Description of Fit Statistics Report uses the following notation:
Here y is the nx1 vector of observations, is a vector of fixed-effect parameters, γ is a vector of random-effect parameters, and ε is a vector of errors.
The vectors γ and ε are assumed to have a multivariate normal distribution where
and p is the rank of X. Use the residual likelihood only for model comparisons where the fixed effects portion of the model is identical.
where k is the number of estimated parameters (including intercept and variance and covariance terms in the model) and n is the number of observations in the data set. See Burnham and Anderson (2004) and Akaike (1974).
-2loglikelihood + k log(n)
where k is the number of parameters and n is the sample size.
If there are problems with model convergence, a warning message is displayed below the fit statistics. Convergence Score Test shows the warning that suggests the cause and possible solutions to the convergence issue. It also includes a test of the relative gradient at the final iteration. If this test is non-significant, the model might be correct but not fully reaching the convergence criteria. In this case, consider using the model and results with caution. For details, see Convergence Score Test.
Convergence Score Test
a t test for the hypothesis that the estimate equals zero
Tests whether the true value of the parameter is zero. The t Ratio is the ratio of the estimate to its standard error. Given the usual assumptions about the model, the t Ratio has a Student’s t distribution under the null hypothesis.
Lists the p-value for a two-sided test of the t Ratio.
For each random effect in the model, this report gives an estimate known as the best linear unbiased predictor (BLUP), its standard error, and a Wald-based confidence interval.
Shows a significance test for each fixed effect in the model. The test for a given effect tests the null hypothesis that all parameters associated with that effect are zero. An effect might have only one parameter as for a single continuous explanatory variable. In this case, the test is equivalent to the t test for that term in the Fixed Effects Parameter Estimates report. A nominal or ordinal effect can have several associated parameters, based on its number of levels. The effect test for such an effect tests whether all of the associated parameters are zero.
Gives the computed F ratio for testing that the effect is zero.
Gives the p-value for the effect test.