Unrestricted model: A mixed model (i.e., with random and fixed factors) is termed unrestricted if a random factor is allowed to have fixed cross factors amongst its components of variation estimated in the population. This freedom influences the choice of error Mean Square for random effects. It is generally used for unbalanced designs analysed with a General Linear Model. Balanced and orthogonal designs can be analysed with a restricted model.
Doncaster, C. P. & Davey, A. J. H. (2007) Analysis of Variance and Covariance: How to Choose and Construct Models for the Life Sciences. Cambridge: Cambridge University Press.