[R-sig-ME] between-blocks variation in intercepts estimated as zero by lmer in RB design???

[Duncan Mackay]

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. 
> 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