External Email - Use Caution
Hello Guodong,
On Mi, 2019-11-06 at 11:28 +0800, Liu Guodong wrote:
External Email - Use Caution
Hi Kersten,
Thank you so much for the reply and that helps a lot.
There are still some questions that I hope you can help me.
1.For the first model in you last email, you said 'To get the mean for group B, one would need to add the beta weights of the two regressors.’. I wonder if the beta weights should be 1 for regressors1 and 1 for regressor2, and the mean for group B is regressor2 plus regressor1 with the condition the value of group B is bigger than group A.
I am not sure if I understand correctly, but I suppose what you have in mind is the contrast weights rather than the beta weights.
With beta weights I am referring to the parameters estimated by the model (beta values), so you can't specify those. With contrast weights I am referring to the elements of the contrast vector or matrix (often 0, +1, or -1). These are specified by the user and are used to create weighted sums or differences of the beta weights, which in turn are evaluated for statistical significance.
In the first model for the t-test that we discussed in the previous mail, the hypothesis that B>A would be assessed by a contrast vector like [ 0 +1 ], assuming that the first regressor is the intercept and the second regressor codes 1 for group B and 0 for group A.
Keep in mind that in multi-variable regression models, the interpretation of (sums or differences) of parameter estimates is conditional on all other estimates being zero. So in a longitudinal model, for example, it is not the overall mean of e.g. A or B, but the mean at time zero.
2.Is there any P-value for the lme_fit_FS function to present the quality of the fitting?
No, not really. I also don't think that goodness of fit would be assessed by means of a p-value / hypothesis test, but rather by computing the R^2 statistic. For the LME tools, this needs to be calculated manually, I believe.
3.As you said before, if I have 3 group A,B,C for this model, and group A is reference group, the regressor1 is the mean of group A, and regressor2 and 3 reflect the difference between group A and B,C. But if I want to know the difference between B and C, what should I do. From the F-test, there only have a P-value to reflect how different between group B and C, I wonder can I compute a value the same as regressor 2 to reflect the difference?
To get the difference between two non-reference groups, you would specify a 'difference contrast', which has -1 and +1 at the appropriate columns, and zeros otherwise.
Best regards,
Kersten
Thanks!
Best regards, Guodong
Date: Tue, 5 Nov 2019 09:48:06 +0000 From: "Diers, Kersten /DZNE" Kersten.Diers@dzne.de Subject: Re: [Freesurfer] LME model contrast matrix (Diers, Kersten /DZNE) To: "freesurfer@nmr.mgh.harvard.edu" <freesurfer@nmr.mgh.harvard.ed u> Message-ID: 1572947286.4016.34.camel@dzne.de Content-Type: text/plain; charset="utf-8"
External Email - Use Caution
Hello Guodong,
consider as an analogy a two-sample t-test, where we simply compare two groups A and B:
If formulated as a regression problem, a commonly used model matrix for this test (but others are possible, too) will consist of two columns, one being all ones (the intercept), the other being zero for group A and one for group B.
The beta value for the first regressor should reflect the mean for group A (which is chosen as the reference group), and the beta value for the second regressor should reflect the difference between group A and B, which is the primary interest for this comparison. To get the mean for group B, one would need to add the beta weights of the two regressors.
The LME design matrices follow the same logic.
Alternatively, as said before, other design matrices are possible. In the above toy example, one could also use a matrix with two columns, where column 1 is one for group A and zero for group B, and column 2 is zero for group A and one for group B, thus omitting the overall intercept. Then, the beta weights would directly reflect the means of A and B. To get the difference between groups A and B, one would need to subtract the beta weights.
Mathematically, the two above models are equivalent. This also implies that one should not specify a model where there is an intercept, a regressor for group A, and a regressor for group B, because in this case, the regressors would be linearly dependent. Since having an overall intercept is advantageous (especially in more complex modelling situations than this toy example), the first model is the preferred one.
Hope this helps,
Kersten
On So, 2019-11-03 at 16:33 +0800, Liu Guodong wrote:
????????External Email - Use Caution????????
Dear Kersten:? The ?1 and ?2 in the tutorial model is the regressing coefficients for all the subjects not only for the control subjects because all the intercept are one. I wonder why the reference group is control group in this case?
Thanks in advance.
Best regards, Guodong
Date: Thu, 24 Oct 2019 08:06:28 +0000 From: "Diers, Kersten /DZNE" Kersten.Diers@dzne.de Subject: Re: [Freesurfer] LME model contrast matrix To: "freesurfer@nmr.mgh.harvard.edu" <freesurfer@nmr.mgh.harvar d.ed u> Message-ID: 1571904388.10840.18.camel@dzne.de Content-Type: text/plain; charset="utf-8"
???????External Email - Use Caution????????
Hi Guodong,
On Di, 2019-10-22 at 16:05 +0800, Liu Guodong wrote:
????????External Email - Use Caution????????
Hello FreeSurfer Developers,
I'm doing the LME tutorial, and I have some questions .
- Why don?t we need to put the healthy controls in the
designed matrix X?
Because that would be mathematically redundant, given the intercept and the other group regressors.?
In general, one chooses a reference group (in this case, controls), and this group is implicitly modeled (by the intercept). The other group regressors will then model the difference between that particular group and the reference group.
- What?s the interpretation of the first row of the contrast
matrix [1 0 0 0 0], does it mean first group minus healthy group?
I assume that we are talking about the first example, i.e. the simple univariate case (not mass-univariate).
Just to be precise, the first row of the contrast matrix would be [ 0 0 0 1 0 0 0 0 0 0 0 0 0 0], right?
The fourth regressor (which this contrasts tests) is "colum 3 * time", i.e. the interaction between the first group and time. This would indicate to which extent the slope across time in this group is different from the slope of the reference group.
- There is a pvalue and a vector sgn from the result of F-
test, I know the interpretation of the sgn, but I don?t know the hypothesis of the pvalue, could you please help me with that?
Strictly speaking, we test (and try to reject) the null hypothesis that the ?parameter estimate (or a linear combination of parameter estimates) is zero.
Best regards,
Kersten
Thanks in advance!
Best regards, Guodong
Freesurfer mailing list Freesurfer@nmr.mgh.harvard.edu https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer
Freesurfer mailing list Freesurfer@nmr.mgh.harvard.edu https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer
End of Freesurfer Digest, Vol 189, Issue 5
Freesurfer mailing list Freesurfer@nmr.mgh.harvard.edu https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer