[R-sig-ME] random effect model

[Ben Bolker]

On 15-12-10 10:16 PM, li li wrote:
> Hi all,
>   I have a very simple data set "data". Here both day and analysts are
> considered as random.
> I fit the mod1 and mod2 as below. The random effect in both models come out
> to be zero and same results are returned from both models. It seems very
> strange to me. Anyone have an explanation or suggestion?
>   Thanks. Hanna
> 

This is very common when trying to fit random factors with small (e.g.
<6) numbers of levels of the grouping variable: see e.g.

http://glmm.wikidot.com/faq (search for "Why is my random effect
variance estimated as zero, or correlations estimated as +/- 1? What
should I do about it?")

or

https://rpubs.com/bbolker/4187

> 
> 
>> data
>                values day analyst
> stat_d1p1 -0.06357455   1       1
> stat_d1p2 -0.05564684   1       2
> stat_d1p3  0.16145903   1       3
> stat_d2p1  0.07763253   2       1
> stat_d2p2 -0.02988389   2       2
> stat_d2p3 -0.16899311   2       3
> stat_d3p1 -0.13545138   3       1
> stat_d3p2 -0.07537850   3       2
> stat_d3p3 -0.01313345   3       3
>> library(lme4)
>> library(lmerTest)
> 
>> mod1 <- lmer(values ~ 1+(1|day),data=data)
>> summary(mod1)
> Linear mixed model fit by REML t-tests use Satterthwaite approximations to
>   degrees of freedom [lmerMod]
> Formula: values ~ 1 + (1 | day)
>    Data: data
> REML criterion at convergence: -11.7
> Scaled residuals:
>     Min      1Q  Median      3Q     Max
> -1.3311 -0.4103 -0.2162  0.2019  1.9192
> Random effects:
>  Groups   Name        Variance Std.Dev.
>  day      (Intercept) 0.00000  0.0000
>  Residual             0.01034  0.1017
> Number of obs: 9, groups:  day, 3
> Fixed effects:
>             Estimate Std. Error       df t value Pr(>|t|)
> (Intercept) -0.03366    0.03389  8.00000  -0.993     0.35
>>
> 
>> mod2 <- lmer(values ~ 1+(1|analyst),data=data)
>> summary(mod2)
> Linear mixed model fit by REML t-tests use Satterthwaite approximations to
>   degrees of freedom [lmerMod]
> Formula: values ~ 1 + (1 | analyst)
>    Data: data
> REML criterion at convergence: -11.7
> Scaled residuals:
>     Min      1Q  Median      3Q     Max
> -1.3311 -0.4103 -0.2162  0.2019  1.9192
> Random effects:
>  Groups   Name        Variance Std.Dev.
>  analyst  (Intercept) 0.00000  0.0000
>  Residual             0.01034  0.1017
> Number of obs: 9, groups:  analyst, 3
> Fixed effects:
>             Estimate Std. Error       df t value Pr(>|t|)
> (Intercept) -0.03366    0.03389  8.00000  -0.993     0.35
>>
> 
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