I have a question about my use of a mixed model/lmer. The basic model is this:
lmer(DV ~ group * condition + (1|pptid), data= df)
Group and condition are both factors: group has two levels (groupA, groupB) and condition has three levels (condition1, condition2, condition3). It's data from human subjects, so pptid is a random effect for each person.
The model found the following with p value output:
Estimate MCMCmean HPD95lower HPD95upper pMCMC Pr(>|t|)
(Intercept) 6.1372 6.1367 6.0418 6.2299 0.0005 0.0000
groupB -0.0614 -0.0602 -0.1941 0.0706 0.3820 0.3880
condition2 0.1150 0.1151 0.0800 0.1497 0.0005 0.0000
condition3 0.1000 0.1004 0.0633 0.1337 0.0005 0.0000
groupB:condition2 -0.1055 -0.1058 -0.1583 -0.0610 0.0005 0.0000
groupB:condition3 -0.0609 -0.0612 -0.1134 -0.0150 0.0170 0.0148
Now, I know that the rows listed compare each level of the factors to the reference level. For group, the reference is groupA and for condition, the reference is condition1.
Would I be correct in interpreting this output in the following way:
- No overall differences between the groups (hence groupB having a p of >.05)
- Overall differences between condition 1 and condition 2, and between condition 1 and condition 3.
- Differences between groupA, condition 1 versus groupB, condition 2 and also between groupA, condition 1 versus group B, condition 3.
Is that correct? I think I'm a little confused about how to interpret this with regards to interactions between levels of two different factors.
I've read various questions on here and done some web searches, and managed to get contrasts set up with glht: would that be a better way to look at the differences between the groups and conditions? I figured that would be the case given the signs of interactions being present here.
Best Answer
Using the given regression table, we can compute the table of expected value of the dependent variable,
DV
, for each combination of the two factors, which might make this more clear (Note I've used the ordinary estimates, not the MCMC estimates):$$ \begin{array}{c|cc} \phantom{} & {\rm GroupA} & {\rm GroupB} \\ \hline {\rm Condition1} & 6.1372 & 6.0758 \\ {\rm Condition2} & 6.2522 & 6.0853 \\ {\rm Condition3} & 6.2372 & 6.1149 \\ \end{array} $$
I'll answer your question by responding to your interpretations, referencing this table.
No overall differences between the groups (hence groupB having a p of >.05)
The $p$-value you're referring to is only restricting focus to the reference level of the variable
Condition
, so it's only testing the difference between the groups whenCondition=1
(the first row of the table), i.e. it's only testing whether $6.1372$ is significantly different from $6.0758$.It's not testing whether there is an overall difference between the groups. To do that test, you'd have to leave
Condition
out of the model entirely and test the significance ofGroup
.Overall differences between condition 1 and condition 2, and between condition 1 and condition 3.
Similarly to the first interpretation, this is only comparing
Condition2
andCondition3
to the reference level (Condition1
) whenGroup=A
. That is, this is only testing whether the second and third entries in the first column are significantly different from $6.1372$. To test for overall differences in the condition variable, you'd need to leaveGroup
out of the model and testcondition
alone.Differences between groupA, condition 1 versus groupB, condition 2 and also between groupA, condition 1 versus group B, condition 3.
The interaction terms test whether the effect of one variable depends on the level of the other variable.
For example, significance of the
groupB:condition2
term tells you that difference betweenCondition1
andCondition2
is different whenGroup=A
vs.Group=B
. Referencing the table, this means that $$6.2522-6.1372=.115$$ is significantly different from $$6.0853-6.0758=.0095$$ In this particular case it looks likeCondition2
is different fromCondition1
inGroupA
but much less so inGroupB
, and that's how I'd interpret this. It appears a similar dynamic is occurring, to a lesser extent, with regard toCondition3
.