[R-sig-ME] Refitting model with ML -- why search for optimal theta again?

[Christoph Huber]

Hi Jake and Cesko,

You answer, Jake, triggered a follow-up question:

> 
>> why can't I simply [...] take the already-found optimal θ values and plug
>> them into the ML formula? Why do we need to search for the optimal θ 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 θ
> estimates. The statistical theory underlying the likelihood ratio test only
> holds for ML estimates of θ, 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>



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