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.di...@dzne.de> > > Subject: Re: [Freesurfer] LME model contrast matrix (Diers, Kersten > > /DZNE) > > To: "freesurfer@nmr.mgh.harvard.edu" <freesur...@nmr.mgh.harvard.ed > > u> > > Message-ID: <1572947286.4016.34.ca...@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.di...@dzne.de> > > > > Subject: Re: [Freesurfer] LME model contrast matrix > > > > To: "freesurfer@nmr.mgh.harvard.edu" <freesur...@nmr.mgh.harvar > > > > d.ed > > > > u> > > > > Message-ID: <1571904388.10840.18.ca...@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 . > > > > > > > > > > 1. 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. > > > > > > > > > > > > > > > > > > > 2. 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. > > > > > > > > > > > > > > > > > > > 3. 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 _______________________________________________ Freesurfer mailing list Freesurfer@nmr.mgh.harvard.edu https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer
