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**RE: Clarification on contrasts in CONN 2nd-level multivariate analysis**Oct 12, 2018 03:10 AM | Martyn McFarquhar

RE: Clarification on contrasts in CONN 2nd-level multivariate analysis

Hi Alfonso,

This is turning into a very interesting conversation!

Apologies for the error in the code, you are indeed correct on all counts. However, I should clarify what I meant as I was simply saying that partitioned-errors are more sensitive than

Even with the changes to the code, the approaches do not agree. I think we should be aiming for better than "close enough" with these methods, and the two-stage approach (based on Will Penny's recommendations) is still not estimating the F-statistic correctly nor the degrees of freedom for the within-subject models with > 2 levels. This can't be due to differences in the treatment of sphericity because the SPSS results I've reported have not adjusted for non-sphericity and nor have the SPM results. As such, the results should be

My thinking is that the non-sphericity correction should not be necessary in order to achieve the "correct" F-statistic when sphericity is assumed. This speaks to a larger issue in terms of the GLM implementation in other packages that do assume sphericity (such as FSL) where the model we use should allow us to achieve the classical results, under assumptions of sphericity. If one wished to assume sphericity then the two-level models (given in the script I sent, not the ones you have indicated) do not actually achieve the classical results under assumptions of sphericity. My aim would be to get the models to agree under assumptions of sphericity and then apply the non-sphericity correction, as I don't think the correction should be seen as an integral part of the model, but rather an adjunct control for liberal/conservative conclusions when the assumptions are not adequately met.

Additionally, although the code you provided does give the same F-statistic it does not appear to give the same degrees of freedom (SPSS-like = 1.9781,55.3860 [which agrees with the Greenhouse-Geisser correction], CONN-like [2-dimensions] = 1.5814, 44.2780, CONN-like [3-dimensions] = 1.9781,55.3860 [again, Greenhouse-Geisser]). And so the 2-dimension model will give a different

Furthermore, even if the degrees of freedom agree with the Greenhouse-Geisser correction, this correction should be applied to the original F-statistic of 1.167, rather than the F-statistic of 1.1006 produced by the code. As such, the SPSS Greenhouse-Geisser corrected results of F(1.98,55.39) = 1.167, p = 0.319 is still not matched by the non-sphericity-corrected results of F(1.98,55.39) = 1.1009, p = 0.340.

I know this seems like splitting hairs, but we need to be convinced that the models we are using are appropriate and I still think the best way to do so is make sure we can achieve equivalency with the classical results in the textbooks (and implemented in other software)

Looking forward to hearing your thoughts!

Best wishes,

- Martyn

This is turning into a very interesting conversation!

Apologies for the error in the code, you are indeed correct on all counts. However, I should clarify what I meant as I was simply saying that partitioned-errors are more sensitive than

*pooled*errors and that the two-stage approach, although claiming to implement partitioned errors, does not agree with the partitioned error approaches in other software. My point was just that we need to get the partitioned-errors*right.*Even with the changes to the code, the approaches do not agree. I think we should be aiming for better than "close enough" with these methods, and the two-stage approach (based on Will Penny's recommendations) is still not estimating the F-statistic correctly nor the degrees of freedom for the within-subject models with > 2 levels. This can't be due to differences in the treatment of sphericity because the SPSS results I've reported have not adjusted for non-sphericity and nor have the SPM results. As such, the results should be

*identical*.My thinking is that the non-sphericity correction should not be necessary in order to achieve the "correct" F-statistic when sphericity is assumed. This speaks to a larger issue in terms of the GLM implementation in other packages that do assume sphericity (such as FSL) where the model we use should allow us to achieve the classical results, under assumptions of sphericity. If one wished to assume sphericity then the two-level models (given in the script I sent, not the ones you have indicated) do not actually achieve the classical results under assumptions of sphericity. My aim would be to get the models to agree under assumptions of sphericity and then apply the non-sphericity correction, as I don't think the correction should be seen as an integral part of the model, but rather an adjunct control for liberal/conservative conclusions when the assumptions are not adequately met.

Additionally, although the code you provided does give the same F-statistic it does not appear to give the same degrees of freedom (SPSS-like = 1.9781,55.3860 [which agrees with the Greenhouse-Geisser correction], CONN-like [2-dimensions] = 1.5814, 44.2780, CONN-like [3-dimensions] = 1.9781,55.3860 [again, Greenhouse-Geisser]). And so the 2-dimension model will give a different

*p*-value to the SPSS and 3-dimension model. I suppose the question in then whether this is to be expected or not as to my mind all the models are testing the same hypothesis with the same data and so the conclusions should be invariant to this sort of choice? This is the claim made by the two-stage approach, but as far as I can tell it still does not agree.Furthermore, even if the degrees of freedom agree with the Greenhouse-Geisser correction, this correction should be applied to the original F-statistic of 1.167, rather than the F-statistic of 1.1006 produced by the code. As such, the SPSS Greenhouse-Geisser corrected results of F(1.98,55.39) = 1.167, p = 0.319 is still not matched by the non-sphericity-corrected results of F(1.98,55.39) = 1.1009, p = 0.340.

I know this seems like splitting hairs, but we need to be convinced that the models we are using are appropriate and I still think the best way to do so is make sure we can achieve equivalency with the classical results in the textbooks (and implemented in other software)

*before*adding on additional corrections (particularly when these corrections are not available in all software). This is easy enough when dealing with 2-levels, but > 2-levels is still a sticking point for me.Looking forward to hearing your thoughts!

Best wishes,

- Martyn

## Threaded View

Title | Author | Date |
---|---|---|

Martyn McFarquhar |
Oct 4, 2018 | |

Alfonso Nieto-Castanon |
Oct 5, 2018 | |

Martyn McFarquhar |
Oct 5, 2018 | |

Alfonso Nieto-Castanon |
Oct 5, 2018 | |

Martyn McFarquhar |
Oct 8, 2018 | |

Alfonso Nieto-Castanon |
Oct 8, 2018 | |

Martyn McFarquhar |
Oct 9, 2018 | |

Alfonso Nieto-Castanon |
Oct 9, 2018 | |

Ali Amad |
Oct 11, 2018 | |

Alfonso Nieto-Castanon |
Oct 12, 2018 | |

Ali Amad |
Oct 19, 2018 | |

Martyn McFarquhar |
Oct 11, 2018 | |

Alfonso Nieto-Castanon |
Oct 11, 2018 | |

Martyn McFarquhar |
Oct 12, 2018 | |

Alfonso Nieto-Castanon |
Oct 12, 2018 | |

Martyn McFarquhar |
Oct 15, 2018 | |

Martyn McFarquhar |
Oct 5, 2018 | |