[R-sig-ME] heteroscedastic model in lme4

[Doran, Harold]

Arrrg, that whole level 1 level 2 thing eats me up. There are random
effects and everything else is just a covariate. Not quite sure what
your data are, but a random slope can account for the non-constant
variance. Just a random intercept is compound symmetry where random
intercept and slope is a more general covariance structure that allows
for the variance to be different over time.



> -----Original Message-----
> From: Rense Nieuwenhuis [mailto:rense.nieuwenhuis at gmail.com] 
> On Behalf Of Rense Nieuwenhuis
> Sent: Thursday, January 15, 2009 8:01 AM
> To: ONKELINX, Thierry
> Cc: Doran, Harold; Alan Cobo-Lewis; r-sig-mixed-models at r-project.org
> Subject: Re: [R-sig-ME] heteroscedastic model in lme4
> 
> Dear all,
> 
> I'm currently working on a similar problem in which I expect 
> the within-group variance to change over years. Of course, in 
> an ideal world correlation structures would be readily 
> available in lme4, but as Thierry already states, this is not 
> the case.
> 
> I have been considering a different approach to solve the 
> problem, based on statements on heteroscedasticity made by 
> Snijders & Bosker (1999, page 119). This only works for 
> heteroscedasticity at the second (or higher) level, and if 
> this heteroscedasticity can be related to an observed variable.
> 
> He argues that the random part of the second level can be defined as:
> U0j + U1j*zj
> "Thus, strange as it may sound, the level-two variable Z 
> formally gets a random slope at level two".
> 
> In my understanding, this would lead to something like:
> 
> glmer(Count ~ A + B + (B|Group), family=poisson)
> 
> assuming that B measures a  'group'-level characteristic.
> 
> I'm still trying to get a firm grasp on the matter, but 
> possibly this solution can help out in certain situations,
> 
> kind regards,
> 
> Rense Nieuwenhuis
> 
> 
> 
> 
> 
> On 15 jan 2009, at 11:13, ONKELINX, Thierry wrote:
> 
> > glmer(Count ~ A + B + (1|Group), family = poisson)
> 
> 
> 
> 
> 
> @book{Snijders:1999,
> 	Author = {Snijders, Tom A.B. and Bosker, Roel J.},
> 	Date-Added = {2009-01-15 13:48:53 +0100},
> 	Date-Modified = {2009-01-15 13:49:35 +0100},
> 	Publisher = {Sage},
> 	Title = {Multilevel Analysis, an introduction to basic 
> and advanced multilevel modelling},
> 	Year = {1999}}
> 
>