test for significance of interaction in linear mixed models in nlme in R
mixed-models, r
Solution
I respectfully disagree with @sven-hohenstein
In R, the default coding for categorial variables is treatment contrast coding. In treatment contrasts, the first level is the reference level. All remaining factor levels are compared with the reference level.
First, the fixed effects are specified here with a zero intercept, `... ~ 0 + ...`. This means that the `condition` coding is no longer `contr.treatment`. If I'm not mistaken, the main effects of `Control` and `Treatment` are now interpretable as their respective deviations from the group mean...
In your model, the factor items has three levels: E1, E2, and E3. The two contrasts test the difference between (a) E2 and E1, and (b) E3 and E1. The main effects of these contrasts are estimated for the level Control of the factor condition, since this is the reference category of this factor.
...when the value of `items` is at its reference level of `E1`! Therefore:
- Main effect `Control` = how much `Control:E1` observations deviate from the mean of item `E1`.
- Main effect `Treatment` = how much `Treatment:E1` observations deviate from the mean of item `E1`.
- Main effect `E2` = how much `Control:E2` observations deviate from the mean of item `E2`.
- Main effect `E3` = how much `Control` observations deviate from the mean of item `E3`.
- Interaction `Treatment:E2` = how much `Treatment:E2` observations deviate from the mean of item `E2`
- Interaction `Treatment:E3` = how much `Treatment:E3` observations deviate from the mean of item `E3`.
Thanks for the pointer to `estimable`, I haven't tried it before. For custom contrasts, I've been (ab)using `glht` from the `multcomp` package.
Problem
I use `lme` function in the `nlme` R package to test if levels of factor `items` has significant interaction with levels of factor `condition`. The factor `condition` has two levels: `Control` and `Treatment`, and the factor `items` has 3 levels: `E1,...,E3`. I use the following code: ``` f.lme = lme(response ~ 0 + factor(condition) * factor(items), random = ~1|subject) ``` where `subject` is the random effect. In this way, when I run: ``` summary(f.lme)$tTable ``` I will get the following output: ``` factor(condition)Control factor(condition)Treatment factor(items)E2 factor(items)E3 factor(condition)Treatment:factor(items)E2 factor(condition)Treatment:factor(items)E3 ``` together with `Value, Std.Error, DF, t-value, p-value` columns. I have two questions: If I want to compare `Control` vs. `Treatment`, shall I just use `estimable()` function in `gmodels` and make a contrast of `(-1,1,0,0,0,0)`? I am interested in whether levels of `items`, i.e. `E1, E2, E3` are different across `condition`, so I am interested in whether the interaction terms are significant (by just checking the `p-value` column??): `factor(condition)Treatment:factor(items)E2 factor(condition)Treatment:factor(items)E3` However, how can I tell if `factor(condition)Treatment:factor(items)E1` is significant or not? It is not shown in the summary output and I think it has something to do with the contrast used in R... Thanks a lot!