compare arbitrary (non-nested) linear models

When comparing two unrelated models, is it possible to determine which model better explains the data? It seems compare tests whether the altlme better explains the actual data (relative to lme) than random data generated by lme. So compare(model1, model2) and compare(model2, model1) can both be significant. Thanks

Answer 1

[Alexis Villacis]

you can use AIC and BIC

also if the number of parameters is the same, then you can do Likelihood dominance test