SPM in Practice

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SPM in Practice
March 2006 Yael Weisberger
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SPM- Data conversionAnalyzer
SPM
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SPM- Data conversionAnalyzer
SPM
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SPM software -2D interpolation
Interpolated voxel spaced
EEG
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Hierarchal model

• Yx(1)b(1) e(1)
• b(1)x(2)b(2) e(2)
• 1st level observation model for multiple ERP
• Within ERP- temporal effect fixed effect
  (single subject)
• 2cnd level model 1st level parameters over
  subjects trial types
• Between ERP- experimental effect (group,
  condition) random effect (population inference)
• Need to estimate associated error covariance

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1st level observation modeltemporal matrix

• Yx(1)b(1) e(1)
• b(1)x(2)b(2) e(2)
• Y ERP for each subject trial
• X(1) I(NsubjectsNtypes) X(t)
• X(t) N bines X N p models temporal components
  of single ERP
• X(t) - Any linear transform of ERP- wavelets
• fig 1, p 501

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SPM software -1st level

• The contrasts are an average of the interpolated
  images in the time interval you have specified.

120-170 ms
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E-mail
gt 2. Is there a way to do more sophisticated
temporal matrixes, for example gt specify
wavelets in the 1st level as described in
KiebelFriston, 2004b ? gt gt 3. Is the 1st
level design not to be estimated? I'm asking this
since there gt is no SPM file created in 1st
level , however according the SPM5 manual, gt
KiebelFriston paper and the version before
update 456, it was possible to gt make single
subject inference from the 1st level. gt For
SPM5, these two things didn't make it into the
software. The main reason was that with 1st
level design matrices it can easily happen that
you specify design matrices that don't capture
all your interesting effects. This is due to the
huge variability of evoked responses over
different types of experiments. You would lose a
lot of sensitivity, at the 2nd level, if you
used the 'wrong' kind of first level design
matrix. Note that you still can do a 1st level
analysis by averaging over single trials (i.e.,
1st lvl single trials, 2nd lvl effects averaged
within trial type).
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2cnd level design matrix

• Yx(1)b(1) e(1)
• b(1)x(2)b(2) e(2)
• X(2)x(d) Ip (p from 1st level time matrix)
• X(d) subject trial type specific treatment
  effect
• Example x(d) 1 subjects X I types-
• averages over
  subjects across trial types
• Fig 3. p506

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Design matrix- Example

• MMN experiment
• 2 groups control,dyslexic
• 3 Deviant types 10,5,2.5

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2cnd level-full factorial- 2factors
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2cnd level-full factorial- 2factors

• E-mail
• gt 2cnd level
• gt 1. Full factor analysis 4 factors- got a
  message that it can't run
• gt this design.
• gt
• This is a slight limitation of the software.
  However, I'd recommend
• breaking your design apart and not attempt to
  model everything in one
• huge model. If possible, you should keep the
  tests at the 2nd level as
• simple as possible, e.g. a 1-sample t-test. The
  disadvantage of this
• approach is that you have, inconveniently, to
  specify one model for each
• hypothesis. The advantage of that approach is
  that the modelling is
• simpler, with respect to variance parameters.

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2cnd level- 2 sample t-test
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Estimation

• After specifying the model..
• Estimate the parameters using ML or ordinary
  least squares (OLS)
• Variance parameters by ReML

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SPM-software estimation
B1- dyslexic
B2 controls
Residual sum of squares
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Contrast estimation

• For general linear model Y XB E with data Y,
  design matrix X, parameter vector B, and
  (independent) errors E, a contrast c'B of the
• parameters (with contrast weights c) is
  estimated by c'b, where b are the parameter
  estimates given by bpinv(X)Y.

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T,F contrasts

• simple contrasts for SPMT-
• tests the null hypothesis c'B0 against the
  one-sided alternative c'Bgt0, where c is a column
  vector.
• "F-contrasts" for SPMF-
• two-sided alternative c'B0.
• contrast weights is a matrix
• Testing the significance of effects modelled by
  multiple columns

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Inference-contrasts

• Contrast- linear combination of parameter
  estimates that defines a specific null hypothesis
  about the parameters

T-values
After FWE correction
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Different levels of inference

• The p values are based on the probability of
  obtaining c, or more,clusters of k, or more,
  resels above u, in the volume S analysed
  P(u,k,c).
• set-level For specified thresholds u, k, the
  set-level inference is based on the observed
  number of clusters C, P(u,k,C).
• cluster-level For each cluster of size K the
  cluster-level inference is based on P(u,K,1)
• voxel-level for each voxel (or selected maxima)
  of height U, in that cluster, the voxel-level
  inference is based on P(U,0,1).

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thresholding

• The SPM is subject to thresholding on the basis
  of height (u) and the number of voxels comprising
  its clusters k.
• The height threshold is specified as above in
  terms of an uncorrected p value or statistic.
• Clusters can also be thresholded on the basis
  of their spatial extent. If you want to see all
  voxels simply enter 0.
• In this instance the 'set-level' inference can be
  considered an 'omnibus test based on the number
  of clusters that obtain.

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End