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Consider the following data set (given at the end of the question):

library(ggplot2)
ggplot(r,aes(x=f1,y=y,color=f2))+geom_boxplot()

enter image description here

I would like to model heterogeneity of variance for group G1 and G2 i.e. $$ y_{i}= \alpha_{f_1(i)}+\beta_{f_2(i)}+\epsilon_{i,f_1(i)} $$

$$ \epsilon_{i,f_1(i)} \sim N(0,\sigma^2_{f_1(i)}) $$

I understand that I can deal with this situation using gls in the following way (is this right?):

library(nlme)
gls(y~f1+f2,data=r,weights=varIdent(form=~1|f1))

Can I model the same using lme4 ?

Dataset:

    r=structure(list(y = c(-1.1316848130928, -0.396385594646378, 0.589690880032218, 
1.52321001912788, 0.390206765971789, -0.509282412635648, -0.725329736745712, 
2.50210743407235, 0.677569006955778, 0.546293721541106, 0.928337039971113, 
0.335722723953903, 1.09606155785715, 0.272679200873732, 1.04494107739702, 
-0.233868295453055, -1.73712355434937, 0.66453596677335, 0.301670616352279, 
1.98486059866201, 1.55151382625759, 1.32067952567205, 0.0530713533439635, 
-5.68894059915804, -0.62963609076646, 4.60610931183804, -2.89621567919518, 
-1.56512624418944, -1.10723477595581, 2.14274736934952, 0.146245941642455, 
3.44615219319318, 5.58531974836602, 4.37660570630301, 2.49834207960278, 
2.05485687567195, 4.49542423692705, 3.75639698016655, 3.26594495479936, 
-0.153851788423289), f1 = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L), .Label = c("G1", "G2"), class = "factor"), f2 = structure(c(1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L), .Label = c("C1", "C2"), class = "factor")), .Names = c("y", 
"f1", "f2"), row.names = c(NA, -40L), class = "data.frame")
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  • 2
    $\begingroup$ In general, no. But you can fit a mixed model including a variance structure with lme. $\endgroup$ – Roland Dec 8 '17 at 9:37
  • $\begingroup$ @Roland. Does it mean that it is possible when the variance structure is know e.g. sigma_{G1} = 2 sigma_{G2} ? $\endgroup$ – peuhp Jan 18 '18 at 10:23
  • $\begingroup$ where the 2 is a coefficient that is estimated by the model. But you can also model the variance in dependence of a continuous covariate. $\endgroup$ – Roland Jan 18 '18 at 13:09
  • $\begingroup$ @Roland thanks for your reply. But if the coefficient "2" is estimated, I do not see why the model in my question cannot be written for lmer ? can you help me to understand ? can you provide an example ? thanks $\endgroup$ – peuhp Jan 19 '18 at 9:03
  • $\begingroup$ lme4 doesn't offer facilities for fitting variance heterogeneity models. You are welcome to contribute code to lme4 that implements this. $\endgroup$ – Roland Jan 19 '18 at 10:23

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