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I measured explorative behaviour of 29 individuals repeatedly (at least twice) since I’m interested in how consistent they are through time. It seems, based on the attached plot, that there are clear differences between individuals in exploration. However, when I use a Linear mixed effect model with ID as a random variable

Model1<-lmer(Explo~1+(1|ID) ,data=OnlyMJ)

Linear mixed model fit by REML t-tests use Satterthwaite approximations to degrees of freedom [lmerMod] Formula: Explo ~ 1 + (1 | ID) Data: OnlyMJ

REML criterion at convergence: 254.5

Scaled residuals: Min 1Q Median 3Q Max -1.0565 -0.6838 -0.1794 0.3894 4.0976

Random effects: Groups Name Variance Std.Dev. ID
(Intercept) 0.000 0.00 Residual 2.754 1.66
Number of obs: 66, groups: ID, 30

Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) -0.02594 0.20428 65.00000 -0.127 0.899

enter image description hereThe random effect (between individual variance in exploration) is zero. This seems very weird and I can’t explain this. I have no idea what the problem is.

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  • $\begingroup$ What output do you get from ranef(Model1)? $\endgroup$ – Ian_Fin Sep 8 '16 at 14:27
  • $\begingroup$ see tinyurl.com/glmmFAQ, search for "random effect variances estimated as zero" ... $\endgroup$ – Ben Bolker Sep 8 '16 at 14:29
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    $\begingroup$ These boxplots are deceptive, because almost all are representing only two values! $\endgroup$ – whuber Sep 8 '16 at 14:50
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You say that each individual had at least two measurements, but from your output there are only 66 observations on 30 individuals, so only six individuals (at most) had more than two measurements. Two is the absolute minimum you need to calculate a mean and a standard distribution -- the random intercept is assumed to be a Normal distribution -- which will have a LOT of uncertainty. Looking at the plot, you have at least five individuals with essentially zero variance, and at least five individuals with a HUGE variance (probably caused by only two observations each).

I'd say you have too little data that's too noisy. The "clear" differences you see are mostly illusory because of the lack of data resulting in huge swings.

See also this Stack Exchange posting.

Here is a box plot of 30 individuals, where I chose two random normal numbers (mean 0, sd 2) for each:

Plot of 30 individuals, two random normal each

Compare to where I picked twenty numbers for each (same mean and sd):

Plot of 30 individuals, twenty random normal each

The first plot looks a lot like your plot. If I chose more than twenty each, it would even out even further.

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