Akaike Information Criterion (AIC)
The Linear Mixed Effects object uses the smaller-is-better form of Akaike’s Information Criterion:
AIC = –2LR + 2s
where:
LR is the restricted log-likelihood function evaluated at the final fixed parameter estimates 
and the final variance parameter estimates 
.
s is the rank of the fixed effects design matrix X plus the number of parameters in q (i.e., s = rank(X) + dim(q)).
Schwarz Bayesian Criterion (SBC)
The Linear Mixed Effects object uses the smaller-is-better form of Schwarz’s Bayesian Criterion:
SBC = –2LR + slog(N – r)
where:
LR is the restricted log-likelihood function evaluated at the final estimates 
and 
.
N is the number of observations used.
r is the rank of the fixed effects design matrix X.
s is the rank of the fixed effects design matrix X plus the number of parameters in q (i.e., s = rank(X) + dim(q)).
Note: AIC and SBC are only meaningful during comparison of models. A smaller value is better, negative is better than positive, and a more negative value is even better.
Hessian eigenvalues
The eigenvalues are formed from the Hessian of the restricted log likelihood. There is one eigenvalue per variance parameter. Positive eigenvalues indicate that the final parameter estimates are found at a maximum.