




Hello Jarrod,
Thank you for your response. Your answer does help somewhat, but I think my main difficulty is translating between the algebraic representation of the model in MLwiN and the formula syntax of MCMCglmm. The user manual for the latter does not elaborate much on the 'rcov' argument, unfortunately; and I have trouble understanding its relation to the specification of random effects on the individual level in the 'random' argument. 
I have created a more simple model in MLwiN to provide a better learning example: https://dl.dropboxusercontent.com/u/18527706/mcmc-modexample.png
 To clarify, x0 is the vector of 1's (the constant), x1 is a dummy variable pertaining to the fixed part only, and x2 is a continuous variable. My research question is whether individual-level variance is dependent on x2. To keep things simple I only include the random intercept on the country level. 
Now, on SO (http://stats.stackexchange.com/questions/83148/specifying-a-multilevel-model-in-mcmcglmm-r-that-is-heteroskedastic-at-level) it has been suggested that the call for this model could be as follows: 
MCMCglmm(y~x1+x2, random=~us(1):country + us(1+x2):individual,
                  rcov=~us(x2):units, data=data,
                  prior=prior)
Would that be correct? What would be the difference for model with and without the 'rcov' option? 
Unfortunately, the model does not converge in MCMCglmm, so I cannot compare based on the estimates. In MLwiN I had to use hierarchical clustering for the model to converge, is that functionality also present in MCMCglmm? 

Thank you!
Kind regards,Maxim



> Date: Thu, 6 Feb 2014 15:32:31 +0000
> From: j.hadfield@ed.ac.uk
> To: kovla123@hotmail.com
> CC: r-sig-mixed-models@r-project.org
> Subject: Re: [R-sig-ME] MCMCglmm model for heteroskedasticity at level one
> 
> 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@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]]
> >
> > _______________________________________________
> > R-sig-mixed-models@r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >
> >
> 
> 
> 
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