Why am I getting a Variance of 0 for my random effect

On 08/11/2010 02:25 PM, Douglas Bates wrote:

On Wed, Aug 11, 2010 at 1:13 PM, Kevin E. Thorpe
<kevin.thorpe at utoronto.ca> ?wrote:

Hello.

I'm getting a variance of 0 on a random effect and I don't know why.

It's not a bug - it's a feature. ?ML estimates or REML estimates of
variance components can be zero. ?This simply indicates that the
variability in the response associated with the factor, RN in your
case, is not sufficient to warrant the additional complexity in the
model.

I suspect I've not set the model up correctly. ?My transcript is below
with my own comments sprinkled in for time to time.

A little bit about the data (which I will provide off-list if requested).
?We have nurses managing an aspect of patient care
according to different algorithms. ?Interest focuses on of the
algorithms result in different outcomes. ?I have restricted this
to only nurses who did each algorithm twice (in case my problem
was being caused by some nurses doing only one algorithm, possibly
only one time).

I figured that since I have multiple observations per nurse, I
should treat nurse as a random effect, but maybe I confused myself
again.

You are quite correct that it is appropriate to allow for the
possibility of RN having an effect on the response and that it should
be incorporated as a random effect if it were in the model but the
results indicate that RN does not have sufficient effect on the
response.

Thanks Doug. ?Your response is helpful, as always. ?If RN does not
contribute a random effect, would it be appropriate to revert to a
standard regression model, or is it best to leave the unimportant
random effect? ?In the case of ordinary regression, dropping
variables based on their p-values compromises inference. ?Does the
same apply with dropping a random effect with no variance?

Kevin

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library(lattice)
library(lme4)

str(data1)

'data.frame': ? 72 obs. of ?3 variables:
?$ RN ? ? ? ?: int ?1 1 2 3 7 7 9 9 15 15 ...
?$ Assignment: Factor w/ 2 levels "E","N": 1 1 1 1 1 1 1 1 1 1 ...
?$ AUChr ? ? : num ?12.26 7.23 9.26 4.04 10.31 ...

tmp1<-
with(data1,aggregate(AUChr,list(RN=RN,Assigment=Assignment),mean))
names(tmp1)[3]<- "Mean"

tmp2<-
with(data1,aggregate(AUChr,list(RN=RN,Assignment=Assignment),var))
names(tmp2)[3]<- "Variance"

meanvar<- merge(tmp1,tmp2)

The point of this is to show that the means are not all the same,
nor are the variances.

meanvar

? RN Assignment ? Mean ?Variance
1 ? 1 ? ? ? ? ?E ?9.745 ?12.65045
2 ? 1 ? ? ? ? ?N ?7.185 ? 1.36125
3 ?15 ? ? ? ? ?E 10.605 ?15.07005
4 ?15 ? ? ? ? ?N 10.385 ? 4.41045
5 ?16 ? ? ? ? ?E ?8.175 ? 0.00845
6 ?16 ? ? ? ? ?N ?8.420 ? 1.03680
7 ? 2 ? ? ? ? ?E ?7.300 ? 7.68320
8 ? 2 ? ? ? ? ?N ?6.950 ? 1.00820
9 ?21 ? ? ? ? ?E ?9.670 ? 9.41780
10 21 ? ? ? ? ?N 10.535 ? 2.44205
11 22 ? ? ? ? ?E ?7.720 ? 2.04020
12 22 ? ? ? ? ?N ?7.930 ? 1.21680
13 24 ? ? ? ? ?E ?9.555 ?10.35125
14 24 ? ? ? ? ?N ?9.330 ? 0.38720
15 25 ? ? ? ? ?E ?8.240 ? 0.92480
16 25 ? ? ? ? ?N ?9.485 ? 0.00125
17 27 ? ? ? ? ?E ?8.635 ? 0.08405
18 27 ? ? ? ? ?N ?7.745 ? 3.72645
19 28 ? ? ? ? ?E ?9.635 ? 8.61125
20 28 ? ? ? ? ?N ?8.315 ?10.35125
21 ?3 ? ? ? ? ?E ?6.005 ? 7.72245
22 ?3 ? ? ? ? ?N 11.435 ?55.44045
23 31 ? ? ? ? ?E ?9.590 ? 9.94580
24 31 ? ? ? ? ?N 10.570 ?16.70420
25 35 ? ? ? ? ?E ?9.055 ? 0.32805
26 35 ? ? ? ? ?N ?9.925 ?14.41845
27 36 ? ? ? ? ?E ?9.040 ? 2.08080
28 36 ? ? ? ? ?N ?7.395 ? 1.14005
29 ?5 ? ? ? ? ?E ?8.430 ? 3.38000
30 ?5 ? ? ? ? ?N 17.385 139.94645
31 ?6 ? ? ? ? ?E ?6.930 ? 0.24500
32 ?6 ? ? ? ? ?N ?8.330 ? 1.72980
33 ?7 ? ? ? ? ?E 10.650 ? 0.23120
34 ?7 ? ? ? ? ?N ?7.375 ? 0.09245
35 ?9 ? ? ? ? ?E ?8.885 ? 7.56605
36 ?9 ? ? ? ? ?N ?8.405 ? 0.73205

Model with "Assignment" (algorithm).

lmer(AUChr~Assignment+(1|RN),data=data1,REML=FALSE)

Linear mixed model fit by maximum likelihood
Formula: AUChr ~ Assignment + (1 | RN)
? Data: data1
? AIC ? BIC logLik deviance REMLdev
?365.7 374.8 -178.8 ? ?357.7 ? 356.9
Random effects:
?Groups ? Name ? ? ? ?Variance Std.Dev.
?RN ? ? ? (Intercept) 0.0000 ? 0.0000
?Residual ? ? ? ? ? ? 8.4152 ? 2.9009
Number of obs: 72, groups: RN, 18

Fixed effects:
? ? ? ? ? ?Estimate Std. Error t value
(Intercept) ? 8.7703 ? ? 0.4835 ? 18.14
AssignmentN ? 0.5131 ? ? 0.6837 ? ?0.75

Correlation of Fixed Effects:
? ? ? ? ? ?(Intr)
AssignmentN -0.707


Model without the algorithm variable.

lmer(AUChr~(1|RN),data=data1,REML=FALSE)

Linear mixed model fit by maximum likelihood
Formula: AUChr ~ (1 | RN)
? Data: data1
? AIC ? BIC logLik deviance REMLdev
?364.3 371.1 -179.1 ? ?358.3 ? 358.5
Random effects:
?Groups ? Name ? ? ? ?Variance Std.Dev.
?RN ? ? ? (Intercept) 0.000 ? ?0.0000
?Residual ? ? ? ? ? ? 8.481 ? ?2.9122
Number of obs: 72, groups: RN, 18

Fixed effects:
? ? ? ? ? ?Estimate Std. Error t value
(Intercept) ? 9.0268 ? ? 0.3432 ? ?26.3

sessionInfo()

R version 2.11.1 Patched (2010-07-21 r52598)
Platform: i686-pc-linux-gnu (32-bit)

locale:
?[1] LC_CTYPE=en_US ? ? ? LC_NUMERIC=C ? ? ? ? LC_TIME=en_US
?[4] LC_COLLATE=C ? ? ? ? LC_MONETARY=C ? ? ? ?LC_MESSAGES=en_US
?[7] LC_PAPER=en_US ? ? ? LC_NAME=C ? ? ? ? ? ?LC_ADDRESS=C
[10] LC_TELEPHONE=C ? ? ? LC_MEASUREMENT=en_US LC_IDENTIFICATION=C

attached base packages:
[1] stats ? ? graphics ?grDevices utils ? ? datasets ?methods ? base

other attached packages:
[1] lme4_0.999375-34 ? Matrix_0.999375-42 lattice_0.18-8

loaded via a namespace (and not attached):
[1] grid_2.11.1 ? nlme_3.1-96 ? stats4_2.11.1

proc.time()

? user ?system elapsed
?3.488 ? 0.056 ? 3.536

--
Kevin E. Thorpe
Biostatistician/Trialist, Knowledge Translation Program
Assistant Professor, Dalla Lana School of Public Health
University of Toronto
email: kevin.thorpe at utoronto.ca ?Tel: 416.864.5776 ?Fax: 416.864.3016