# lrtest.systemfit: Likelihood Ratio test for Equation Systems

### Description

Testing linear hypothesis on the coefficients of a system of equations by a Likelihood Ratio test.

### Usage

 1 2 ## S3 method for class 'systemfit' lrtest( object, ... )

### Arguments

 object a fitted model object of class systemfit. ... further fitted model objects of class systemfit.

### Details

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).

### 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".

### References

Greene, W. H. (2003) Econometric Analysis, Fifth Edition, Prentice Hall.