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In the context of comparing one family or subset of models with another, one would usually report the posterior probabilities (over models) – or the corresponding exceedance probability. Generally, one is hoping to see that one family has a 95% or greater posterior probability, in relation to competing models or hypotheses.
However, it is also useful to report the results of a model comparison even when there is no definitive 'winner'. In other words, you can still report the most probable model, noting that the data could not disambiguate definitively between the various hypotheses considered.
This answer assumes you have a well-defined question that can be cast in terms of subsets or families of models (for example the presence or absence of backward connections). If you are scoring hundreds or thousands of models, then this is typically done to access a Bayesian model average of the model parameters – for subsequent analysis at the between subject level.
I hope this helps.
With best wishes – Karl
Many thanks for your e-mail. Although the prototype routines were distributed with SPM8, they were not included in the GUI. I would recommend that you use SPM12 – because the routines have now been optimised and debugged. I'm copying this to Guillaume because he may be able to tell you how to get the most recent version of SPM.
The issue of non-significant Bayes factors is – I presume – a question of model dilution. This is usually resolved using family comparisons. The new post optimisation routines allow you to specify families, and therefore make your model comparisons more efficient (see help section below). However, I do not know if anybody has actually use them routinely yet.
With best wishes – Karl
function
DCM = spm_dcm_post_hoc(P,fun)% Post hoc optimisation of DCMs (under the Laplace approximation)
% FORMAT DCM = spm_dcm_post_hoc(P,[fun])
%
% P - character/cell array of DCM filenames
% - or cell array of DCM structures
%
% fun - optional family definition function: k = fun(A,B,C,D)
% k = 1,2,...,K for K families or proper subsets of a partition
% of model space - a function of the adjacency matrices: e.g.,
%
% fun = inline('any(spm_vec(B(:,:,2))) + 1','A','B','C','D')
%
% returns 1 if there are no bilinear parameters for the 2nd
% bilinear effect and 2 if there are. fun should be an inline
% function or script. NB: Model posteriors over families with
% and without free parameters (in A,B,C and D) are evaluated
% automatically and saved in DCM_BPA (DCM.Pp)
%
%--------------------------------------------------------------------------
% This routine searches over all possible reduced models of a full model
% (DCM) and uses post hoc model selection to select the best. Reduced
% models mean all permutations of free parameters (parameters with a non-
% zero prior covariance), where models are defined in terms of their prior
% covariance. The full model should be inverted prior to post hoc
% optimization. If there are more than 16 free-parameters, this routine
% will implement a greedy search: This entails searching over all
% permutations of the 8 parameters whose removal (shrinking the prior
% variance to zero) produces the smallest reduction (greatest increase)
% in model evidence. This procedure is repeated until all 8 parameters
% are retained in the best model or there are no more parameters to
% consider. When several DCMs are optimized together (as in group studies),
% they are checked to ensure the same free parameters have been specified
% and the log-evidences are pooled in a fixed effects fashion.
%
% This application of post hoc optimization assumes the DCMs that are
% optimized are the same model of different data. Normally, this would be
% a full model, in the sense of having the maximum number of free
% parameters, such that the set of reduced models is as large as possible.
% In contrast spm_dcm_search operates on different DCMs of the same data
% to identify the best model, after inverting the full(est) model
%
% The outputs of this routine are graphics reporting the model reduction
% (optimisation) and a DCM_opt_??? for every specified DCM that contains
% reduced conditional parameters estimates (for simplicity, the original
% kernels and predicted states are retained). The structural and functional
% (spectral embedding) graphs are based on Bayesian parameter averages
% over multiple DCMs, which are stored in DCM_BPA.mat. This DCM also
% contains the posterior probability of models partitioned according to
% whether a particular parameter exists or not:
%
% DCM.Pp - Model posterior over parameters (with and without)
% DCM.Ep - Bayesian parameter average under selected model
% DCM.Cp - Bayesian parameter covariance under selected model
% DCM.Pf - Model posteriors over user specified families
% DCM.fun - User-specified family definition function
% DCM.files - List of DCM files used for Bayesian averaging
%
%__________________________________________________________________________
% Copyright (C) 2010-2012 Wellcome Trust Centre for Neuroimaging
% $Id: spm_dcm_post_hoc.m 4807 2012-07-26 16:15:49Z guillaume $