Mixed model variance estimates

#1
Hello,
With the mixed model
y_ij = mu + alpha_i + epsilon_ij
where alpha_i a random effect with distribution assumed normal and epsilon_ij is also assumed normal
is it reasonable to estimate the total variance using the sample variance
1/(n-1)*sum(yij - mu)^2
where mu is the overall mean, or is it best to use something like maximum likelihood estimation?
Thanks!
- Clark