The test statistic is:
\[\begin{align} X^2 = 2 (LL_u - LL_r)\end{align}\]
where:
\(LL_u\) is the log-likelihood of the unrestricted model estimated using the Calibrated Weight,
\(LL_r\) is the log-likelihood of the restricted model estimated using the Calibrated Weight,
\(p \approx \Pr(\chi^2_{k_u - k_r} \ge X^2)\), and
\(k_u\) and \(k_r\) are the number of parameters of the unrestricted and restricted models respectively.