# Why is my Mixed Effects Model (LME) results different from my repeated measures ANCOVA (AOV) results?

I have been trying to compare the effect of a treatment over time, controlling for a continuous covariate. So two groups (treatment vs control) are given different treatments and compared pre and post. Then I add a continuous covariate into the equation to see if the original effect is still significant. I'm predicting an interaction effect whereby the control group is not different across time, but the treatment group is. The covariate is not of interest, but it is significantly different between groups so there's very likely a confound, so that's why i added it, but that's not why I'm here today.

Basically, the lme command from the nlme package is giving totally different F statistics to aov. I had thought that repeated measures anova was within the general linear model and so were the same as mixed models. My gut says to trust the results of the mixed model, but I don't know how to reconcile the difference. In my original data, it even goes from highly significant to non significant.

My groups are unbalanced but all people went through all time points. Also, my covariate is recorded individually at each time point. If any of those facts sets off any bells.

NOTE: this isn't an off topic question just about R, it's more about why ANOVA/ANCOVA is the same/different from mixed effects models. This probably has something to do with setting contrasts or specifying the model for the SS or something rather than anything to do with R.

Here is some mock data, that is 'like' my original data, but not exactly the same.

    id<-c(1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13,14,14)
group<-c(1,1,1,1,1,1,2,2,2,2,2,2,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2)##group 1 is control
time<-c(1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2)
outcome<-c(10,11,12,11,10,11,10,19,10,20,12,20,10,10,11,12,11,10,13,20,10,21,9,19,10,13,10,13)
covariate<-c(80,82,80,83,79,80,70,80,69,75,69,80,80,84,80,81,80,82,79,85,72,85,72,85,72,73,73,74)

mydata<-as.data.frame(cbind(id,group,time,outcome,covariate))
summary(aov(outcome~factor(group)*factor(time)+covariate+Error(id)))
anova(lme(outcome~factor(group)*factor(time)+covariate, random=~1|id, data=mydata))


Here is my output for ANOVA

    > summary(aov(outcome~factor(group)*factor(time)+covariate+Error(id)))

Error: id
Df Sum Sq Mean Sq
factor(group)  1  4.255   4.255

Error: Within
Df Sum Sq Mean Sq F value   Pr(>F)
factor(group)               1  94.98   94.98   57.99 1.33e-07 ***
factor(time)                1 137.29  137.29   83.81 5.87e-09 ***
covariate                   1  98.60   98.60   60.20 9.78e-08 ***
factor(group):factor(time)  1  39.55   39.55   24.15 6.49e-05 ***
Residuals                  22  36.04    1.64
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


Here is my output for the mixed effects model

    > anova(lme(outcome~factor(group)*factor(time)+covariate, random=~1|id, data=mydata))
numDF denDF   F-value p-value
(Intercept)                    1    12 1249.4127  <.0001
factor(group)                  1    12   23.7548   4e-04
factor(time)                   1    11  115.8036  <.0001
covariate                      1    11   75.0274  <.0001
factor(group):factor(time)     1    11   28.0040   3e-04


As you can see totally different. Any help would be greatly appreciated.