Hi Jake and Cesko, You answer, Jake, triggered a follow-up question:
why can't I simply [...] take the already-found optimal ? values and plug them into the ML formula? Why do we need to search for the optimal ? values again? even if the values found by ML differ from those found by REML, shouldn't the REML values be preferred?
Optimizing the likelihood vs. the REML criterion leads to different ? estimates. The statistical theory underlying the likelihood ratio test only holds for ML estimates of ?, not REML estimates. You can compute the likelihood value for the REML estimates, as you do in your code example, but this doesn't change the fact that they are REML estimates and not ML estimates.
I thought it is valid to test for random slope correlations with the anova command while setting refit = F. Say, we have two lmer models with a 2-level factor "a? and a random factor "A?. Say, these two models differ only in their random slope correlations, like that: remlfit1 <- lmer(y ~ a + (1 | A) + (0 + a | A ), data = mydata) remlfit2 <- lmer(y ~ a + (a | A ), data = mydata) Is it then valid to test for the correlation parameter between "(Intercept)? and "a? with: anova(remlfit1, remlfit2, refit = F) ? The response to Cesko made me doubt this approach. Many thanks, Christoph ? Dr. Christoph Huber-Huber Center for Mind/Brain Sciences (CIMeC) University of Trento Corso Bettini 31 38068 Rovereto (TN), Italy e-mail: christoph.huberhuber at unitn.it <mailto:christoph.huberhuber at unitn.it>