[R-sig-ME] Specify the appropriate model for an Event Related Potentials (ERPs) study: what should I do with trial order (and other terms)
Paolo Canal
paolo.canal at iusspavia.it
Tue Nov 8 12:18:05 CET 2016
Dear Mixed-Group,
I have acquired my data from one Experiment using a rather common
paradigm in psycholinguistics. The experiment aimed at investigating the
electro-physiological correlates of reading Typical (e.g., /chair/) vs
Atypical (e.g., /foot rest/) members of a number (N=85) of semantic
categories (e.g., /a kind of //Furniture/). In particular, we were
interested in looking at differences associated with Education level
(University N=24 vs non-University students N=23), and a three
individual predictors. My issue is how to deal with some factors that
are absolutely important in allowing for a better fit of the model, but
make interpretations too "complicated".
The two main factors of interest thus Typicality (categorical, Typical
vs Atypical) and Education (categorical, Hi vs Low Education). I already
know that the choice of taking these factors as dichotomic is
questionable, but I believe, defensible: in fact, although the measure
of Typicality is actually continuous (a proportion varying from 0 to 1)
it is paired within each semantic category, because when we selected the
materials we took the pair of exemplars that showed the largest
difference in Typicality, so within each category is the difference in
typicality that actually matters. Treating Education as categorical is
less defensible, but in some way we wanted to compare the predictive
power of this variable with more continuous variables representing a set
of abilities (3 cognitive measure, one of which moderated by years of
education and age), in some way to possibly show that some brain
mechanisms are better described when accounting for individual variation
rather than group differences.
I used lmer in lme4 to analyze the effect of my independent variables on
the average EEG voltage (continuous) from a set of EEG channels in two
different time-windows of interest (I know GAMM would be even more
appropriate than LMM, as what I am dealing with here are time-series,
but I am not yet ready to try).
I first determined the random effect structure, selecting three grouping
factors (subject, semantic category and channel) which are clusters of
repeated measures: for each item I have several subjects, for each
subject I have several items and for each channel I have several items
and subjects (perhaps channel might be nested in subject and item rather
than stand alone, any hints?). For each grouping factor, I allowed
intercepts to vary (e.g., 1|subject). Moreover, because I wanted to be
conservative and data are rather malleable (no convergence failure, no
variance = 0 or 1, not too high correlations between terms) I included a
set of terms to adjust by-subject and by-item slopes. I allowed
by-subject and by-item slope adjustments for Typicality (as it varies
within subjects and within semantic category) and by-item slope
adjustments for Education level.
Things get more complicated when thinking of the influence of two
variables that actually account for a lot of variation in the data:
frequency of use of words and trial order. The first variable is also
theoretically important and I want to include it as fixed effect; the
second variable increases models' fit but because it makes the results
less straightforward to interpret, I would not like to include in the
fixed part of the model.
This brings me to the fixed effect structure and the actual questions to
the list:
The initial design was very simple (2X2 plus covariates). The strategy
was to fit the simple model Typicality + Frequency and evaluate if
adding the interaction between Education (or the three covariates) and
Typicality leads to relevant increase in likelihood, using always with
the same random structure (the complex one).
Now I am not so sure this is appropriate and I have a list of doubts:
- Am I allowed to use the same complex random structure to compare the
likelihood of models that have "simpler" fixed effects? In principle I
guess it is correct to have the same random structure across comparisons.
- I am not interested in the effect of serial presentation (trial
order), as it increases the order of the highest interaction. Is it
appropriate to use it in the random structure only, or should I always
discuss it in interaction with my factors of interest?
Thanks for any help
Paolo
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