[R-sig-ME] Why am I getting a Variance of 0 for my random effect

Wed Aug 11 20:13:22 CEST 2010

Hello.

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

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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