Hi Leonardo,
In principle what you want to do is possible, although implementing it in SPM will be tricky. The main issue is the fact that you have a within-subject/repeated measures factor in your design. If you want all levels of condition available at the second level then you will need to specify the model using the Flexible Factorial module. Here you will only be able to look at the within-subject main effects, as well as the within-subject x between-subject interactions. To look at the between-subject main effects you would need to specify a second model containing only the between-subject factors, after averaging over the within-subject (so averaging over condition for each subject). The reason for this is that SPM only uses the overall variance of the model in the denominator of the test statistics, however, mixed designs require a minimum of 2 variance components (the between and within) for the different tests. As SPM has no facility for this, you need to force it to be correct by using different models.
You can read about all of this in the introduction of my NeuroImage paper from earlier this year: http://www.sciencedirect.com/science/article/pii/S1053811916001622
The other tricky thing is that the Flexible Factorial module requires you to understand how to specify contrasts in over-parameterised designs, as they are less intuitive than the standard cell means contrasts used in SPM. You can read more about that (albeit not in the context of repeated measurements) here: http://journal.frontiersin.org/article/10.3389/fnins.2016.00270/full
If you still want to go down the full repeated-measures road, have a look at the Multivariate and Repeated Measures (MRM) toolbox: http://www.click2go.umip.com/i/s_w/mrm.html
All that being said, the conventional way to do this in SPM would be to create the within-subject contrasts at the 1st-level, and then take those to the 2nd-level. In your case there are 3 conditions (A,B,C), so for each subject you would have 3 contrasts: A-B, A-C and B-C. Then you would have 3 between-subject models for each of these contrasts. Interpretation can become more tricky, but this is the usual way around the repeated-measures issue. If you create these models using the Full Factorial module then SPM will automatically create the main effects and interaction contrasts for you.
With regards to the continuous covariate of interest (biomarker), bear in mind that the main effect test will be assessing whether the regression slope for that covariate is 0. This model will implicitly assume that the slope is the same for every group in the design. In order to assess interactions with the biomarker, you need to tell SPM to create an interaction term with the covariate. This will split biomarker in the design matrix, and a separate slope for each grouping will be estimated. Differences between these slopes can then be tested for.
Finally, the issue of assessing a main effect in the presence of an interaction can be understood from a simple logical perspective. An interaction tells you that one effect differs depending on the levels of another factor. If that is true, how can it be meaningful to assess that effect ignoring (so averaging over) that other factor? In brain imaging it is a little more tricky, however, the use of contrast masking here can really help by allowing you to mask out the interaction effect when looking at the main effects.
So, to summarise in relation to your questions
- "Would it be feasible or sensible to have everything in one model?"
It would be feasible and is perfectly sensible (though 4-way models are hard to interrogate), however, in SPM it will be difficult to do correctly. I would look into this more, and have a look at alternative software, and then decide whether you want to go down this road.
- "From what I understand, with this model, by using contrasts I can fairly easily investigate the main effects of: condition, diagnosis, lifestyle and biomarker"
Yes. The main effect of biomarker will be a test on the regression slope against 0.
- "By specifying in the model that my biomarker interacts with each factor, I can also explore the two-way interactions (condition*biomarker, diagnosis*biomarker, etc.)"
Yes. Biomarker will be split by the different groupings, and you can look for differences between the slopes.
- "Is it possible to investigate 3 and/or 4 level interactions such as condition*diagnosis*biomarker or condition*diagnosis*lifestyle*biomarker?"
Possibly in SPM, but my hunch is that it would be difficult. Alternative software may make this easier to do.
- "I keep hearing that if an interaction is present in the model, the main effect should not be interpreted. This seems strange to me and I would like to know if you think this applies to SPM. For example, if I had condition*diagnosis*biomarker in the model, could condition*diagnosis still be interpreted?"
As I said above, this more of a logical argument. If you know that diagnosis*biomarker differs depending on the level of condition, how is it sensible to ignore that and just look at diagnosis*biomarker averaged over condition? What would that tell you?
Hope that all helps.
Best wishes
Martyn
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Martyn McFarquhar, PhD
Neuroscience and Psychiatry Unit
G.708 Stopford Building
The University of Manchester
Oxford Road
Manchester
M13 9PL
Tel: +44 (0) 161 275 7764
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