[R-sig-ME] between-blocks variation in intercepts estimated as zero by lmer in RB design???
Duncan Mackay
duncan.mackay at flinders.edu.au
Tue Feb 8 00:44:58 CET 2011
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
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