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Consider first the case of a single parameter, θ. Let l be the log-likelihood function for θ and let x be the data. The score is the derivative of the log-likelihood function with respect to θ:
The test statistic is asymptotically Chi-square distribution with k degrees of freedom. Here k is the number of unbounded parameters.
Let be the value of where the algorithm terminates. Note that the relative gradient evaluated at is the score test statistic. A p-value is calculated using a Chi-square distribution with k degrees of freedom. This p-value gives an indication of whether the value of the unknown MLE is consistent with . The number of unbounded parameters listed in the Random Effects Covariance Parameter Estimates report equals k.

Help created on 3/19/2020