[R-sig-ME] between-blocks variation in intercepts estimated as zero by lmer in RB design???
Douglas Bates
bates at stat.wisc.edu
Tue Feb 8 17:08:09 CET 2011
I referred to "the second plot" but did not include it. This is the
file that I meant to include.
On Tue, Feb 8, 2011 at 10:06 AM, Douglas Bates <bates at stat.wisc.edu> wrote:
> On Mon, Feb 7, 2011 at 5:44 PM, Duncan Mackay
> <duncan.mackay at flinders.edu.au> wrote:
>> Hello,
>> I am having difficulty understanding why lmer is estimating the variation among intercepts of random groups (blocks) as zero in the following case:-
>>
>> I have samples of the no. of exotic species taken from two positions in each of 38 sites. (see data frame "rb.data" below). The data are coded as follows:-
>>> str(rb.data)
>> 'data.frame': 76 obs. of 3 variables:
>> $ site : Factor w/ 38 levels "AMD1","BR1","DA1-1",..: 1 2 3 4 5 6 7 8 9 10 ...
>> $ exotic : num 2 8 9 12 9 5 9 11 6 6 ...
>> $ position: Factor w/ 2 levels "above","below": 2 2 2 2 2 2 2 2 2 2 ...
>>>
>>
>> I have run a standard random-blocks analysis on these data as follows:-
>>
>>> summary(lmer(exotic ~ position + (1|site), data=rb.data))
>> Linear mixed model fit by REML
>> Formula: exotic ~ position + (1 | site)
>> Data: rb.data
>> AIC BIC logLik deviance REMLdev
>> 519.8 529.1 -255.9 516.1 511.8
>> Random effects:
>> Groups Name Variance Std.Dev.
>> site (Intercept) 0.000 0.0000
>> Residual 53.526 7.3162
>> Number of obs: 76, groups: site, 38
>>
>> Fixed effects:
>> Estimate Std. Error t value
>> (Intercept) 12.526 1.187 10.554
>> positionbelow -4.053 1.678 -2.415
>>
>> Correlation of Fixed Effects:
>> (Intr)
>> positionblw -0.707
>>
>>
>> So why, oh why, does lmer estimate the variance among the site intercepts as zero??? A plot of the data obtained by:-
>>> with(rb.data, interaction.plot(position,site,exotic))
>> suggests to me that the intercepts are actually quite variable, however a look at the fitted coefficients shows that lmer has fit the same intercept for each site.
>
> I would plot the data using lattice as
>
> dotplot(reorder(site, exotic) ~ sqrt(exotic), rb.data,
> group=position, type=c("p","a"), auto.key=list(columns=2,lines=TRUE))
>
> assuming that exotic is actually a count and thus a square root
> transformation would help to stabilize the variance. From the
> enclosed plot you can see that in some ways the average is being
> driven by the above counts. The below counts are more-or-less
> constant whereas the above counts go from very low to very high. So
> the above counts are what are driving the variation.
>
> The model that you are fitting only considers the mean count for each
> location as a random effect so it is modeling the data as in the
> second plot where there is not a great deal of variability in the
> averages compared to the residual variability, which leads to an
> estimate of zero for the between-site variance.
>
> If you fit this as a generalized linear mixed model with the Poisson
> family you do get a non-zero variance estimate for the site term but
> even this model is not getting at the pattern in the data.
>
>> (gm1 <- glmer(exotic ~ position + (1|site), rb.data, poisson))
> Generalized linear mixed model fit by maximum likelihood ['merMod']
> Family: poisson
> Formula: exotic ~ position + (1 | site)
> Data: rb.data
> AIC BIC logLik deviance
> 302.9469 309.9391 -148.4734 296.9469
>
> Random effects:
> Groups Name Variance Std.Dev.
> site (Intercept) 0.09967 0.3157
> Number of obs: 76, groups: site, 38
>
> Fixed effects:
> Estimate Std. Error z value
> (Intercept) 2.47856 0.06922 35.81
> positionbelow -0.39087 0.07234 -5.40
>
> Correlation of Fixed Effects:
> (Intr)
> positionblw -0.422
>
> The problem with even this fit is that the pattern in the data is not
> that of an additive model.
>
>
>
>>> coef(rb.exotic.lme)
>> $site
>> (Intercept) positionbelow
>> AMD1 12.52632 -4.052632
>> BR1 12.52632 -4.052632
>> DA1-1 12.52632 -4.052632
>> DA1-2 12.52632 -4.052632
>> DA1-3 12.52632 -4.052632
>> .......
>>
>>
>> ..................................... I think I'm missing something pretty basic here!!
>>
>> Many thanks for any help,
>> Regards,
>> Duncan
>>
>>
>>
>>> rb.data
>> site exotic position
>> 1 AMD1 2 below
>> 2 BR1 8 below
>> 3 DA1-1 9 below
>> 4 DA1-2 12 below
>> 5 DA1-3 9 below
>> 6 DA1-4 5 below
>> 7 DA1-5 9 below
>> 8 MAY1 11 below
>> 9 PH1 6 below
>> 10 PH2 6 below
>> 11 RA1 9 below
>> 12 RA2 11 below
>> 13 RB1 14 below
>> 14 RB2 20 below
>> 15 RB3 13 below
>> 16 RB4-1 9 below
>> 17 RB6-1 9 below
>> 18 RB6-2 5 below
>> 19 RB7-2 5 below
>> 20 RB8-1 10 below
>> 21 RLCL1 9 below
>> 22 RLCL2 12 below
>> 23 ROW1 12 below
>> 24 ROW2 9 below
>> 25 RS1 5 below
>> 26 RS2/RS3 5 below
>> 27 SC1 5 below
>> 28 SC2-2 5 below
>> 29 SC5-1 10 below
>> 30 SC7 8 below
>> 31 SC8 5 below
>> 32 TH5-1 12 below
>> 33 TH5-2 11 below
>> 34 WI5 1 below
>> 35 WI6-1 6 below
>> 36 WI6-2 13 below
>> 37 WR2-1 6 below
>> 38 WR2-2 6 below
>> 39 AMD1 27 above
>> 40 BR1 16 above
>> 41 DA1-1 4 above
>> 42 DA1-2 4 above
>> 43 DA1-3 5 above
>> 44 DA1-4 5 above
>> 45 DA1-5 6 above
>> 46 MAY1 13 above
>> 47 PH1 22 above
>> 48 PH2 19 above
>> 49 RA1 16 above
>> 50 RA2 13 above
>> 51 RB1 7 above
>> 52 RB2 5 above
>> 53 RB3 4 above
>> 54 RB4-1 3 above
>> 55 RB6-1 1 above
>> 56 RB6-2 4 above
>> 57 RB7-2 13 above
>> 58 RB8-1 8 above
>> 59 RLCL1 6 above
>> 60 RLCL2 15 above
>> 61 ROW1 6 above
>> 62 ROW2 7 above
>> 63 RS1 27 above
>> 64 RS2/RS3 29 above
>> 65 SC1 15 above
>> 66 SC2-2 18 above
>> 67 SC5-1 7 above
>> 68 SC7 25 above
>> 69 SC8 33 above
>> 70 TH5-1 4 above
>> 71 TH5-2 3 above
>> 72 WI5 20 above
>> 73 WI6-1 2 above
>> 74 WI6-2 3 above
>> 75 WR2-1 30 above
>> 76 WR2-2 31 above
>>
>>
>> ______________________________________________________________________________
>> Dr. Duncan Mackay
>> School of Biological Sciences
>> Flinders University
>> GPO Box 2100
>> Adelaide
>> S.A. 5001
>> AUSTRALIA
>>
>> Phone 61-8-82012627
>> FAX 61-8-82013015
>>
>> http://www.flinders.edu.au/science_engineering/biology/our-school/staff-postgrads/academic-staff/mackay-duncan.cfm
>>
>>
>>
>> ______________________________________________________________________________
>> Dr. Duncan Mackay
>> School of Biological Sciences
>> Flinders University
>> GPO Box 2100
>> Adelaide
>> S.A. 5001
>> AUSTRALIA
>>
>> Phone 61-8-82012627
>> FAX 61-8-82013015
>>
>> http://www.flinders.edu.au/science_engineering/biology/our-school/staff-postgrads/academic-staff/mackay-duncan.cfm
>>
>>
>>
>> _______________________________________________
>> R-sig-mixed-models at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>
>
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