The HPLMIXED Procedure

Fit Statistics

The "Fit Statistics" table provides some statistics about the estimated mixed model. Expressions for $-2$ 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 $\mb{V}$ 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 9.9.

Table 9.9: Information Criteria

Criterion

Formula

Reference

AIC

$-2\ell + 2d$

Akaike (1974)

AICC

$-2\ell + 2d n^*/(n^*-d-1)$

Hurvich and Tsai (1989)

   

Burnham and Anderson (1998)

BIC

$-2\ell + d \log n$ for $n>0$

Schwarz (1978)


Here $\ell $ denotes the maximum value of the (possibly restricted) log likelihood; d is the dimension of the model; and n equals the number of effective subjects as displayed in the "Dimensions" table, unless this value equals 1, in which case n 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 n equals the number of valid observations for maximum likelihood estimation and $n-p$ for restricted maximum likelihood estimation, where p equals the rank of $\bX $. For AICC (a finite-sample corrected version of AIC), $n^*$ equals the number of valid observations for maximum likelihood estimation and $n-p$ equals the number of valid observations for restricted maximum likelihood estimation, unless this number is less than $d+2$, in which case it equals $d+2$. When $n=0$, the value of the BIC is $-2\ell $. For restricted likelihood estimation, d equals q, the effective number of estimated covariance parameters. For maximum likelihood estimation, d equals $q+p$.