Hello,
I have a dataset with a three-level structure. Participants reported an outcome of interest for 3-4 aspects of an incident, and they reported 4 types of incidents (1 incident for each level of 2 * 2 factors). I draw the structure in the figure below.
I have two questions:
(1) How should I structure the covariance matrix for residuals? I expect that the residuals for each person to correlate. Also, I expect that the residuals within each event correlate stronger. I prefer not to use an unstructured matrix, as the number of parameters would be too large. (If it cannot be done in SPSS, then R, preferably in nlme or lme4 packages.)
In SPSS, I'm using this syntax:
MIXED Y BY Valence Type Aspect
/FIXED = Valence Type Valence*Type | SSTYPE(3)
/REPEATED=Type*Valence*Aspect | SUBJECT(participant_ID) COVTYPE( )
(2) As is illustrated in the figure below, one aspect of the outcome is not applicable to the type 2 events (type 2 events only have 3 level-1 categories). I assume that when I want to assess the effect of incident type, I should exclude the number 4 aspect that is only applicable to type 1 incidents so that the results would reflect the difference between types including same level-1 outcomes. But, excluding number 4 or including it results in a negligible difference. Can I just report that, and then include the number 4 in subsequent analyses? Especially as excluding data from the number 4 will cost substantial statistical power.
Thank you in advance.
Are you sure Type is a level and not a variable? Is Type 1 and Type 2 a 'sample' of all the different Types that could occur - that is a random classification, if so then that suggests they are a level in a mixed model, but if those two exhaust the Types that can occur (or there are only a few Types) that suggests a fixed classification and I would treat it as a dummy variable in the fixed part of the model. See Structures and classifications here
http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#mlmbkgrd
Thank you for your reply, Dr. Kelvyn Jones
As you mentioned, Type is not a random factor, rather it is a binary within subject fixed factor (social/non-social), like Valence. I considered the interaction of these two factors to introduce another level to the model, because in this research, each participant reported four events (one event per each of 2 Types * 2 Valence), and so the residuals within each event (or within each category of this 2 * 2 interaction) are correlated. The 3-level structure is based on correlations of residuals; I considered the scores for each person as level-3 data; scores for each event within each person as level-2 data; and the scores for different aspects of each event (also a within subject fixed factor) as level-1 data.
I would appreciate any note on my view of the data structure.
I would use
MIXED Y BY Valence Type Aspect participant_ID
/FIXED = Valence Type Valence*Type | SSTYPE(3)
/RANDOM=participant_ID Aspect | COVTYPE(VC).
(for an intercept only model, or you open the slopes for the 3 fixed effects also: valence*participant_ID etc, all in the random line.
what do you think?
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