RL30 Restricted and Unrestricted Models in the Domain of Mixed Models
*Jennifer Smith, Geron Corporation 


There has been controversy about whether the restricted or unrestricted model is more appropriate but very few people are aware of the implications of this choice. SAS implements the unrestricted model whereas many textbooks describe the restricted model and do not even discuss the unrestricted model. There are a few people with strong opinions on either side and I think it’s an issue that people should be aware of and discuss more openly. The implications for this choice are huge. Consider the textbook case of a mixed model analysis of variance with 1 fixed factor and 1 random factor. The Expected Mean Squares would suggest that the appropriate error term for the fixed factor is the interaction term whereas the appropriate error term for the random factor is the error mean squares. In contrast, the unrestricted model results in Expected Mean Squares that suggest the interaction term should be the denominator for both.