David,
Just to supplement my other reply which was:
> Hi David,
>
> Apologies for the delay in replying.
>
> The weighting that is effectively applied to each subject is not
> currently stored in the feat stats directory. It is a function of:
>
> S: the lower-level variance (var_filtered_func_data in the feat dir)
> beta: the non-outlier random-effects variance
> (mean_outlier_random_effects_var1 in the stats dir)
> beta_outlier: the additional random-effects variance for outliers
> (mean_random_effects_var1 in the stats dir),
> probout: the probability of being an outlier (prob_outlier1 in the
> stats dir)
>
> Note that the 1's in the file names indexes the variance group. Then:
>
> weighting(i) = 1/(sqrt(A(i))
> where A(i)=(beta(i)+S(i))*(1-probout)^2 +(beta(i)+beta_outlier(i)
> +S(i))*probout.^2;
> and i indexes the subject.
>
> We'll have a think about perhaps putting this in as an output in a
> future release.
Strictly, the relevant eqn should have been:
A(i)=(beta+S(i))*(1-probout(i))^2 +(beta+beta_outlier
+S(i))*probout(i).^2;
apologies for that.
So this equation applies at any level in the hierarchy (e.g. 2nd or
3rd) above the first level when random effects with outlier inference
is being used.
If you want the weighting that is effectively being used without
outlier inference then naturally this corresponds to probout(i)=0, i.e:
A(i)=beta+S(i);
Note that these weightings correpond to flame1. Weightings for ols
would be the same but with S(i)=0. If flame2 is being used then the
weighting is integrated over the uncertainty in the random effects
variance and so can not be summarised with a single equation.
Cheers, Mark.
----
Dr Mark Woolrich
EPSRC Advanced Research Fellow University Research Lecturer
Oxford University Centre for Functional MRI of the Brain (FMRIB),
John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK.
Tel: (+44)1865-222782 Homepage: http://www.fmrib.ox.ac.uk/~woolrich
On 4 Jun 2009, at 20:15, David Paulsen wrote:
> Dear List,
>
> As I understand it, there are two ways in which individual's second
> level
> parameter estimates are differentially weighted in third level
> statistics:
> based on variance of second and first level PEs and if outlier
> deweighting
> is used.
>
> I would like to know the weights that were used for each subject at
> the
> third level, in both cases. Is there anyway to retrieve this
> information?
>
> Please & Thank You,
> David
>
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