[Lme4-authors] Fixing the level 1 residual variance
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 ...