 2003, p. 349).
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".
Arne Henningsen arne.henningsen@googlemail.com
Greene, W. H. (2003) Econometric Analysis, Fifth Edition, Prentice Hall.
systemfit, lrtest
(package "lmtest"),
linearHypothesis.systemfit
data( "Kmenta" )
eqDemand <- consump ~ price + income
eqSupply <- consump ~ price + farmPrice + trend
system <- list( demand = eqDemand, supply = eqSupply )
## unconstrained SUR estimation
fitsur <- systemfit( system, "SUR", data = Kmenta )
# create restriction matrix to impose \eqn{beta_2 = \beta_6}
R1 <- matrix( 0, nrow = 1, ncol = 7 )
R1[ 1, 2 ] <- 1
R1[ 1, 6 ] <- -1
## constrained SUR estimation
fitsur1 <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = R1 )
## perform LR-test
lrTest1 <- lrtest( fitsur1, fitsur )
print( lrTest1 ) # rejected
# create restriction matrix to impose \eqn{beta_2 = - \beta_6}
R2 <- matrix( 0, nrow = 1, ncol = 7 )
R2[ 1, 2 ] <- 1
R2[ 1, 6 ] <- 1
## constrained SUR estimation
fitsur2 <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = R2 )
## perform LR-test
lrTest2 <- lrtest( fitsur2, fitsur )
print( lrTest2 ) # acceptedPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.