I am currently working through Andy Field's "Discovering Statistics Using R". I've just got to chapter 14 "Mixed designs". He's talking about how you can use an LME in much the same way as an ANOVA.
It's all pretty clear but there's a bit where he's talking about applying contrast weightings (pages 617 and 618) where he's lost me. All throughout this book so far contrast weightings have been described in what I would consider a pretty standard way: 0 means an item is not included in a particular contrast, and positive items are compared with negative items. So if you'd wanted compare group 1 with group 3 while ignoring group 2, you'd use weightings like (-1, 0, 1).
However here Field talks about if an item is always coded as a 0, it acts as a "baseline condition". I don't get this. If it's coded as a 0, surely it won't be included in any analysis at all?
Essentially we have a situation where we wish to compare the first group against the second, and another situation where we wish to compare the 3rd group against the second. I enclose some of my code with my rather confused annotations as well.
# Mixed design as a GLM
# Setting contrasts
# Here they don't have to be orthogonal and you can see the output of the contrast
# I'm a bit unclear on Field's logic at this point since usually setting a contrast
# weight of 0 indicates that a particular condition is not included in this particular
# analysis, whereas here he seems to suggest that setting a weight of 0 indicates something
# forms part of the baseline condition.
# Something specific to LMEs perhaps?
# Contrasts for looks
AttractivevsAv
Hi Gavin,
my response may not be totally helpful as I don't have Andy Field's book at hand right now and my response is more general than what you may be looking for. Note that there are generally different ways to code categorical variables in regression models, see e.g., http://www.ats.ucla.edu/stat/r/library/contrast_coding.htm for an overview.
Best,
Bettina
Hi Gavin,
[Assuming the independent variables in question are categorical, and you are using dummy coding / treatment coding] a condition coded as all 0s corresponds to the intercept.
You are stumbling across the difference between effect coding (with -1s, 0s and 1s) and dummy coding (all 0s and 1s). In R, effect coding is called sum-to-zero coding and in Bettina's link above it is called deviation coding. Many people have used dummy coding for decades, but to make a regression produce the same estimates as an ANOVA you have to use effect coding. The overall fit of the model will be the same (R2) but the regression weights will vary.
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