[R-sig-ME] Random effects correlations and factor reference levels

[paul debes]

Hi Chris,

do you really need the treatment contrast?
I think the results based on the treatment contrasts for the random  
effects are more difficult to interpret than what you suggested (I can't  
interpret them either). If you simply remove the intercept: "random =  
~Machine-1|Worker" your interpretations of the worker-score correlations  
between machine levels hold and you get the actual variance estimates for  
each level of machine.

Best,
Paul




On Tue, 13 Oct 2015 16:57:32 +0300, Christopher Knight  
<Chris.Knight at manchester.ac.uk> wrote:

> I am fitting mixed effects models where there is a random effect which  
> acts differently on each level of a factor, much as in the Machines  
> example from the nlme package:
>
> library(nlme)
>
>> M1 <- lme(fixed = score ~ Machine, random = ~Machine|Worker,  
>> data=Machines)
>> VarCorr(M1)
> Worker = pdLogChol(Machine)
>             Variance   StdDev    Corr
> (Intercept) 16.6405306 4.0792806 (Intr) MachnB
> MachineB    34.5466908 5.8776433  0.484
> MachineC    13.6150244 3.6898543 -0.365  0.297
> Residual     0.9246296 0.9615766
>
> I was interpreting these correlations to mean that the estimate of  
> workers’ scores on Machine B (or more precisely their BLUPS, interpreted  
> as something like their residuals from the average on Machine B) are  
> weakly positively correlated with their scores on Machine C (r=0.297).  
> Because Machine A is the reference level of the factor ‘Machine’ (with  
> treatment contrasts), I was also interpreting the ‘(Intercept)’ to  
> represent Machine A, i.e. that the scores of the workers on Machine A  
> are somewhat positively correlated with their scores on Machine B  
> (r=0.484), but negatively with their scores on Machine C (r=-0.365).
>
> If this were true, I would expect these conclusions to be robust to  
> exactly which machine is the reference level in the contrasts for the  
> Machine factor, but apparently they are not:
>
>> Machines$Machine <- relevel(Machines$Machine, ref = "B")
>> M2 <- update(M1)
>> VarCorr(M2)
> Worker = pdLogChol(Machine)
>             Variance   StdDev    Corr
> (Intercept) 74.3956398 8.6252907 (Intr) MachnA
> MachineA    34.5466902 5.8776433 -0.910
> MachineC    35.2950235 5.9409615 -0.882  0.805
> Residual     0.9246296 0.9615766
>
> What is going on here/what am I misinterpreting?
>
> As expected, these two models appear to be equivalent by anova(M1,M2),  
> yet the correlation among workers between machines A and B appears to be  
> strongly negative in the second case (r = -0.91), where it seems  
> moderately positive in the first case (r=0.484) and intervals() on the  
> two models suggests no overlap of (admittedly pretty broad) confidence  
> intervals in this case. Add to that the differences in the estimated  
> variance components/standard deviations – each model has an identical  
> residual, but very different individual values (that for Machine C going  
> from 13.6 to 35) and totals; at the same time the estimate for the  
> variance among workers on Machine B in model M1 (34.5466908)  is  
> suspiciously similar (albeit not quite identical) to the estimate for  
> variance among workers on Machine A in model M2 (34.5466902).
>
> The values are pretty much the same fitting with lmer (though in  
> practice I need the correlation and weights arguments available with  
> lme), which makes it feel like a problem with my interpretation. Or is  
> it really just a case of too little data to resolve such ±subtle  
> parameters clearly?
>
> Dropping the fixed effect doesn’t make things much better and, on the  
> models I am running in anger, there is more data and the differences are  
> even more pronounced. It looks a bit like this issue:  
> http://stats.stackexchange.com/questions/82102/changing-reference-level-for-contrasts-changes-results-in-r-3-0-2-lme4-1-1-2-vs
> which was framed in terms of versions but, given that I get very similar  
> issues using nlme and lme4, it doesn’t seem likely to be a version issue  
> here (albeit I don’t have old versions immediately to hand to test this  
> on).
>
> Any insights much appreciated,
>
> Chris
>
> running nlme_3.1-122 in R 3.2.2 on OS X 10.10.5
>
>
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-- 
Paul Debes
DFG Research Fellow
University of Turku
Department of Biology
Itäinen Pitkäkatu 4
20520 Turku
Finland