# Likelihood Ratio Test

$\displaystyle{ X^2 = 2 (LL_u - LL_r) }$
$\displaystyle{ LL_u }$ is the log-likelihood of the unrestricted model estimated using the Calibrated Weight,
$\displaystyle{ LL_r }$ is the log-likelihood of the restricted model estimated using the Calibrated Weight,
$\displaystyle{ p \approx \Pr(\chi^2_{k_u - k_r} \ge X^2) }$, and
$\displaystyle{ k_u }$ and $\displaystyle{ k_r }$ are the number of parameters of the unrestricted and restricted models respectively.