[R-lang] trouble with mixed-model

[Roger Levy]

Francisco Torreira wrote:
> Dear Roger and Florian,
> 
> Thanks so much for your comments. A model with random slopes but no
> random intercepts (e.g. (0+type|spk)) also seems to lead to
> singularity. As I said in my previous message, this happens too for a
> model with both random intercept and slop (e.g. (1+type|spk)). I
> understand Roger's suggestion to merge levels 'e' and 'i'. However, if
> I am fitting the model, it's precisely to compare the level means :-)
> 
> I have therefore fitted a model with a random intercept and calculated
> the CI for the level means using Baayen's pvals.fnc().
> I suppose that the CI obtained this way are not equivalent to the ones
> obtained with post-hoc comparison procedures (e.g. TukeyHSD). Does
> anyone have an idea how to do this with a mixed model?  

Dear Francisco,

I don't really know much about the Tukey HSD procedure (can you suggest 
a reference?), but the Bonferroni correction, for example, could be 
applied to the t-test-based p-values returned by pvals.fnc().  The 
MCMC-based confidence intervals are Bayesian confidence intervals and 
thus represent the model's posterior beliefs about the likely parameter 
values, not degree of unlikeliness of seeing the data under the null 
hypothesis.  As such, they don't seem very philosophically compatible 
with something like the Bonferroni correction, which at heart asks the 
question "if my null hypothesis is really true, how many times would I 
expect to get at least one false positive if I conduct multiple tests?". 
   On the other hand, in the simulated-data cases of the Baayen et al. 
paper, the MCMC-based p-values are generally pretty close to the 
p-values you'd want for a classical hypothesis test, so there's nothing 
to stop you in practice from applying the ordinary Bonferroni correction 
to the MCMC-derived p-values.

Hope that is useful. I'd be curious to hear what other people have to 
say about this.

Roger