Can anyone tell me the difference between using

`aov()`

and`lme()`

for analyzing longitudinal data and how to interpret results from these two methods?Below, I analyze the same dataset using

`aov()`

and`lme()`

and got 2 different results. With`aov()`

, I got a significant result in the time by treatment interaction, but fitting a linear mixed model, time by treatment interaction is insignificant.`> UOP.kg.aov <- aov(UOP.kg~time*treat+Error(id), raw3.42) > summary(UOP.kg.aov) Error: id Df Sum Sq Mean Sq F value Pr(>F) treat 1 0.142 0.1421 0.0377 0.8471 Residuals 39 147.129 3.7725 Error: Within Df Sum Sq Mean Sq F value Pr(>F) time 1 194.087 194.087 534.3542 < 2e-16 *** time:treat 1 2.077 2.077 5.7197 0.01792 * Residuals 162 58.841 0.363 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > UOP.kg.lme <- lme(UOP.kg~time*treat, random=list(id=pdDiag(~time)), na.action=na.omit, raw3.42) > summary(UOP.kg.lme) Linear mixed-effects model fit by REML Data: raw3.42 AIC BIC logLik 225.7806 248.9037 -105.8903 Random effects: Formula: ~time | id Structure: Diagonal (Intercept) time Residual StdDev: 0.6817425 0.5121545 0.1780466 Fixed effects: UOP.kg ~ time + treat + time:treat Value Std.Error DF t-value p-value (Intercept) 0.5901420 0.1480515 162 3.986059 0.0001 time 0.8623864 0.1104533 162 7.807701 0.0000 treat -0.2144487 0.2174843 39 -0.986042 0.3302 time:treat 0.1979578 0.1622534 162 1.220053 0.2242 Correlation: (Intr) time treat time -0.023 treat -0.681 0.016 time:treat 0.016 -0.681 -0.023 Standardized Within-Group Residuals: Min Q1 Med Q3 Max -3.198315285 -0.384858426 0.002705899 0.404637305 2.049705655 Number of Observations: 205 Number of Groups: 41`

**Answer**

Based on your description, it appears that you have a repeated-measures model with a single treatment factor. Since I do not have access to the dataset (`raw3.42`

), I will use the Orthodont data from the `nlme`

package to illustrate what is going on here. The data structure is the same (repeated measurements for two different groups – in this case, males and females).

If you run the following code:

```
library(nlme)
data(Orthodont)
res <- lme(distance ~ age*Sex, random = ~ 1 | Subject, data = Orthodont)
anova(res)
```

you will get the following results:

```
numDF denDF F-value p-value
(Intercept) 1 79 4123.156 <.0001
age 1 79 122.450 <.0001
Sex 1 25 9.292 0.0054
age:Sex 1 79 6.303 0.0141
```

If you run:

```
res <- aov(distance ~ age*Sex + Error(Subject), data = Orthodont)
summary(res)
```

you will get:

```
Error: Subject
Df Sum Sq Mean Sq F value Pr(>F)
Sex 1 140.46 140.465 9.2921 0.005375 **
Residuals 25 377.91 15.117
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
age 1 235.356 235.356 122.4502 < 2e-16 ***
age:Sex 1 12.114 12.114 6.3027 0.01410 *
Residuals 79 151.842 1.922
```

Note that the F-tests are exactly identical.

For `lme()`

, you used `list(id=pdDiag(~time))`

, which not only adds a random intercept to the model, but also a random slope. Moreover, by using `pdDiag`

, you are setting the correlation between the random intercept and slope to zero. This is a different model than what you specified via `aov()`

and hence you get different results.

**Attribution***Source : Link , Question Author : biostat_newbie , Answer Author : Wolfgang*