I can’t decide between two ways to specify my model: I have 1 participant who completed say 100 behavioural measurements, in the beginning and then every 10 measurements, we would ask them to rate their mood.
Should my model be
behaviour ~ 1 + mood
or
behaviour ~ 1+ mood + (1+mood| block_of_10_trials)
I’m unsure what to do because even though we have 100 unique behavioural measurements, there are only 10 unique mood measurements that I have then expanded (i.e. the 10 behavioural measurements following a mood rating all have the same mood rating attached)
Yet another alternative would be:
behaviour_average_every_10_ measurements ~ 1+ mood
So here then, my design matrix would only have 10 rows.
I’d be very grateful for any thoughts on this.
Your second specification will not work, because it asks how the effect of mood varies across blocks, but there’s no information to estimate a within-block effect of mood because there’s no within-block variation in mood.
Your first possibility might be a good model for your data. It could be improved if any of the following is true:
- the mood measurement induces some stochastic change in behavior when it happens, so that behavior changes stochastically across trials in a “blocked” manner.
- the relationship between behavior and
mood isn’t perfectly linear, so that the expected residual differs by block
- behavior changes across trials for a reason unrelated to
mood and unrelated to the blocking induced by the mood measurement.
These possibilities suggest some additional models. 1 & 2 would both suggest a model like
behaviour ~ 1 + mood + (1 | block_of_10_trials)
Possibility 3 would suggest a model like
behavior ~ 1 + mood + measurement_index (linear relationship with measurement_index) or
behavior ~ 1 + mood + s(measurement_index)
These could also be combined, though it might be flogging your data a bit hard to include both the random effect and the smooth term above. But
behavior ~ 1 + mood + measurement_index + (1 | block_of_10_trials)
feels like it might be reasonable, if something like this is consistent with your domain expertise.
Thank you for explaining this in detail, this is extremely helpful! I need to think some more about how to include this.
I think I have already included something that is a bit like your suggestions with:
behavior ~ 1 + mood + measurement_index
by doing
[1] behaviour ~ 1+ measurement index
-> get the residual
[2] residual ~ mood
the reason i’ve been doing it like this is that I’m not sure yet how to best code mood - they rate different emotions and they could be combined in different ways. So I was thinking that the two step process is overall faster (and then maybe once I have results I will rerun something like what you suggest to be sure it’s not an artefact of this approach)