# FBA design / contrast matrices for three groups

#1

Hello experts!

I’m trying to compute FBA, and would appreciate your advice on statistical matrices construction. We have three groups: typical population (T), disease population (D), and disease-related (Dr) population. My first version of design matrix is this:

1 1 0 0
1 0 1 0
1 0 0 1

Where the first column is intercept, the second is T group, the third is D group, and the fourth is Dr group. N lines for N subjects.
The contrast matrix for me to see the difference between groups:

(1) D > T 0 -1 1 0 (2) D < T 0 1 -1 0
(3) Dr > T 0 -1 0 1 (4) Dr < T 0 1 0 -1

Now comes the puzzle. Since fixelcfestats only accepts a single contrast, will I need to run the analysis twice? First, I will run (1) and (2) (supplying (1) and requesting -negative output as well), and then run (3) and (4) in the same manner? My question is whether this would be a correct way of running this type of analysis.

Thank you!

Olga

#2

Hi Olga,

This design matrix may misbehave as it is rank-deficient: the sum of columns 2-4 is equivalent to column 1, and therefore there are an infinite number of solutions for the beta values. While the GLM code is designed to still work in such circumstances, and due to the nature of your intended contrasts it shouldn’t actually have an effect on your t-values, it’s nevertheless avoided as best practise.

You could simply omit the first column entirely:

``````1 0 0
1 0 0
0 1 0
0 1 0
0 0 1
0 0 1
``````

(for two subjects in each group)

Moreover, while you have three groups in your experiment, none of your hypotheses actually require all three groups to be present in the model at the same time; and `fixelcfestats` can’t (currently) test more than one hypothesis at a time. So you could simply construct two separate design matrices: One for comparing T and D, one for comparing T and Dr; then run `fixelcfestats` separately for each.

Rob

#3

Hi Rob,

Thank you! That’s what I ended up doing. Watched a bunch of Jeanette Mumford’s brain stats videos, and read a lot of GLM theory…

If you don’t mind, can I piggyback on here with a couple of questions? First, I’m a little pained by the FWE correction. Is there an option to use FDR instead?

Second, may be a little silly question, but being new to these processes I’m trying to gain a thorough understanding of it all. I ran a simple correlation using a single group to see if some behavioral measures associate with WM “integrity” (for lack of a better word…). The results look interesting, but I could not wrap my head around what the absolute effect output would mean in this scenario. I “discovered” it’s identical to my beta of interest. Am I understanding it right that it just is designed to create this output?

Thanks!

#4

Watched a bunch of Jeanette Mumford’s brain stats videos, and read a lot of GLM theory

I’m sure there’s plenty of people on here interested in better understanding the GLM - and I don’t really want to spend an inordinate amount of time writing documentation on it - so if you can provide links to what you found useful I’m sure I’m not the only one who would be appreciative

I’m a little pained by the FWE correction. Is there an option to use FDR instead?

Currently no. I suppose it would technically be possible, but would require someone motivated enough to do it.

… I could not wrap my head around what the absolute effect output would mean in this scenario. I “discovered” it’s identical to my beta of interest. Am I understanding it right that it just is designed to create this output?

The “absolute effect” is the inner product of the beta values with the contrast vector. So if your contrast is a single “1” and zeroes in all other columns, then yes it is identical to the beta value of that column. In certain circumstances it can be used in certain calculations and/or have a certain interpretation, but it’s best understood from the underlying fundamental mathematics.

#5

Rob,

Thanks for detailed response!