% Random effects analyses for SPM'96 using a multi-level approach
%_______________________________________________________________________
%
% In general mixed effects models (with both random and fixed effects)
% are difficult to analyse. However, in functional neuroimaging the
% models are fairly simple, balanced, and the only random effect of
% concern is the subject by condition interaction: Further, the models
% are seperable into individual subject models. This enables a basic
% mixed effects analysis to be easily be carried out in two stages,
% corresponding to the two levels of variability in question. The first
% level is the intra-subject level, the second the inter-subject
% (intra-population) level.
%
% The key is to avoid repeated measures: If we have only one scan per
% condition per subject, then the residual variance incorporates the
% appropriate inter and intra-subject variance components, and effects
% a mixed effects analysis appropriate for population inference. With
% repeated measures the trick then is to collapse over replications to
% give a single summary image representative of each condition for each
% subject. Such collapsing may be as simple as a straight mean of the
% replicate observations, or can be a sophisticated weighted mean of
% adjusted data effected via the General Linear Model, enabling removal
% of confounds. (See spm_adjmean_ui & spm_adjmean_fmri_ui for further
% details on computing adjusted mean images).
%
% Basically:
%   1. Collapse data to single scan per condition per subject
%      (See spm_adjmean_ui & spm_adjmean_fmri_ui, and their help)
%   2. Run collapsed data as a multisubject "conditions only" design in SPM-PET
%      ( No need for grand mean scaling or global normalisation )
%      ( if spm_adjmean{_fmri}_ui used correctly                )
%    - Can include more than two conditions, but should only consider
%      contrasting them in pairs.
%    - Can compare groups using "multistudy-conditions only" and using
%      examining interaction of pairs of conditions:
%      E.g: 2 studies, 2 conditions per study: [-1 +1 +1 -1] & [+1 -1 -1 +1]
%
% For example, consider a simple multi-subject two condition PET
% activation study. A simple analysis would be to proportionally scale
% the images to have the same global value; compute mean images for
% each condition for each subject; and assess using a paired t-test.
% This was effectively what Worsley et al. proposed in their seminal
% 1992 paper, with the exception that they used a globally pooled
% variance estimate (now deemed inappropriate).
%
%                           ----------------
%
% A paper is currently (20/02/1998) in preparation. In the interim, you
% are referred to the relevant correspondance on the SPM disussion
% list: Messages are archived at the UK's Academic MailBase facility:
%
% Discussion with Jack Van-Horn: concerning appropriate variances...
%       http://www.mailbase.ac.uk/lists/spm/1997-11/0011.html
%       http://www.mailbase.ac.uk/lists/spm/1997-11/0015.html (APH)
%       http://www.mailbase.ac.uk/lists/spm/1997-11/0028.html
%       http://www.mailbase.ac.uk/lists/spm/1997-12/0005.html (APH)
% 
% APH to Eric Zahrahn:
% Subject by task interactions & group by task interactions...
%       http://www.mailbase.ac.uk/lists/spm/1997-12/0031.html (APH)
% 
% Discussion with Darren Gitelman: adjusting images...
%       http://www.mailbase.ac.uk/lists/spm/1998-01/0001.html (DG)
%       http://www.mailbase.ac.uk/lists/spm/1998-01/0036.html (APH)
% 
% Dsicussion with Andy Saykin: Multisubject and Between Group fMRI Analyses...
%                               (one scan per condition per subject)...
%       http://www.mailbase.ac.uk/lists/spm/1997-12/0004.html (AS)
%       http://www.mailbase.ac.uk/lists/spm/1997-12/0006.html (KJF)
%       http://www.mailbase.ac.uk/lists/spm/1997-12/0013.html (APH)
% 
% Queries are included in replies where relevant, so only the (APH)
% replies need be looked up.
%
%
% ======================================================================
%
% The basic random effects kit for SPM96 consists of:
%
%     spm_RandFX.man        1.3      - This file
%     spm_adjmean_ui.m      1.5.1.1  - Adjusted means for PET designs
%     spm_adjmean_fmri_ui.m 1.2.1.1  - Adjusted means for fMRI
%     spm_hrf.m             1.2      - Approx HRF for fMRI
%     spm_sptop.m           1.7      - SParse TOePlitz update
%                                      (v1.2 came with SPM96)
%
% ...and includes updates to two SPM interface routines, allowing easy
% launching of the new programs:
%
%     spm.m                 1.26.1.2 - "Mean" button altered to "AdjMean", calls
%                                      spm_adjmean_ui or spm_adjmean_fmri_ui
%                                      according to the current SPM mode,
%                                      PET of fMRI
%     spm_help.m            1.15.1.2 - Menu topic changed to reflect new
%                                      AdjMean button
%
% spm_sptop.m (v1.7), spm.m (v1.26.1.2) & spm_help.m (v1.15.1.2) are
% backwards compatible with the versions supplied with SPM96, so the
% SPM96 random effects kit can be installed over an SPM96
% installation.
%_______________________________________________________________________
% @(#)spm_RandFX.man	1.3 Andrew Holmes 98/02/20