After some research, I'll answer to my own question, because I think it could be of use to others. It's actually surprising that the topic is not so clear in our community.

Although less sensitive, obtaining first-level contrasts to be later taken to the second-level is the easiest and the recommended way for SPM, at least in the case of a within-subjects design. This approach partitions the GLM error into separate components, which does not offer concerns about non-sphericity and controls false-positive results (when compared to pooled error).

Regarding repeated-measures design, one can then create 1st-level ANOVA contrasts for each run and average them in ImCalc (for SPM users). The one takes the averages to the 2nd-level contrast, which can be the mean across subjects.

For references, please refer to:

- Henson R.N. (2015) Analysis of Variance (ANOVA). In: Arthur W. Toga, editor. Brain Mapping: An Encyclopedic Reference, vol. 1, pp. 477-481.

- McFarquhar M. (2019). Modeling Group-Level Repeated Measurements of Neuroimaging Data Using the Univariate General Linear Model. Frontiers in Neuroscience, vol. 13.

Thanks to Guillaume Flandin for helping me to clarify this topic.

Hi Gustavo

Thank you for sharing this. I am currently facing similar problems. As I understood your answer, it is recommended to model more complex 1st level contrast and then enter into a simple 2nd level model, is that correct?

Hi Pengfei,

Yes, I'd recommend that. You create the contrasts you want in the first level. Then you compute the interaction and the main effects, for example, if it's a 2x2 design, by using ImCalc for each subject. Finally, you compute the average again across subjects using the subject-specific contrasts you created earlier.

Hi Miguel,

Your analysis seems ok, except by the "Group Effects" at the end. They are t-tests for me, and they would not produce F-contrasts. And you are not computing the interaction, as you referred in the question.

Nevertheless, notice that you have one of the factors that is within-subject (cond). In this case, it's recommended to use a different approach in SPM, because it controls for false-positive results (see literature in my comment above).

I would then recommend you to compute the contrasts cond X minus baseline for each subject. Then, using ImCalc, you can compute each main effect and interaction from the contrasts you have created earlier. In a "third-level" analysis, then you compute the average across subjects using a one-sample t-test.

Hi Gustavo Pamplona,

Could you develop a bit on the "using ImCalc" part maybe? O rwould you have snippet of code that give an example?

Thanks in advance,

David

Hi David Munoz Tord,

Let's say you have two factors, letter (A and B) and number (1 and 2) in your 2x2 factorial design. So, as described above, you've created, for each subject, contrasts A1, A2, B1, and B2 (condition minus baseline).

Then, in ImCalc you can easily compute A1 + A2 - B1 - B2 as the main effect of letter, A1 - A2 + B1 - B2 as the main effect of number, and A1 - A2 - B1 + B2 as the interaction.

I hope it helps!

Gustavo

Hi, Gustavo,

Thanks a lot for this sharing, it indeed helps me a lot.

I have a more complicated design, which is a 2 way (3 groups x 2 conditions) mixed design. Contrast images are A1, A2, B1, B2, C1, and C2.

For testing group effect, I ran a one-way ANOVA by comparing the contrast images of group A(condition 1+condition 2), group B(condition 1+ condition 2), and group C(condition 1 + condition 2).

Then, for testing the effect of condition, I ran a paired t test by comparing condition 1 and condition 2 across all subjects.

My question is about the interaction effect.

By using the code "Con = spm_make_contrasts([k1 k2])"

the interaction effect is

[1 -1 -1 1 0 0

0 0 1 -1 -1 1]

which is corresponding to

[(A1-A2)-(B1-B2)

(B1-B2)-(C1-C2)]

What should I do?

If I do a two-sample t(?), I can only run either (A1-A2)-(B1-B2) or (B1-B2)-(C1-C2)

How can I test two effects altogether?

I hope I explain my question well.

Thanks in advance and Looking forward to your reply :)

Yin-Hua Chen

Hi Yin-Hua,

A mixed-measures ANOVA doesn't follow the same logic as for the repeated measures ANOVA, because levels of a factor are not expressed within each subject in the between-subject ANOVA.

This is what I would probably do:

1) Compute first-level contrasts for each one of your conditions and each subject

Let's say that in your case you have S1, S2, ..., SN subjects and C1 and C2 conditions. This way, you will compute the contrasts S1C1, S1C2, S2C1, S2C2, ..., SNC1, SNC2. For example, if you have 60 subjects (considering all groups), you will have 120 contrasts.

2) Then, average the contrasts within each group, for separate conditions

Let's say that in your case you have groups Ga, Gb, and Gc. Now, you will average the contrasts separately for each condition. This way, you will end up with GaC1, GaC2, GbC1, GbC2, GcC1, GcC2 (now, only 6 contrasts).

3) Compute the contrasts for main effect of group and interaction

As you pointed out, if you compute spm_make_contrasts([3 2]), you will get the main effect of factor 1, 2 and interaction. Just follow then and compute:

Main effect of group:

contrast_A = GaC1+GaC2 - (GbC1+GbC2)

contrast_B = GbC1+GbC2 - (GcC1+GcC2)

Interaction

contrast_C = (GaC1-GaC2) - (GbC1-GbC2)

contrast_D = (GbC1+GbC2) - (GcC1-GcC2)

4) Compute the second-level contrasts for main effect and interaction

Define an F-contrast putting together contrast_A and contrast_B. This is the final F-contrast for the main effect of group (notice that you don't need that first one-way ANOVA computed separately in the beginning as you mentioned, but computed in a similar way to the interaction).

Define an F-contrast putting together contrast_C and contrast_D. This is the final F-contrast for the interaction.