[R-sig-ME] quick question regarding your "residual" command for your lmer command - please help me

[Douglas Bates]

Again, I will defer to the R-Sig-Mixed-Models mailing list.

On Wed, Aug 29, 2012 at 6:52 AM, Yugo Nakamura <yugonakamura25 at gmail.com> wrote:
> To Professor Bates,
>
> Thank you for your reply and for adding me on to the list.  I will check
> your commands again.
>
> To shorten my question, I essentially get confused when researches study the
> level 1 residuals pooled across the groups and not within groups separately.
>
> I just do not see why and what this analysis entail or suggest for the
> multilevel analysis and assumptions that do not take the grouping into
> consideration.
>
> Your thoughts and expertise will be deeply appreciated.
>
> Above
>
>
> On Tue, Aug 28, 2012 at 11:25 PM, Douglas Bates <bates at stat.wisc.edu> wrote:
>>
>> I have taken the liberty of cc:'ing the
>> R-SIG-Mixed-Models at R-project.org mailing list on this reply.  Many of
>> those who read that list will be able to help you, often more quickly
>> than I am able to do.
>>
>> Your question is a bit confusing in that you say you are using lmer
>> and then quote the documentation for residuals.lme.  The nlme package,
>> containing lme and supporting methods, and the lme4 package,
>> containing lmer, are different.  You should not expect the
>> documentation for one to apply to the other.
>>
>> On Tue, Aug 28, 2012 at 8:20 AM, Yugo Nakamura <yugonakamura25 at gmail.com>
>> wrote:
>> > To Professor Bates,
>> >
>> > I am terribly sorry for this impromptu email.  I have been using your
>> > lmer
>> > command for my dissertation (at the University of Washington) but I am
>> > having some difficulty to fully understand the outputs.  Your expertise
>> > will
>> > be deeply appreciated.  I would like to thank you in advance for your
>> > time.
>> >
>> > My question pertains to the Residual command of the lmer and the
>> > variance
>> > estimates of the level 1 residuals in the  lmer output.  I am not
>> > certain as
>> > to how these figures are calculated and what these estimates really
>> > imply.
>> >
>> > The definition of the residual are as follow.
>> >
>> > residuals.lme {nlme}
>> > The residuals at level i are obtained by subtracting the fitted levels
>> > at
>> > that level from the response vector (and dividing by the estimated
>> > within-group standard error, if type="pearson"). The fitted values at
>> > level
>> > i are obtained by adding together the population fitted values (based
>> > only
>> > on the fixed effects estimates) and the estimated contributions of the
>> > random effects to the fitted values at grouping levels less or equal to
>> > i
>> >
>> > http://stat.ethz.ch/R-manual/R-patched/library/nlme/html/residuals.lme.html
>> >
>> > Is this definition saying that, the residuals are defined by subtracting
>> > the
>> > fitted values from the fixed effects and the empirical Bayes estimate of
>> > the
>> > level 2 residuals?
>> >
>> > I calculated the variance of these residuals and it gave me the same
>> > estimate of the variance estimate of the "Residuals" (level 1) in the
>> > lmer
>> > output.
>> >
>> > But my question then is, is this variance estimate the "within group
>> > variance" explained in different textbooks of multilevel analysis?  But
>> > if
>> > so I find it slightly too big..  I have learned that within group
>> > variance
>> > are normally distributed with mean zero and constant variance for each
>> > and
>> > every group.   That is, the variance is calculated within/for each and
>> > every
>> > group and this variance is constant across all groups (quite strong
>> > assumption).
>> >
>> > But the variance estimate and the residual command above seems to give
>> > us
>> > the pooled residuals regardless of the groups.  That is, the variance is
>> > the
>> > estimate of the variance across all the residuals regardless/ignoring of
>> > the
>> > group.   Is this so?   If this is the case, isn't this variance the sum
>> > of
>> > all the within group variances (simply because the sum of normal
>> > distribution is also a normal distribution with the mean and variance
>> > also
>> > summed)?  Thus, to get a within group variance (for each group) I should
>> > divide your Residual variance estimate by the number of groups?
>> >
>> > I hope I was able to make sense.  It will be great if you could share me
>> > your expertise.    If there is a link that describes all the details of
>> > your
>> > command, that will be very helpful as well.
>> >
>> > Thank you so much in advance for your time and cooperation!
>> >
>> > yours,
>> >
>> > Yugo Nakamura
>> >
>> >
>> >
>> >
>
>