[R-sig-ME] [Lme4-authors] Fixing the level 1 residual variance

[Ben Bolker]

On 14-05-02 05:45 PM, Douglas Bates wrote:
> On Fri, May 2, 2014 at 4:23 PM, Ben Bolker <bbolker at gmail.com
> <mailto:bbolker at gmail.com>> wrote:
> 
>     On 14-05-02 03:43 PM, Douglas Bates wrote:
>     > On Fri, May 2, 2014 at 9:23 AM, Charlotte Arndt
>     <arndtch at uni-landau.de <mailto:arndtch at uni-landau.de>
>     > <mailto:arndtch at uni-landau.de <mailto:arndtch at uni-landau.de>>> wrote:
>     >
>     >     Dear Sir / Madam,
>     >     I am analyzing some data by means of multivariate multilevel
>     models
>     >     and want to fix the residual variance on level 1 to zero. In HLM,
>     >     you can do this by fixing the level 1 residual variance (sigma
>     >     square) to a very small value, e.g. 0.00001. Is it possible to
>     >     constrain the level 1 residual variance with lme4? It would be
>     >     great, if I could use lme4 for my analyses. Thanking you in
>     advance.
>     >
>     >
>     > I forget how the "levels" are numbered in the multilevel modeling
>     > literature but as you say "residual variance" I imagine you are
>     > referring to the variance of the conditional distribution of the
>     > response given the random effects.  The way the model is defined
>     and fit
>     > in the lme4 package the covariance matrix of the random effects is
>     > defined relative to this variance.  In other words it would not be
>     > possible to fit the model in the way you describe.
>     >
>     > Actually I can't imagine how such a model could make sense.  Where
>     does
>     > the variability in the conditional distribution get absorbed?
> 
> 
>       Actually, this can be done with blme.   See
> 
> 
> But what does it mean?  What model is being fit? 

   This is essentially the same model that is being fitted when one
computes the likelihood profile for the residual variance; that is, the
scaled deviance is computed on the basis of the theta parameters, then
the deviance is computed on the basis of the specified residual variance.

 code from devfun2:

 thpars <- Sv_to_Cv(pars,n=vlist,s=sigma)
 .Call(lmer_Deviance, pp$ptr(), resp$ptr(), thpars)
 sigsq <- sigma^2
 pp$ldL2() - ldW + (resp$wrss() + pp$sqrL(1))/sigsq +
                    n * log(2 * pi * sigsq)

where ldW  is the sum of the log weights (if any)

  Makes sense to me ...