[R-sig-ME] Vedr. lmer (lme4): % total variance explained by random effect

[Reinhold Kliegl]

There is a recent paper that may give you a start on why this is a
difficult question.

Edwards, L.J. et al. (2008). An R2 statistic for fixed effects in the
linear mixed model.
Statistics in Medicine, 27, 6137-6157.
DOI: 10.1002/sim.3429

Reinhold Kliegl


On Sun, Aug 2, 2009 at 11:27 PM, Liliana Martinez<ltiana_m at yahoo.com> wrote:
> Yes, I hoped too that somebody would answer this question. I read in Baayen (2008, pp.258-259,  http://www.monkproject.org/MONK.wiki/attachments/2006595/2130450) that the variance described by a random effect can be calculated by dividing the amount of variance accounted for by the random effects with the variance explained jointly by the random and fixed effects . Is there a less roundabout way?
>
>
> regards
>
> Liliana Martinez
>
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> ________________________________
> Fra: Katharina May <may.katharina at googlemail.com>
> Til: r-sig-mixed-models at r-project.org
> Sendt: Søndag, august 2, 2009 17:23:38
> Emne: Re: [R-sig-ME] lmer (lme4): % total variance explained by random effect
>
> Hi,
>
> just out of curiosity because nobody is answering:
> is it not not possible to calculate the variance described by a random
> effect on slope and intercept as percentage of the total variance
> (variance of random effect + unexplained variance)?
>
> Would be more than happy if somebody can help me...
>
> Thanks,
>
>       Katharina
>
>
> 2009/7/24 Katharina May <may.katharina at googlemail.com>:
>> Hello,
>>
>> just to say sorry if this questions may be somewhat "inappropriate": I'm a
>> bachelor student,
>> recently started with R and with trying to understand mixed models, but I'm
>> somewhat stuck with
>> the following problem and hope somebody might be able to help me finding a
>> solution:
>>
>> How can I get the variance (in % of the total variance) which is explained
>> by the random effect (both on slope
>> and intercept together)?
>> My aim is to say something like xx% of the variance is explained by the
>> random effect...
>>
>> As I'm not sure how to deal with this I would be more than happy for any
>> hints...
>>
>> Thank you very much and With Best Wishes from Freising/Germany,
>>
>>                         Katharina
>>
>>
>>
>> here an example output of a mixed model I use with 1 random effect on both
>> slope and intercept,
>> fitted with method=ML:
>>
>>
>> Linear mixed model fit by maximum likelihood
>> Formula: log(AGB) ~ log(BM_roots) + (log(BM_roots) |
>> as.factor(biomass_data[which(biomass_data$woody ==      1), 2]))
>>    Data: biomass_data[which(biomass_data$woody == 1), ]
>>    AIC   BIC logLik deviance REMLdev
>>  588.6 619.6 -288.3    576.6     583
>> Random effects:
>>  Groups                                                     Name
>>                          Variance   Std.Dev.   Corr
>>  as.factor(biomass_data[which(biomass_data$woody == 1), 2]) (Intercept)
>> 1.7568529  1.325463
>>                                                             log(BM_roots)
>>                           0.0071313  0.084447  -0.393
>>  Residual
>> 0.0809467 0.284511
>> Number of obs: 1282, groups: as.factor(biomass_data[which(biomass_data$woody
>> == 1), 2]), 22
>>
>> Fixed effects:
>>               Estimate Std. Error t value
>> (Intercept)    1.33062    0.29669    4.48
>> log(BM_roots)  0.93182    0.02441   38.17
>>
>> Correlation of Fixed Effects:
>>             (Intr)
>> log(BM_rts) -0.446
>>
>>
>
>
>
> --
> Time flies like an arrow, fruit flies like bananas.
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