Dear Donald McLaren
I want to make interaction between factor 1 (A,B)and factor 2(C,D,E). age and gender (M,F)
as covariates, I can get 12 classes: ACM ADM AEM BCM BDM BEM ACF ADF AEF BCF BDF BEF and make the contrast:
+ACM -ADM 0 -BCM +BDM 0 +ACF -ADF 0 -BCF +BDF 0 0 0 0 0 0 0 0 0 0 0 0 0
0 +ADM -AEM 0 -BDM +BEM 0 +ADF -AEF 0 -BDF +BEF 0 0 0 0 0 0 0 0 0 0 0 0 0
is correct? thanks!
Bo Xiang
At 2012-11-22 08:55:29,"MCLAREN, Donald" <mclaren.donald@gmail.com> wrote:
>Please explain what are the columns represent.
>
>Best Regards, Donald McLaren
>=================
>D.G. McLaren, Ph.D.
>Research Fellow, Department of Neurology, Massachusetts General Hospital and
>Harvard Medical School
>Postdoctoral Research Fellow, GRECC, Bedford VA
>Website: http://www.martinos.org/~mclaren
>Office: (773) 406-2464
>=====================
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>On Wed, Nov 21, 2012 at 2:50 PM, <xiangbo_2010@126.com> wrote:
>> No, I want to compute the interaction between factor 1 and factor 2 ,
>> gender and age as covariates. thanks
>>
>> Bo Xiang
>>
>> ÔÚ 2012-11-22 04:22:06£¬"Douglas N Greve" <greve@nmr.mgh.harvard.edu> дµÀ£º
>>>Hi Bo, I don't understand the contrast you are trying to make. Are you
>>>really trying to compute the interaction between four variables (factor
>>>1, factor 2, gender, and age)?
>>>doug
>>>
>>>On 11/21/2012 10:49 AM, xiangbo_2010 wrote:
>>>> Dear Donald McLaren
>>>> Thank you for your reply! I make the contrast according to your method
>>>> is following£¬but I want to make interaction between factor 1 (A,B)and
>>>> factor 2(C,D,E), gender (M,F) and one continuous variable (age) as
>>>> covariates, the following contrast:
>>>> 2 -2 0 -2 2 0 2 -2 0 -2 2 0 0 0 0 0 0 0 0 0 0 0 0 0
>>>> 0 2 -2 0 -2 2 0 2 -2 0 -2 2 0 0 0 0 0 0 0 0 0 0 0 0
>>>>
>>>> is correct? Thanks!
>>>> Bo Xiang
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> At 2012-11-21 04:07:37,"MCLAREN, Donald"<mclaren.donald@gmail.com <mailto:mclaren.donald@gmail.com>> wrote:
>>>> >On Tue, Nov 20, 2012 at 12:56 PM, Douglas N Greve
>>>> ><greve@nmr.mgh.harvard.edu <mailto:greve@nmr.mgh.harvard.edu>> wrote:
>>>> >> Thanks Donald. Is this the standard way to do this? I had used 8 rows
>>>> >> instead of 4 with the difference being that 8 rows gives you an opportunity
>>>> >> to look for an effect in males OR females.
>>>> >
>>>> >Yes. Having 8 rows would tell you if you have an interaction between
>>>> >factor 1 and 2 in either males or females. My 4 rows only tell you if
>>>> >the interaction exists. Technically speaking, one would run the
>>>> >three-way interaction first. If nothing existed then you do the
>>>> >two-way interaction as I suggested. If there is a three-way
>>>> >interaction, then you would use Doug's approach of the interaction in
>>>> >either males or females.
>>>> >
>>>> >If there is an effect in both
>>>> >> males and females but the effects go in opposite directions, then the 4 row
>>>> >> implementation will resolve to 0 (no effect). Or am I misunderstanding
>>>> >> something (again:)?
>>>> >
>>>> >Nope. You are right. If the male and female effects are different,
>>>> >then they could cancel each other out. If you suspect this to be the
>>>> >case, then you should be able to demonstrate a three-way interaction.
>>>> >
>>>> >> thanks!
>>>> >> doug
>>>> >>
>>>> >>
>>>> >> On 11/20/2012 01:50 PM, MCLAREN, Donald wrote:
>>>> >>>
>>>> >>> Bo,
>>>> >>>
>>>> >>> Doug asked me to chime in on your issue. Here are some points that you
>>>> >>> (and others) will hopefully find useful.
>>>> >>>
>>>> >>> (1) Inferences are two-step process. First, you create and estimate
>>>> >>> the design matrix. Every column in the design matrix accounts can
>>>> >>> account for some of the variance in the data. Second, you have
>>>> >>> contrasts that allow you to infer specific effects. Because the model
>>>> >>> contains your covariates, you are always controlling for the
>>>> >>> covariates and by extension any factor/covariate not in the contrast.
>>>> >>>
>>>> >>> (2) Forming contrasts is often the most difficult thing to do. I
>>>> >>> assume that your three factors (1, 2, and gender) are all
>>>> >>> between-subject factors. If one of them is a within-subject factor
>>>> >>> please let me know and disregard the rest of the email. The final
>>>> >>> F-contrast will have 4 rows (factor 1 levels-1)*(factor 2 levels
>>>> >>> -1)=(3-1)*(3-1)=2*2=4
>>>> >>>
>>>> >>> The following is an outline for creating contrasts:
>>>> >>> (a) Start simple - difference between levels of 1 factor
>>>> >>> (b) Define your null hypothesis: AO=AP=AQ
>>>> >>> (c) Make it equal to 0: AO-AP=0 AND AP-AQ=0
>>>> >>> (d) Repeat for the other levels of the factor...
>>>> >>> BO-BP=0 AND BP-BQ=0
>>>> >>> CO-CP=0 AND CP-CQ=0
>>>> >>>
>>>> >>> (e) Now combine them AO-AP=BO-BP=CO-CP AND AP-AQ=BP-BQ=CP-CQ
>>>> >>>
>>>> >>> (f) Make them equal to 0:
>>>> >>> AO-AP-BO+BP=0
>>>> >>> BO-BP-CO+CP=0
>>>> >>> AP-AQ-BP+BQ=0
>>>> >>> BP-BQ-CP+CQ=0
>>>> >>>
>>>> >>> (g) Expand them to include gender, for example:
>>>> >>> AO-AP-BO+BP=0 becomes FAO-FAP-FBO+FBP+MAO-MAP-MBO+MBP=0
>>>> >>>
>>>> >>> Since the contrast now has 2 columns per level, you should divide all
>>>> >>> values by 2. This will produce the correct amplitude and statistics.
>>>> >>> If you leave the values as 1 and -1, then you will have an incorrect
>>>> >>> amplitude, but the statistics will still be correct.
>>>> >>>
>>>> >>> (h) Fill in the respective columns of your design matrix.
>>>> >>>
>>>> >>> (3) The degrees of freedom are defined based on the rows of the
>>>> >>> F-matrix and the number of rows in the design matrix. The F-test has a
>>>> >>> numerator and denominator degrees of freedom. F(n,d).
>>>> >>>
>>>> >>> Best Regards, Donald McLaren
>>>> >>> =================
>>>> >>> D.G. McLaren, Ph.D.
>>>> >>> Research Fellow, Department of Neurology, Massachusetts General Hospital
>>>> >>> and
>>>> >>> Harvard Medical School
>>>> >>> Postdoctoral Research Fellow, GRECC, Bedford VA
>>>> >>> Website: http://www.martinos.org/~mclaren
>>>> >>> Office: (773) 406-2464
>>>> >>> =====================
>>>> >>> This e-mail contains CONFIDENTIAL INFORMATION which may contain PROTECTED
>>>> >>> HEALTHCARE INFORMATION and may also be LEGALLY PRIVILEGED and which is
>>>> >>> intended only for the use of the individual or entity named above. If the
>>>> >>> reader of the e-mail is not the intended recipient or the employee or
>>>> >>> agent
>>>> >>> responsible for delivering it to the intended recipient, you are hereby
>>>> >>> notified that you are in possession of confidential and privileged
>>>> >>> information. Any unauthorized use, disclosure, copying or the taking of
>>>> >>> any
>>>> >>> action in reliance on the contents of this information is strictly
>>>> >>> prohibited and may be unlawful. If you have received this e-mail
>>>> >>> unintentionally, please immediately notify the sender via telephone at
>>>> >>> (773)
>>>> >>> 406-2464 or email.
>>>> >>>
>>>> >>>
>>>> >>> On Tue, Nov 20, 2012 at 8:17 AM, xiangbo_2010<xiangbo_2010@126.com <mailto:xiangbo_2010@126.com>>
>>>> >>> wrote:
>>>> >>>>
>>>> >>>> Dear doug
>>>> >>>> Thank you for your reply!
>>>> >>>> +AOM -BOM -APM -BPM 0 0 0 0 0
>>>> >>>> +AOM -BOM 0 0 -AQM +BQM 0 0 0
>>>> >>>> +AOM 0 -APM 0 0 0 -COM +CPM 0
>>>> >>>> +AOM 0 0 0 -AQM -COM 0 +CQM
>>>> >>>> there should be use 1 -1 or 0.5 -0.5? whether the -BPM should be change
>>>> >>>> BPM?
>>>> >>>> Thanks
>>>> >>>>
>>>> >>>> Bo Xiang
>>>> >>>>
>>>> >>>>
>>>> >>>>
>>>> >>>>
>>>> >>>>
>>>> >>>>
>>>> >>>> At 2012-11-19 07:23:31,"Douglas Greve"<greve@nmr.mgh.harvard.edu <mailto:greve@nmr.mgh.harvard.edu>> wrote:
>>>> >>>>
>>>> >>>>
>>>> >>>> Hi Bo, you can think of the Ftest as a logical 'OR' between the t-test
>>>> >>>> contrasts indicated in each row. Each row is a difference of differences,
>>>> >>>> so
>>>> >>>>
>>>> >>>> 1. (A-B)om - (A-B)pm --> Does the difference between A and B differ
>>>> >>>> between
>>>> >>>> groups O and P for Males?
>>>> >>>> 2. (A-B)om - (A-B)qm
>>>> >>>> 3. (A-C)om - (A-C)pm
>>>> >>>> 4. (A-C)om - (A-C)qm
>>>> >>>> 5. (A-B)of - (A-B)pf --> Does the difference between A and B differ
>>>> >>>> between
>>>> >>>> groups O and P for Females?
>>>> >>>> 6. (A-B)of - (A-B)qf
>>>> >>>> 7. (A-C)of - (A-C)pf
>>>> >>>> 8. (A-C)of - (A-C)pf
>>>> >>>>
>>>> >>>> I've put together the first 9 columns of the first 4 rows. The last 9
>>>> >>>> columns are all 0s. For the last for rows, the 0s and below matrix are
>>>> >>>> swapped to give you the same for the females
>>>> >>>>
>>>> >>>> doug
>>>> >>>>
>>>> >>>> AOM BOM APM BPM AQM BQM COM CPM CQM
>>>> >>>>
>>>> >>>> --------------------------------------------------------------------------
>>>> >>>> +AOM -BOM -APM -BPM 0 0 0 0 0
>>>> >>>> +AOM -BOM 0 0 -AQM +BQM 0 0 0
>>>> >>>> +AOM 0 -APM 0 0 0 -COM +CPM 0&! nbsp;&nb sp;
>>>> >>>>
>>>> >>>> +AOM 0 0 0 -AQM -COM 0 +CQM
>>>> >>>>
>>>> >>>>
>>>> >>>>
>>>> >>>> On 11/17/12 9:21 PM, xiangbo_2010 wrote:
>>>> >>>>
>>>> >>>> Hi Freesurfer experts,
>>>> >>>>
>>>> >>>> I'm very sorry to bother you, but I am very confused with the following
>>>> >>>> questions:
>>>> >>>>
>>>> >>>> My experimental design includes three discrete factors: factor 1 with
>>>> >>>> three
>>>> >>>> levels (A,B,C ); factor 2 with three levels (O,P,Q); gender (F, M), and
>>>> >>>> one
>>>> >>>> covariate.
>>>> >>>>
>>>> >>>> So I can get 18 classes: FAO, FAP,FAQ,FBO,FBP,FBQ,FCO,FCP,FCQ,MAO,
>>>> >>>> MAP,MAQ,MBO,MBP,MBQ,MCO,MCP,MCQ. I want to perform the interaction
>>>> >>>> between
>>>> >>>> factor 1 and factor 2 regressing out the effect of gender and one
>>>> >>>> covariate,
>>>> >>>> but I don't know the rules for setting the contrasts for the F-test. The
>>>> >>>> contrast matrix I used is:
>>>> >>>>
>>>> >>>> 1 1 1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
>>>> >>>> 0
>>>> >>>>
>>>> >>>> 1 -1 0 1 -1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
>>>> >>>> 0
>>>> >>>>
>>>> >>>> 1 1 1 0 0 0 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
>>>> >>>> 0
>>>> >>>>
>>>> >>>> 1 0 -1 1 0 -1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
>>>> >>>> 0
>>>> >>>>
>>>> >>>> 0 0 0 0 0 0 0 0 0 1 1 1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
>>>> >>>> 0
>>>> >>>>
>>>> >>>> 0 0 0 0 0 0 0 0 0 1 -1 0 1 -1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
>>>> >>>> 0
>>>> >>>>
>>>> >>>> 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
>>>> >>>> 0
>>>> >>>>
>>>> >>>> 0 0 0 0 0 0 0 0 0 1 0 -1 1 0 -1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
>>>> >>>> 0
>>>> >>>>
>>>> >>>> is it correct?
>>>> >>>>
>>>> >>>>
>>>> >>>>
>>>> >>>> Any help will be very appreciated.
>>>> >>>>
>>>> >>>>
>>>> >>>>
>>>> >>>> Best wishes,
>>>> >>>>
>>>> >>>>
>>>> >>>>
>>>> >>>> Bo Xiang
>>>> >>>>
>>>> >>>>
>>>> >>>>
>>>> >>>>
>>>> >>>>
>>>> >>>>
>>>> >>>>
>>>> >>>>
>>>> >>>>
>>>> >>>>
>>>> >>>>
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>>>> >>>>
>>>> >>>>
>>>> >>>>
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>>>> >>
>>>> >> --
>>>> >> Douglas N. Greve, Ph.D.
>>>> >> MGH-NMR Center
>>>> >> greve@nmr.mgh.harvard.edu <mailto:greve@nmr.mgh.harvard.edu>
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