Presenting results of a mixed model containing factors
Sarah Dryhurst <s.dryhurst at ...> writes:
I am running a mixed effects model using the following code: m1<- lmer(DV~TMT*TMT2+(1|Block/TMT1),verbose=T) An example dataset is here: http://pastebin.com/bHug5kTt The two explanatory variables are both factors with two levels (treatment and control). Treatment 2 is split within Treatment 1 which is in turn within block. The model output I get is as follows (sorry for the formatting!) Linear mixed model fit by REML Formula: Richness ~ NT * WT + (1 | Block/WT) Data: rich2013 AIC BIC logLik deviance REMLdev 93.04 101.3 -39.52 81.87 79.04 Random effects: Groups Name Variance Std.Dev. WT:Block (Intercept) 3.3667e+00 1.8348e+00 Block (Intercept) 8.2334e-19 9.0738e-10 Residual 6.1667e-01 7.8528e-01 Number of obs: 24, groups: WT:Block, 12; Block, 6
Note here that your among-block variance is effectively zero ...
Fixed effects:
Estimate Std. Error t value
(Intercept) 12.0000 0.8148 14.728
NTNX -0.5000 0.4534 -1.103
WTS -3.6667 1.1523 -3.182
NTNX:WTS 3.3333 0.6412 5.199
Correlation of Fixed Effects:
(Intr) NTNX WTS
NTNX -0.278
WTS -0.707 0.197
NTNX:WTS 0.197 -0.707 -0.278
I have a few questions - i'm sorry if this is not the right place to
ask them (they are quite simple!):
In interpreting this model, am I correct in thinking that the output I
get tells me the effect of one level of each factor compared with the
other level of that factor, and also the effect of the interaction in
terms of the effect of one combination of treatments compared to
another combination of treatments?
As is generally true in R modeling (with the default treatment contrasts), the main effects represent the difference between the treatment and the control at the baseline level of the other effect. The interaction represents the difference between the double-treatment effect and the combined (additive) effect of the two treatments.
My main concern lies in how to report this model in a paper or thesis. It seems to be common practice to the "main effect" of each factor in a model (and perhaps the main effect of an interaction?), and then to discuss the difference between factor levels later. Is this correct? If the above is correct, in an lm, I would simple use summary.aov(model) to give me the summary of the main effects of each explanatory factor and the interaction and report these, along with their test statistic and p value (subjective, I know). However I do not know how to do this in lme4, or indeed if this is even a correct approach.
Specifically then, I am wondering: a) Is the extraction of these "main effects" possible in lme4 and if so, how is it done?
The "main effects" are the effects you see, but they have to be interpreted carefully.
b) How best to present the results of the two treatments... c) How best to present the results of the interaction between the two treatments at all levels of this interaction (so for all combinations of factor levels that make up the 2x2 factorial experiment). I have struggled to find much information relating to how to present such models online...
Most of these questions aren't specific to lme4, it's just that the standard suite of answers get more complicated in _any_ situation (glm(), lmer(), etc.) where there isn't a simple, unique additive decomposition of effects. There is a fair amount of controversy even about how to handle main effects in the presence of interactions (the "SAS type III SSQ/marginality" argument): e.g. google for "venables exegeses linear models". There is a strong effect of the interaction in your case. If you want to get 'average' effects of the main effects, which may or may not make sense, you can use sum-to-zero contrasts. Ben Bolker