I'm the author of the ez package for R, and I'm working on an update to include automatic computation of likelihood ratios (LRs) in the output of ANOVAs. The idea is to provide a LR for each effect that is analogous to the test of that effect that the ANOVA achieves. For example, the LR for main effect represents the comparison of a null model to a model that includes the main effect, the LR for an interaction represents the comparison of a model that includes both component main effects versus a model that includes both main effects and their interaction, etc.
Now, my understanding of LR computation comes from Glover & Dixon (PDF), which covers basic computations as well as corrections for complexity, and the appendix to Bortolussi & Dixon (appendix PDF), which covers computations involving repeated-measures variables. To test my understanding, I developed this spreadsheet, which takes the dfs & SSs from an example ANOVA (generated from a 2*2*3*4 design using fake data) and steps through the computation of the LR for each effect.
I would really appreciate it if someone with a little more confidence with such computation could take a look and make sure I did everything correctly. For those that prefer abstract code, here is the R code implementing the update to ezANOVA() (see esp. lines 15-95).