Hi,
I have a question about using "lme" and "aov" for the
following dataset. If I understand correctly, using
"aov" with Error term in the formula is equivalent to
using "lme" with default settings, i.e. both assume
compound symmetry correlation structure. And I have
found that equivalency in the past. However, with the
follwing dataset, I got different answers, can anyone
explain what happened here? I have 2 differnt response
variables "x" and "y" in the following dataset, with
"y", I achieved the equivalency between "lme" and
"aov", but with "x", I got different p values for the
ANOVA table.
-------
x<-c(-0.0649,-0.0923,-0.0623,0.1809,0.0719,0.1017,0.0144,-0.1727,-0.1332,0.0986,0.304,-0.4093,0.2054,0.251,-0.1062,0.3833,
0.0649,0.2908,0.1073,0.0919,0.1167,0.2369,0.306,0.1379)
y<-c(-0.0649,-0.0923,0.32,0.08,0.0719,0.1017,0.05,-0.1727,-0.1332,0.15,0.304,-0.4093,0.2054,0.251,-0.1062,0.3833,0.0649,
0.2908,0.1073,0.0919,0.1167,0.2369,0.306,0.1379)
treat<-as.factor(c(1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2))
time<-as.factor(c(1,1,1,1,2,2,2,2,3,3,3,3,1,1,1,1,2,2,2,2,3,3,3,3))
sex<-as.factor(c('F','F','M','M','F','F','M','M','F','F','M','M','F','F','M','M','F','F','M','M','F','F','M','M'))
subject<-as.factor(c(rep(1:4,3),rep(5:8,3)))
xx<-cbind(x=data.frame(x),y=y,treat=treat,time=time,sex=sex,subject=subject)
######## using x as dependable variable
xx.lme<-lme(x~treat*sex*time,random=~1|subject,xx)
xx.aov<-aov(x~treat*sex*time+Error(subject),xx)
summary(xx.aov)
Error: subject
Df Sum Sq Mean Sq F value Pr(>F)
treat 1 0.210769 0.210769 6.8933 0.05846 .
sex 1 0.005775 0.005775 0.1889 0.68627
treat:sex 1 0.000587 0.000587 0.0192 0.89649
Residuals 4 0.122304 0.030576
---
Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.'
0.1 ` ' 1
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
time 2 0.00102 0.00051 0.0109 0.9891
treat:time 2 0.00998 0.00499 0.1066 0.9002
sex:time 2 0.02525 0.01263 0.2696 0.7704
treat:sex:time 2 0.03239 0.01619 0.3458 0.7178
Residuals 8 0.37469 0.04684
anova(xx.lme)
numDF denDF F-value p-value
(Intercept) 1 8 3.719117 0.0899
treat 1 4 5.089022 0.0871
sex 1 4 0.139445 0.7278
time 2 8 0.012365 0.9877
treat:sex 1 4 0.014175 0.9110
treat:time 2 8 0.120538 0.8880
sex:time 2 8 0.304878 0.7454
treat:sex:time 2 8 0.391012 0.6886
#### using y as dependable variable
xx.lme2<-lme(y~treat*sex*time,random=~1|subject,xx)
xx.aov2<-aov(y~treat*sex*time+Error(subject),xx)
summary(xx.aov2)
Error: subject
Df Sum Sq Mean Sq F value Pr(>F)
treat 1 0.147376 0.147376 2.0665 0.2239
sex 1 0.000474 0.000474 0.0067 0.9389
treat:sex 1 0.006154 0.006154 0.0863 0.7836
Residuals 4 0.285268 0.071317
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
time 2 0.009140 0.004570 0.1579 0.8565
treat:time 2 0.012598 0.006299 0.2177 0.8090
sex:time 2 0.043132 0.021566 0.7453 0.5049
treat:sex:time 2 0.069733 0.034866 1.2050 0.3488
Residuals 8 0.231480 0.028935
anova(xx.lme2)
numDF denDF F-value p-value
(Intercept) 1 8 3.0667809 0.1180
treat 1 4 2.0664919 0.2239
sex 1 4 0.0066516 0.9389
time 2 8 0.1579473 0.8565
treat:sex 1 4 0.0862850 0.7836
treat:time 2 8 0.2177028 0.8090
sex:time 2 8 0.7453185 0.5049
treat:sex:time 2 8 1.2049883 0.3488
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