Hi Laurens,

May I suggest that you take a look at the SwE toolbox, http://www.nisox.org/Software/SwE?  SwE stands for sandwich estimator, and this is a common approach used in biostatistics that does not require a balanced design and, in particular, avoids having to use per-subject dummy variables that currently occupy all but one of your design matrix columns.  

Where as SPM must assume a common repeated measures covariance over the brain, this allows any form of correlation at each voxel.

Also, on the issue of working with average data as Donald suggested, we evaluated that in our paper (Guillaume et al, 2014), and found that the heterogeneous variance from differing number of visits per subject can indeed corrupted the inference, leading to inflated false positive rates.

A few starting pointers: .With your small number of subjects, I'd recommend using "Homogeneous" SwE, where correlations are pooled over subjects; with, say, 50+ subjects you can use the "traditional" SwE which makes absolutely no assumptions on the form of the correlations.  The parametric inference mode gives you uncorrected and FDR-corrected tables of results just like SPM.  We have a nonparametric, Wild Bootstrap mode that gives you FWE voxel and cluster inference but we haven't implemented the results table yet (you just get -log10 P-value images that you can subsequently interrogate, but we're working on addressing that limitation.

Let me know if you have any problems/questions with it.  

-Tom

• Guillaume, B., Hua, X., Thompson, P. M., Waldorp, L., & Nichols, T. E. (2014). Fast and accurate modelling of longitudinal and repeated measures neuroimaging data. NeuroImage, 94, 287–302. doi:10.1016/j.neuroimage.2014.03.029

On Tue, Mar 20, 2018 at 3:49 PM, Laurens Winkelmeier <laurens.winkelmeier@zi-mannheim.de> wrote:

Dear SPM experts,

I am having trouble setting up my second level analysis.

In short, I have 18 subjects for which multiple sessions were acquired. After having filtered out sessions not fulfilling the predefined performance criterion, the number of repeated measurements differs strongly between the subjects (varies from 1 to 5 sessions).

I considered the following approaches to solve the issue:

1. Modelling the subject factor by adding all sessions of the same subject in one first level analysis (averaging the sessions). A potential drawback comes up when I go on with the second level analysis. Each contrast map from the first level analysis would be taken into account in equal measure, no matter the number of repeated measurs for each subject.

2. I performed a first level analysis for each session and took all contrast maps into the second level. Additionally, I defined a multiple covariate including a binary regressor for each subject with at least 1 session. The regressors assign the contrast maps to the respective subject. You find the desgin matrix in the attachment.

3. A flexible factorial design?

What is the best way to model the different number of repeated measures? Is my second approach (admittedly a very easy one) appropriate to handle my problem? is SPM even capable to cope with my study design?

Thank you in advance.
best,

Laurens

--

__________________________________________________________

Thomas Nichols, PhD

Professor of Neuroimaging Statistics

Nuffield Department of Population Health | University of Oxford
Big Data Institute | Li Ka Shing Centre for Health Information and Discovery
Old Road Campus | Headington | Oxford | OX3 7LF | United Kingdom
T: +44 1865 743590 | E: [log in to unmask]
W: http://nisox.org | http://www.bdi.ox.ac.uk