The “Fit Statistics” table provides some statistics about the estimated mixed model. Expressions for times the log likelihood are provided in the section Estimating Covariance Parameters in the Mixed Model. If the log likelihood is an extremely large number, then PROC HPLMIXED has deemed the estimated
matrix to be singular. In this case, all subsequent results should be viewed with caution.
In addition, the “Fit Statistics” table lists three information criteria: AIC, AICC, and BIC. All these criteria are in smaller-is-better form and are described in Table 6.8.
Table 6.8: Information Criteria
Criterion |
Formula |
Reference |
---|---|---|
AIC |
|
Akaike (1974) |
AICC |
|
Hurvich and Tsai (1989) |
Burnham and Anderson (1998) |
||
BIC |
|
Schwarz (1978) |
Here denotes the maximum value of the (possibly restricted) log likelihood;
is the dimension of the model; and
equals the number of effective subjects as displayed in the “Dimensions” table, unless this value equals 1, in which case
equals the number of levels of the first random effect specified in the first RANDOM statement or the number of levels of the interaction of the first random effect with noncommon subject effect specified in
the first RANDOM statement. If the number of effective subjects equals 1 and you have no RANDOM statements, then
equals the number of valid observations for maximum likelihood estimation and
for restricted maximum likelihood estimation, where
equals the rank of
. For AICC (a finite-sample corrected version of AIC),
equals the number of valid observations for maximum likelihood estimation and
equals the number of valid observations for restricted maximum likelihood estimation, unless this number is less than
, in which case it equals
. When
, the value of the BIC is
. For restricted likelihood estimation,
equals
, the effective number of estimated covariance parameters. For maximum likelihood estimation,
equals
.