Hi Chris, If you run an ANCOVA model with an interaction (which is what DODS is) then the interpretation of the group effect is ambiguous because the "group" effect varies with age. If there is actually a differential slope between groups, then the p-value of the contrast of the group means (i.e., "intercepts") can/will change considerably depending on whether or not age is demeaned (or centered around any other arbitrary ages).
Tom Nichols had a helpful explanation of the interpretation of various models that he posted to the SPM list back in 2008, which I've included below for your convenience.
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Post from Tom Nicols to SPM list https://www.jiscmail.ac.uk/cgi-bin/wa.exe?A2=ind0803&L=SPM&P=R19616&...
There is always going to be a huge space of models you can consider, and it is *not* advisable to check every model under the sun 'just to be safe'. Rather, always go for the simplest possible model *unless* there is a concern (backed by previous data, the literature) that a more complicated model is warranted.
Hence, if you run the ANCOVA-with-interaction model and find no evidence for an interaction, I'd recommend reverting to the simpler model in which to test the group main effect, as the interpretation of the group effect is unambiguous in the simpler model. If you must test the main effect in the model with an interaction then, yes, using centering is vital, but realize that the entire meaning of "main effect" is different, as the very *direction* of the group effect may flip as you consider different ages.
----------- Notation - General Linear Model
Y = X beta + epsilon
Y is response (data), X is design matrix of predictors, beta is vector of coefficients of predictors, epsilon is random error.
----- Two Sample T Model
Two groups of subjects, 3 in group I, 2 in group II.
Design Matrix Parameterization 1a
1 0 1 0 1 0 0 1 0 1
Coefficient Interpretation
beta1: Mean of Group I beta2: Mean of Group II
Contrast Interpretation
[ -1 1 ] Difference of group means, Group II > Group I
[ 1 0 ] Mean of Group I -- ONLY meaningful group level fMRI
[ 0 1 ] Mean of Group II -- ONLY meaningful group level fMRI
Design Matrix Parameterization 1b
-1 1 -1 1 -1 1 1 1 1 1
Coefficient Interpretation
beta1: Half the group mean difference, Group II > Group I beta2: Overall mean WHEN no group difference
Contrast Interpretation
[ 1 0 ] Half difference of group means, Group II > Group I [ 2 0 ] Difference of group means, Group II > Group I
Both contrasts will give identical T and P-values.
----- Simple Correlation Model
One group of 5 subjects, with age covariate with values: 20 25 30 35 40
Design Matrix Parameterization 2a (no centering)
1 20 1 25 1 30 1 35 1 40
Coefficient Interpretation
beta1: Expected response for Age of 0 beta2: Expected change in response with increase of 1 year (no longitudinal interpretation, only cross-sectional)
Contrast Interpretation
[ 0 1 ] Increase in response with increasing age
[ 1 0 ] NOT MEANINGFUL
Design Matrix Parameterization 2b (covariate centering)
1 -10 1 -5 1 0 1 5 1 10
Coefficient Interpretation
beta1: Expected response for (Age-Average(Age)) of 0, i.e. Age = Average(Age) beta2: Expected change in response with increase of 1 year (no longitudinal interpretation, only cross-sectional)
Contrast Interpretation
[ 0 1 ] Increase in response with increasing age (identical to previous parameterization).
[ 1 0 ] Expected response for an individual with average age, while accounting for (removing from error the) linear effect of age -- ONLY meaningful group level fMRI
----- ANCOVA Model - No Interaction
Two groups of subjects, 3 in group I, 2 in group II. Age covariate with values: 20 25 30 35 40
Design Matrix Parameterization 3a
1 0 20 1 0 25 1 0 30 0 1 35 0 1 40
Coefficient Interpretation
beta1: Expected response of Group I for Age of 0 beta2: Expected response of Group II for Age of 0 beta3: Expected change in response with increase of 1 year (no longitudinal interpretation, only cross-sectional)
Contrast Interpretation
[ 1 0 0 ] NOT MEANINGFUL [ 0 1 0 ] NOT MEANINGFUL
[-1 1 0 ] Difference of group means, Group II > Group I, while accounting for (removing from error the) linear effect of age. (NOTE: No interaction, so differential group effect doesn't vary with age).
[ 0 0 1 ] Increase in response with increasing age. (NOTE: No interaction, so age effect is same for both groups).
Design Matrix Parameterization 3b - Centering
1 0 -10 1 0 -5 1 0 0 0 1 5 0 1 10
Coefficient Interpretation
beta1: Expected response of Group I for Age = Average(Age) beta2: Expected response of Group II for Age = Average(Age) beta3: Expected change in response with increase of 1 year (no longitudinal interpretation, only cross-sectional)
Contrast Interpretation
[ 1 0 0 ] Expected Group I response at Age = average age, while accounting for linear effect of age -- ONLY meaningful group level fMRI
[ 0 1 0 ] Expected Group II ... " ...
[-1 1 0 ] (same as previous parameterization) [ 0 0 1 ] (same as previous parameterization)
----- ANCOVA Model - With Interaction
Two groups of subjects, 3 in group I, 2 in group II. Age covariate with values: 20 25 30 35 40, with group-dependent age effects.
Design Matrix Parameterization 4a
1 0 20 0 1 0 25 0 1 0 30 0 0 1 0 35 0 1 0 40
Coefficient Interpretation
beta1: Expected response of Group I for Age of 0 beta2: Expected response of Group II for Age of 0 beta3: Expected change in response with increase of 1 year for Group I beta4: Expected change in response with increase of 1 year for Group II
Contrast Interpretation
[ 1 0 0 0 ] NOT MEANINGFUL [ 0 1 0 0 ] NOT MEANINGFUL
[-1 1 0 0 ] NOT MEANINGFUL (Difference of group means, Group II > Group I, WHEN Age is 0. Interaction means differential group effect varies with age.)
[ 0 0 1 0 ] Increase in response in Group I with increasing age. [ 0 0 0 1 ] Increase in response in Group II with increasing age.
[ 0 0 -1 1 ] Different in age effects, Group II Age Slope > Group I Age Slope
Design Matrix Parameterization 4b - With Centering
1 0 -10 0 1 0 -5 0 1 0 0 0 0 1 0 5 0 1 0 10
NOTE: Centering of covariate is done BEFORE splitting into two covariates; the split covariates are *not* subsequently centered.
Coefficient Interpretation
beta1: Expected response of Group I for Age = Average(Age) beta2: Expected response of Group II for Age = Average(Age) beta3: Expected change in response with increase of 1 year for Group I beta4: Expected change in response with increase of 1 year for Group II
Contrast Interpretation
[ 1 0 0 0 ] Average Group I response at Age = average age, while accounting for group-specific linear effect of age -- ONLY meaningful group level fMRI
[ 0 1 0 0 ] Average Group II ... " ...
[-1 1 0 0 ] NOT MEANINGFUL, probably. (Difference of group means, Group II > Group I, WHEN Age = Average(Age). Dangerous to test/interpret as, again, interaction means differential group effect varies with age.)
[ 0 0 1 0 ] (same as previous parameterization) [ 0 0 0 1 ] (same as previous parameterization) [ 0 0 -1 1 ] (same as previous parameterization)
On Wed, 2011-03-09 at 22:36 -0500, Douglas Greve wrote:
Hi Michael,
I doubt that the loss of 1 DOF is causing the disappearance. In both models, the test for the difference between groups occurs at a particular age (age=0). This is not a factor in the DOSS model because the lines for the two groups are forced to be parallel (so the difference is the same at all ages). For the DODS, the lines are not constrained to be parallel, so you might have a large or small difference at age=0. If you de-mean the ages (ie, subtract the mean computed over ALL subjects regardless of group), then your test will be at age=MeanAge. This does not get around the problem, but you are at least testing at an age where your data are. In expectation, it should not make a difference, but in practice sometimes it does. If you run the DODS and do not find a difference in the slopes, then you are justified in re-running the fit using DOSS.
doug
On 3/9/11 6:55 PM, Christopher Bell wrote:
Michael,
Thanks for your response. It was helpful. As you suggested the "thickness-age correlation group difference" under DOSS is meaningless, so I have ignored that output. I am currently left with a situation where under the DOSS model I see a large ageXthickness effect (controlling for group) and a nearly identical map under the DODS model. So far so good. When I look at the group difference map, I see a large group difference for the DOSS model, and a LOT less for the DODS model. This would lead me to believe that the extra DOF in the DODS model is removing the group difference because my two groups have different ageXthickness slopes and when this is properly accounted for in the DODS model the group difference largely goes away. However, when I look at the " does the thicknessXage correlation differ between groups" map I see almost nothing significant? I guess my hypothesis is that the slopes are different enough between my groups to wash away the group difference, but not large enough to show up as significant? It would be nice to be able to derive some per group ageXthickness slopes from clusters or ROIS to investigate this further, is this possible? I will probably also start looking into other models, just visually looking at different vertices it appears that most of the groups difference is in the older subjects (in terms of raw thickness values) with less/none difference in younger subjects.
One last aside. The demeaning of covariates still slightly confuses me. In a DOSS model it seems it wouldn't matter where you measure the intercept since both ageXthickness slopes are equal. In the DODS model, it doesn't seem to make sense to measure an intercept of two different slopes, it is more interesting to compare the slopes (in the case of different slopes you will get a different answer at every possible intercept). I am obviously a newbie to GLM and QDEC so sorry for any silly questions.
Chris
On Fri, Mar 4, 2011 at 1:34 PM, Michael Harms mharms@conte.wustl.edu wrote: Hi Chris,
There really shouldn't be a "thickness-age correlation group difference" result with the DOSS model. I have FS 4.1 (rather than 5.0 on my system) but running an analogous model, I see that I do indeed get a verbal "Description" for such a contrast. However, if I compare that to the "thickness-age correlation (accounting for group)" result, I see the exact same map. And if you look at the .mat files in the contrast directory generated by qdec, you'll see that those two contrasts are identical (i.e. [0 0 1]) (or at least they are for qdec with FS 4.1). So, this appears to be a "bug" in the verbal descriptions that qdec provides when using a DOSS model. As to the group difference itself changing between the DOSS and DODS models, that is totally to be expected. Note that in the DODS model, whether or not you demean (center) the age variable has a critical impact on the manner in which you interpret the group contrast. cheers, -MH On Thu, 2011-03-03 at 20:41 -0600, Christopher Bell wrote: > FreeSurfers, > > I have been analyzing my qdec data in version 5.0 and have some > interesting although somewhat confusing results. Basically I have run > a very simple analysis with DODS and DOSS. My discrete factor is group > and my covariate is age, about as simple as can be. > > When I look at the results for DODS I get: > > thickness-age correlation (accounting for group)---result: much of > brain significant > group difference (I assume controlling for age, but it doesn't say > explicitly)--result: one small roi significant > thickness-age correlation group difference--result: one small roi > spatially adjacent to group difference roi > > When I run DOSS I get: > > thickness-age correlation (accounting for group)---result: much of > brain significant > group difference (I assume controlling for age, but it doesn't say > explicitly)--result: much of brain significant > thickness-age correlation group difference--result: much of brain > significant > > I am mostly surprised by how much larger the (group difference), and > the (thickness-age correlation group difference) increase with the > DOSS method. I am also not quite how to interpret the thickness-age > correlation group difference in DOSS. I was thinking the DOSS method > constrained both groups to have the "same slope" and so I was > expecting to get nothing for difference in thickness-age correlation > difference by group; isn't this suggesting my two groups have > significantly different ageXthickness slopes even though they are > constrained to have the same slope by the DOSS method? It would almost > make more sense to me if the results were reversed between DOSS and > DODS. If I had a large thicknessXage correlation group difference > using the DODS method which allows for different slopes. Thanks for > any enlightenment. > > Chris Bell > University of Minnesota > _______________________________________________ > Freesurfer mailing list > Freesurfer@nmr.mgh.harvard.edu > https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer > > > The information in this e-mail is intended only for the person to whom it is > addressed. If you believe this e-mail was sent to you in error and the e-mail > contains patient information, please contact the Partners Compliance HelpLine at > http://www.partners.org/complianceline . If the e-mail was sent to you in error > but does not contain patient information, please contact the sender and properly > dispose of the e-mail.
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