llratio: Calculation of likelihood ratios for nested models
Description
Calculates the likelihood ratio and p-value from a chi-square distribution for two nested models.
Usage
llratio(objX, objY)
Arguments
objX
Either a value of class logLik or a model for which logLik can be applied.
objY
Either a value of class logLik or a model for which logLik can be applied.
Value
A list containing the following items:
ratio
the likelihood ratio statistic.
df
the change in parameters.
p.value
the p-value from a \(\chi^2\) distribution. See Details.
Details
The likelihood ratio statistic is $$LR = \frac{f(X, \hat{\phi}, \hat{\psi})}{f(X, \phi, \hat{\psi_0})}$$
The usual test statistic is $$\Lambda = 2 \cdot (l(\hat{\phi}, \hat{\psi}) - l(\phi, \hat{\psi_0}))$$
Following the large sample theory, if \(H_0\) is true, then $$\Lambda \sim \chi_p^2$$