Dear Prof Donald McLaren
I am sorry to disturb you! I have four discrete variables {factor 1(A,B),
factor 2(C,D), factor 3(G,H), and gender(M,F)} and a continuous variable (age),
I want to use the GLM to analysis the result of the interaction among factor
1(A,B), factor 2(C,D) and factor 3(E,F) regressing out the effect of gender and
age, and I have 16 classes: MACG,MACH, MADG, MADH, MBCG, MBCH, MBDG, MBDH,
FACG,FACH, FADG, FADH, FBCG, FBCH, FBDG, FBDH, so I design the contrast is
following:
1 -1 -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 0 0 1 -1 -1 1 -1 1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
is correct? thank you very much!
look forward for your reply!
Bo Xiang
At 2012-11-21 04:07:37,"MCLAREN, Donald" <mclaren.don...@gmail.com> wrote:
>On Tue, Nov 20, 2012 at 12:56 PM, Douglas N Greve
><gr...@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
>>> =====================
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>>>
>>> On Tue, Nov 20, 2012 at 8:17 AM, xiangbo_2010<xiangbo_2...@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"<gr...@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
>> gr...@nmr.mgh.harvard.edu
>> Phone Number: 617-724-2358
>> Fax: 617-726-7422
>>
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