# [R] random effects with lmer() and lme(), three random factors

Date: Sat 29 Jul 2006 - 09:43:38 EST

Hi, all,

I have a question about random effects model. I am dealing with a three-factor experiment dataset. The response variable y is modeled against three factors: Samples, Operators, and Runs. The experimental design is as follow:

4 samples were randomly chosen from a large pool of test samples. Each of the 4 samples was analyzed by 4 operators, randomly selected from a group of operators. Each operator independently analyzed same samples over 5 runs (runs nested in operator). I would like to know the following things:

(1) the standard deviation within each run;

(3) the standard deviation within operator

With this data, I assumed the three factors are all random effects. So the model I am looking for is

Model: y = Samples(random) + Operator(random) + Operator:Run(random) + Error(Operator) + Error(Operator:Run) + Residuals

I am using lme function in nlme package. Here is the R code I have

1. using lme:

First I created a grouped data using

gx <- groupedData(y ~ 1 | Sample, data=x)

gx\$dummy <- factor(rep(1,nrow(gx)))

then I run the lme

fm<- lme(y ~ 1, data=gx,
random=list(dummy=pdBlocked(list(pdIdent(~Sample-1),

pdIdent(~Operator-1),

pdIdent(~Operator:Run-1)))))

finally, I use VarCorr to extract the variance components

vc <- VarCorr(fm)

```                     Variance           StdDev

```

Operator:Run 1.595713e-10:20 1.263215e-05:20

Sample 5.035235e+00: 4 2.243933e+00: 4

Operator 5.483145e-04: 4 2.341612e-02: 4

Residuals 8.543601e-02: 1 2.922944e-01: 1

2. Using lmer in Matrix package:

fm <- lmer(y ~ (1 | Sample) + (1 | Operator) +

(1|Operator:Run), data=x)

summary(fm)

Linear mixed-effects model fit by REML

Formula: H.I.Index ~ (1 | Sample.Name) + (1 | Operator) + (1 | Operator:Run)

Data: x

AIC BIC logLik MLdeviance REMLdeviance

96.73522 109.0108 -44.36761 90.80064 88.73522

Random effects:

Groups Name Variance Std.Dev.

Operator:Run (Intercept) 4.2718e-11 6.5359e-06

Operator (Intercept) 5.4821e-04 2.3414e-02

Sample (Intercept) 5.0352e+00 2.2439e+00

``` Residual                 8.5436e-02 2.9229e-01

```

number of obs: 159, groups: Operator:Run, 20; Operator, 4; Sample.Name, 4

Fixed effects:

Estimate Std. Error t value

(Intercept) 0.0020818 1.1222683 0.001855

There is a difference between lmer and lme is for the factor Operator:Run. I cannot find where the problem is. Could anyone point me out if my model specification is correct for the problem I am dealing with. I am pretty new user to lme and lmer. Thanks for your help!

Wilson Wang

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