Nested fixed factors in glmer: Error in mer_finalize(ans) : Downdated X'X is not positive definite, 1.

Hello,

I think I would state the question a little bit differently.

Let's consider for instance that you compare a control group to a
treated group on rats, and rats are not the same in the two
groups. The ? rat ? factor is obviously nested in the ? group ? one,
there certainly will be a ? rat ? factor effect, but what I am
interested in is the ? treatment ? factor. If I assume ? rat ? factor
as fixed, then nesting fixed factors makes senses

But, rat factor could be considered as random or fixed. So my way to
reformulate the question would be ? is it possible to imagine an
interesting design in which a ? real ? fixed factor can be nested in
another one ?, the ? real ? fixed factor meaning there is no
alternative to consider it as random --- like if in a group you would
have only male and in the other only female rats. I guess in such a
case, this instead introduces a strong confusion between the two
factors, which is I guess what you meant?

No, going back to the rat: considered as fixed or random for analysis?
IIRC, there is on the FAQ several points of view consider.

Beside the practical one (? is there enough levels to fit a random
effect? ?), the philosophical one is interesting: am I interested in
all rats or only in the one used for the experiment? During one
discussion with one of my masters, he explained to me that if the
experiment is only a proof of concept experiment, one is really
interested in these rats, not all the population, but if one tries to
develop a treatment for curing rats, then one is interested in all
rats. I found this convincing, but I'm open to other points of view to
think further about this.

If accepting that, this would mean that in some cases, nesting fixed
effects makes sense...

And, last, if the coefficients are the same in the two models, the sum
of square decomposition changes. Of course, since they use the same
coefficients, both are obtainable from both models, but with much
efforts...

Best regards,

? 
? Perhaps I am just obtuse (there are those who would say there is
? no "perhaps" about it) but it seems to me that nesting of fixed effects
? makes no sense.
? 
? In the example given below you have in effect a ***single*** factor
? with six levels: a.1, a.2, b.3, b.4, c.5, c.6.  This really means that
? you just have the second "nested" factor with levels 1, 2, 3, 4, 5, 6.
? So just supply the second factor to the formula in the call to glmer()
? and forget about the first factor entirely.  It is redundant when the
? second factor is supplied.
? 
? You *can* use the formula y ~ f1/f2 or equivalently y ~ f1 + f1:f2
? but you'll find that you wind up getting 12 coefficient estimates, six
? of which are "NA".  The values of the six non-NA coefficients will
? be indentical with values of the six coefficient estimate that you get
? from y ~ f2.
? 
?     cheers,
? 
?         Rolf Turner

Emmanuel CURIS
                                emmanuel.curis at parisdescartes.fr

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