How should I report results of a likelihood ratio test? I'm using likelihood ratio testing to assess whether a behavioral model is a better description of my data than a simpler (so called restricted) model.

How should results of such statistical tests be reported?
General reporting recommendations such as that of APA Manual apply. One should report exact p-value and an effect size along with its confidence interval. In the case of likelihood ratio test one should report the test's p-value and how much more likely the data is under model A than under model B.

Example: The data is 7.3, 95% CI [6.8,8.1] times more likely under Model A than under Model B. The hypothesis that the data is equally likely under the two models was rejected with p=0.006. 

The above statements already indicate that likelihood ratio test does not tell you which


  model is a better description of my data


as the likelihood is $p(\mathrm{Data}|\mathrm{Model})$ and to learn which model is a better description of the data you need to compute $p(\mathrm{Model}|\mathrm{Data})$.