[R-sig-ME] [lme4 package] Does the order of rows(trials) in a data frame (long format) affect the results of the lmer model (maybe somehow)?

[Emmanuel Curis]

Hi,

Does it really change the lineary algebra, or does it change its
numerical implementation in computers? Since computer addition is not
commutative, that would explain ordering effects...

> 1 + 1e-15 - 1
[1] 1.110223e-15
> 1 - 1 + 1e-15
[1] 1e-15

> version$version.string
version.string R version 3.0.1 (2013-05-16)

In other words, may be computation with such big matrice can lead to
rounding errors that add-up quickly if matrices are somehow
ill-conditionned?

I'm not familiar with this field, but for instance I noticed that when
you try to compute linear model matrices, coefficients and so one
using the projection formula, even with as few as a tenth of values,
values that should be 0 in the projection matrices (and especially
inverses) are quickly around ~10^-16 and after that, things can get
very bad quiclky, which is solved by adding a « cleaning » of matrices
such as m[ abs( m ) < 1e^-10 ] <- 0...

Of course, the above approach is very very dirty and inefficient and
has only pedagogical interest, but are the more subtle algorithm
robust enough on that aspect for such big matrices?

On Wed, Jan 07, 2015 at 11:12:55PM -0500, Ben Bolker wrote:

«   We have seen one case where the order does change the results slightly
« (https://github.com/lme4/lme4/issues/262) , and have a
« not-yet-reproducible report (see prev link) of a case where the order
« changes the standard error estimates considerably more.  That the
« order affects the results is surprising, but believable; I/we haven't
« had a chance yet to dig through and figure out how the ordering could
« change the linear algebra, but clearly it does.

-- 
                                Emmanuel CURIS
                                emmanuel.curis at parisdescartes.fr

Page WWW: http://emmanuel.curis.online.fr/index.html