# [R] random and group arguments in lme

Peter Dalgaard BSA p.dalgaard at biostat.ku.dk
Thu Apr 13 14:13:57 CEST 2000

```"Eusebio Arenal Gutiérrez" <use at eio.uva.es> writes:

> I want to fit the following model:
>
> Analysis of Variance Table
>
> Response: tiempo
>                Df Sum Sq Mean Sq F value    Pr(>F)
> producto        2 93.631  46.815 63.0511 4.304e-07 ***
> producto:panel  9 43.533   4.837  6.5144  0.001881 **
> Residuals      12  8.910   0.742
> ---
> Signif. codes:  0  `***'  0.001  `**'  0.01  `*'  0.05  `.'  0.1  ` '  1
>
> As panel is random I would need
> ["producto", "Mean Sq"]/["producto:panel", "Mean Sq"] in the cell
> ["producto", "F value"]
> and its p-value, that is
>
> > 46.815/4.837
> [1] 9.67852
> > 2*pf(46.815/4.837, 2, 9, lower.tail=FALSE)
> [1] 0.01143266
>
> How can I fit this model with lme function (of nlme)? What arguments have I
> to put in the random and group arguments?

Assuming that this is a 3x4x2 factorial layout, it would be easier to
use

cf.

> pr<-gl(3,1,24)
> pa<-gl(4,3,24)
> y<-rnorm(24)
> summary(aov(y~pr+Error(pr:pa)))

Error: pr:pa
Df Sum Sq Mean Sq F value  Pr(>F)
pr         2 6.5870  3.2935  3.2109 0.08861 .
Residuals  9 9.2316  1.0257
---
Signif. codes:  0  `***'  0.001  `**'  0.01  `*'  0.05  `.'  0.1  ` '  1

Error: Within
Df  Sum Sq Mean Sq F value Pr(>F)
Residuals 12 16.6469  1.3872

With lme() it seems to be tricky to do the pa:pr interaction
as a groping, but you might do

> pa<-gl(12,1,24)
> lme(y~pr,random=~1|pa)
Linear mixed-effects model fit by REML
Data: NULL
Log-restricted-likelihood: -35.11024
Fixed: y ~ pr
(Intercept)         pr2         pr3
0.5753093  -0.3784748  -1.2511397

Random effects:
Formula: ~1 | pa
(Intercept) Residual
StdDev: 1.669157e-53 1.110096

Number of Observations: 24
Number of Groups: 12
> anova(lme(y~pr,random=~1|pa))
numDF denDF   F-value p-value
(Intercept)     1    12 0.0200734  0.8897
pr              2     9 2.6726312  0.1227

Notice that this is not the same as the balanced analysis, since the
pa random effect would have a negative variance in this case.

--
O__  ---- Peter Dalgaard             Blegdamsvej 3
c/ /'_ --- Dept. of Biostatistics     2200 Cph. N
(*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907
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```