[R-lang] Re: Investigating random slope variance

[T. Florian Jaeger]

Hi Titus,

shrinkage has larger effects on cells with

a) means further away from the predicted marginal mean
b) fewer cells counts.

A good paper to see that is Kliegl et al 2010. I also have some
demonstration of this effect in my lmer intro slides (see a recent blog
post on the HLP lab blog). Note that you might see deviation away from the
marginal mean, because of correlations between the grouping identity (e.g.,
item) and other fixed effects in the model. I don't recall whether you had
other fixed effects predictors in your model? If so, that could also be the
reason for estimates of the random effect correlations.

As far as I know shrinkage does not enforce / bias towards normality of
BLUPs.

I hope of this is helpful.

florian


On Fri, Apr 4, 2014 at 11:20 AM, Titus von der Malsburg
<malsburg@posteo.de>wrote:

>
> On 2014-04-04 Fri 05:10, T. Florian Jaeger <tiflo@csli.stanford.edu>
> wrote:
> > I would be careful making anything out of this. The BLUP estimates of the
> > random effects (and, I assume, their distribution) are affected by
> > shrinkage, which is often a desirable (conservative) feature, although it
> > will make differences appear smaller. So, it's not surprising that the
> > fixed effect model mirrors the empirical means more closely. That doesn't
> > mean though that it's the better model to draw conclusion from (about
> those
> > differences).
>
> Florian, your comment is spot on.  Here is a plot showing the effect of
> shrinkage in my data set:
>
>     http://users.ox.ac.uk/~sjoh3968/R/effect_of_shrinkage.png
>
> Unfilled circles show the empirical mean reading times and differences
> between conditions, one circle for each item.  The dots show the BLUP
> estimates for each item.
>
> The difference is fairly dramatic.  I assumed that shrinkage would pull
> all data points to the mean with the same force (I have the same amount
> of data for all items).  If that were the case, the ordering of items
> would be preserved.  However, shrinkage affects the individual items in
> quite different ways, and some items are even pushed away from the
> overall means (1, 5, 7, 8, 9, 10, 13, 14, 35) effectively expanding a
> subset of the estimates instead of shrinking them.
>
> I must say that I find it hard to swallow that two seemingly valid ways
> to analyze the data (item as random effect or fixed effect) yield
> results that are so different.
>
> Another observation: in the BLUP estimates, the correlation of
> intercepts and slopes seems to be much higher than in the raw data.  The
> correlation of the estimated random intercepts and slopes is -0.86. (The
> summary of the model reports -0.62.)  The correlation of the empirical
> item means and differences is only -0.4.  Why does lmer believe in such
> a high correlation?
>
>   Titus
>
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