[R-sig-ME] MCMCglmm model for heteroskedasticity at level one

[Jarrod Hadfield]

Hi Maxim,

I'm not very clear about the model you want to fit. If we take your  
stackexchange model, do you wish to fit a random intercept-slope model  
(with the covariate x1) at the country level and the residual level?

If so, then random=~us(1 + x1):country fits the country  
intercept/slopes (with covariance between them). The between country  
variance is quadratic in x1:

V_i + 2*x1*V_is + (x1^2)*V_s

where V_i is the variance in intercepts, V_s is the variance in slopes  
and V_is is covariance between intercepts and slopes.

This change in variance with respect to x1 is where the information  
comes from for estimating level-1 heterogeneity. If you fit (assuming  
x1 is always positive):

idh(sqrt(x1)):units

in the *random* effect part of the model, and leave the residual part  
as the default units, then the level-1 variance is linear in x1:

Vu+sqrt(x1)^2*Vs = Vu+x1*Vs

where Vu is the units variance, and Vs is the variance associated with  
the random `slopes' in the random effect part of the model.  Clearly  
you could transform x1 differently.

Not sure if this is useful?

Jarrod











Quoting Maxim Kovalenko <kovla123 at hotmail.com> on Wed, 29 Jan 2014  
15:34:08 +0100:

>
>
> Dear all,
>
> I kindly ask the help of this community with the following issue. My  
> research question is about individual-level variance of employment  
> stability in several European countries. The number of countries is  
> small (N=13), therefore MCMC is a more proper estimation method than  
> ML. Variance on the country level doesn't interest me as much, but I  
> do have to take it into account of course.
> When I run my model in R/MLwiN via R2MLwiN package, its formula is  
> specified as approximately follows:
> y ~ (0|cons+careertype+gender) + (1|cons+careertype) + (2|cons)
> To decode: there fixed part contains the intercept, career type  
> (more or less job mobility) and gender. Random effects on the  
> individual level entail the constant and career type, whereas random  
> effects on level to include only the constant. Therefore it is a  
> random intercept model with heteroskedasticity on level one. For  
> more details on this model please see  
> http://stats.stackexchange.com/questions/83148/specifying-a-multilevel-model-in-mcmcglmm-r-that-is-heteroskedastic-at-level, I have included a screenshot there to give a better  
> idea.
> Is it possible at all to estimate a similar model in MCMCglmm? I  
> cannot figure out how to specify variance at level one to be  
> dependent on one of the predictors.
> Thank you so much in advance for any tips!
> Kind regards,Maxim
> 	[[alternative HTML version deleted]]
>
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>



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