http://spssx-discussion.165.s1.nabble.com/Solving-Two-Equations-using-MATRIX-tp5730174p5730215.html
Yes to your question. And I couldn't agree more about Ray. I'm very fortunate and grateful to have him as a resource.
> On Jul 21, 2015, at 6:17 PM, Bruce Weaver <
[hidden email]> wrote:
>
> Ryan, am I correct in assuming that in your statement of the null hypothesis,
> M[] represents the *mean* of the (population) correlations inside the square
> brackets? Thanks for clarifying.
>
> p.s. - Ray's great, isn't he. If I ever start thinking that I'm getting to
> know quite a bit about statistics & data analysis, I just take a look at
> Ray, and invariably come away in a humbled condition. ;-)
>
>
>
> Ryan Black wrote
>> Thanks for the help, David! This is great!!!
>>
>> The code just needs two modifications....
>>
>> COMPUTE y=y +w(j,k)*w(h,m) *
>> (r(j,h)-r(j,k)*r(k,h))*(r(k,m)-r(k,h)*r(h,m)) +
>> (r(j,m)-r(j,h)*r(h,m))*(r(k,h)-r(k,j)*r(j,h)) +
>> (r(j,h)-r(j,m)*r(m,h))*(r(k,m)-r(k,j)*r(j,m)) +
>> (r(j,m)-r(j,k)*r(k,m))*(r(k,h)-r(k,m)*r(m,h)) .
>>
>> should be
>>
>> COMPUTE y=y +w(j,k)*w(h,m) *
>> ((r(j,h)-r(j,k)*r(k,h))*(r(k,m)-r(k,h)*r(h,m)) +
>> (r(j,m)-r(j,h)*r(h,m))*(r(k,h)-r(k,j)*r(j,h)) +
>> (r(j,h)-r(j,m)*r(m,h))*(r(k,m)-r(k,j)*r(j,m)) +
>> (r(j,m)-r(j,k)*r(k,m))*(r(k,h)-r(k,m)*r(m,h))) .
>>
>> and
>>
>> COMPUTE y=SQRT(.5/??? -1) * y.
>>
>> should be
>>
>> COMPUTE y=SQRT(.5/(??? -1)) * y.
>>
>> x / y = z
>>
>> where,
>>
>> y is the estimated standard error and z is approximately standard normal
>> which tests:
>>
>> Null Hypothesis: M[rho14,rho25,rho36] =
>> M[rho15,rho16,rho24,rho26,rho34,rho35]
>>
>> Thanks again!
>>
>> Ryan
>>
>> p.s., thanks to Ray Koopman for referring me to the appropriate 1980
>> Steiger article which assisted me in constructing the test, and for
>> providing additional guidance / confirmation along the way
>>
>> On Sun, Jul 19, 2015 at 11:37 PM, David Marso <
>
>> david.marso@
>
>> > wrote:
>>
>>> Hi Ryan,
>>> Good to see you here!
>>> Here is a simple MATRIX program.
>>> Please verify that I haven't dropped a stitch.
>>> Curious as to what this is calculating.
>>> Could it be related to the Determinant of a matrix?
>>> If so there is the DET operator .
>>>
>>> MATRIX.
>>> COMPUTE R={1.00, .20, .25, .85, .30, .15;
>>> .20,1.00, .10, .05, .70, .30;
>>> .25, .10,1.00, .35, .40, .80;
>>> .85, .05, .35,1.00, .50, .45;
>>> .30, .70, .40, .50,1.00, .55;
>>> .15, .30, .80, .45, .55, 1.00}.
>>> COMPUTE W={0,0,0, 2,-1,-1;
>>> 0,0,0,-1, 2,-1;
>>> 0,0,0,-1,-1, 2;
>>> 0,0,0, 0, 0, 0;
>>> 0,0,0, 0, 0, 0;
>>> 0,0,0, 0, 0, 0}.
>>>
>>> COMPUTE X=MSUM(R&*W).
>>> COMPUTE y=0.
>>> LOOP j=1 TO 3.
>>> LOOP k=4 TO 6.
>>> LOOP h=1 TO 3.
>>> LOOP m=4 TO 6.
>>> COMPUTE y=y +w(j,k)*w(h,m) *
>>> (r(j,h)-r(j,k)*r(k,h))*(r(k,m)-r(k,h)*r(h,m)) +
>>> (r(j,m)-r(j,h)*r(h,m))*(r(k,h)-r(k,j)*r(j,h)) +
>>> (r(j,h)-r(j,m)*r(m,h))*(r(k,m)-r(k,j)*r(j,m)) +
>>> (r(j,m)-r(j,k)*r(k,m))*(r(k,h)-r(k,m)*r(m,h)) .
>>
>> END LOOP.
>>> END LOOP.
>>> END LOOP.
>>> END LOOP.
>>> COMPUTE y=SQRT(.5/??? -1) * y.
>>> END MATRIX.
>>>
>>>
>>>
>>>
>>> Ryan Black wrote
>>>> Dear SPSS-L,
>>>>
>>>> Suppose we have a 6X6 correlation matrix. I have two equations I need
>>> to
>>>> solve.
>>>>
>>>> The following is GIVEN:
>>>>
>>>> COMPUTE r11 = 1.
>>>> COMPUTE r12 = .20.
>>>> COMPUTE r13 = .25.
>>>> COMPUTE r14 = .85.
>>>> COMPUTE r15 = .30.
>>>> COMPUTE r16 = .15.
>>>> COMPUTE r21 = .20.
>>>> COMPUTE r22 = 1.
>>>> COMPUTE r23 = .10.
>>>> COMPUTE r24 = .05.
>>>> COMPUTE r25 = .70.
>>>> COMPUTE r26 = .30.
>>>> COMPUTE r31 = .25.
>>>> COMPUTE r32 = .10.
>>>> COMPUTE r33 = 1.
>>>> COMPUTE r34 = .35.
>>>> COMPUTE r35 = .40.
>>>> COMPUTE r36 = .80.
>>>> COMPUTE r41 = .85.
>>>> COMPUTE r42 = .05.
>>>> COMPUTE r43 = .35.
>>>> COMPUTE r44 = 1.
>>>> COMPUTE r45 = .50.
>>>> COMPUTE r46 = .45.
>>>> COMPUTE r51 = .30.
>>>> COMPUTE r52 = .70.
>>>> COMPUTE r53 = .40.
>>>> COMPUTE r54 = .50.
>>>> COMPUTE r55 = 1.
>>>> COMPUTE r56 = .55.
>>>> COMPUTE r61 = .15.
>>>> COMPUTE r62 = .30.
>>>> COMPUTE r63 = .80.
>>>> COMPUTE r64 = .45.
>>>> COMPUTE r65 = .55.
>>>> COMPUTE r66 = 1.
>>>>
>>>> COMPUTE wjk14 = 2.
>>>> COMPUTE wjk15 = -1.
>>>> COMPUTE wjk16 = -1.
>>>> COMPUTE wjk24 = -1.
>>>> COMPUTE wjk25 = 2.
>>>> COMPUTE wjk26 = -1.
>>>> COMPUTE wjk34 = -1.
>>>> COMPUTE wjk35 = -1.
>>>> COMPUTE wjk36 = 2.
>>>>
>>>> FIRST EQUATION:
>>>>
>>>> Sum[{j=1,3},{k=4,6}: w[j,k]*r[j,k]]
>>>>
>>>> COMPUTE x = wjk14*r14 + wjk15*r15 + wjk16*r16 +
>>>> wjk24*r24 + wjk25*r25 + wjk26*r26 +
>>>> wjk34*r34 + wjk35*r35 + wjk36*r36.
>>>>
>>>> While x is easy to solve outside of MATRIX, I'm curious how x could be
>>>> solved more efficiently in MATRIX.
>>>>
>>>> Suppose the following is GIVEN as well:
>>>>
>>>> COMPUTE whm14 = 2.
>>>> COMPUTE whm15 = -1.
>>>> COMPUTE whm16 = -1.
>>>> COMPUTE whm24 = -1.
>>>> COMPUTE whm25 = 2.
>>>> COMPUTE whm26 = -1.
>>>> COMPUTE whm34 = -1.
>>>> COMPUTE whm35 = -1.
>>>> COMPUTE whm36 = 2.
>>>>
>>>> SECOND EQUATION:
>>>>
>>>> y = Sqrt[(.5/(N-1))*Sum[{j=1,3},{k=4,6},{h=1,3},{m=4,6}:
>>>> w[j,k]*w[h,m]*(
>>>>
>>>> (r[j,h]-r[j,k]*r[k,h])*(r[k,m]-r[k,h]*r[h,m]) +
>>>>
>>>> (r[j,m]-r[j,h]*r[h,m])*(r[k,h]-r[k,j]*r[j,h]) +
>>>>
>>>> (r[j,h]-r[j,m]*r[m,h])*(r[k,m]-r[k,j]*r[j,m]) +
>>>>
>>>> (r[j,m]-r[j,k]*r[k,m])*(r[k,h]-r[k,m]*r[m,h]))]]
>>>>
>>>> As you can see, y is far more tedious to solve outside of MATRIX. The
>>>> first
>>>> of 81 "Sum[{..." terms could be solved using COMPUTE as follows:
>>>>
>>>> COMPUTE jk14_hm14 =
>>> wjk14*whm14*((r11-r14*r41)*(r44-r41*r14)+(r14-r11*r14)*(r41-r41*r11)+(r11-r14*r41)*(r44-r41*r14)+(r14-r14*r44)*(r41-r44*r41)).
>>>>
>>>> but then I'd have to work it out for the following 80 terms:
>>>>
>>>> compute jk15_hm14 = .
>>>> compute jk16_hm14 = .
>>>> compute jk24_hm14 = .
>>>> compute jk25_hm14 = .
>>>> compute jk26_hm14 = .
>>>> compute jk34_hm14 = .
>>>> compute jk35_hm14 = .
>>>> compute jk36_hm14 = .
>>>>
>>>> compute jk14_hm24 = .
>>>> compute jk15_hm24 = .
>>>> compute jk16_hm24 = .
>>>> compute jk24_hm24 = .
>>>> compute jk25_hm24 = .
>>>> compute jk26_hm24 = .
>>>> compute jk34_hm24 = .
>>>> compute jk35_hm24 = .
>>>> compute jk36_hm24 = .
>>>>
>>>> compute jk14_hm34 = .
>>>> compute jk15_hm34 = .
>>>> compute jk16_hm34 = .
>>>> compute jk24_hm34 = .
>>>> compute jk25_hm34 = .
>>>> compute jk26_hm34 = .
>>>> compute jk34_hm34 = .
>>>> compute jk35_hm34 = .
>>>> compute jk36_hm34 = .
>>>>
>>>> compute jk14_hm15 = .
>>>> compute jk15_hm15 = .
>>>> compute jk16_hm15 = .
>>>> compute jk24_hm15 = .
>>>> compute jk25_hm15 = .
>>>> compute jk26_hm15 = .
>>>> compute jk34_hm15 = .
>>>> compute jk35_hm15 = .
>>>> compute jk36_hm15 = .
>>>>
>>>> compute jk14_hm16 = .
>>>> compute jk15_hm16 = .
>>>> compute jk16_hm16 = .
>>>> compute jk24_hm16 = .
>>>> compute jk25_hm16 = .
>>>> compute jk26_hm16 = .
>>>> compute jk34_hm16 = .
>>>> compute jk35_hm16 = .
>>>> compute jk36_hm16 = .
>>>>
>>>> compute jk14_hm25 = .
>>>> compute jk15_hm25 = .
>>>> compute jk16_hm25 = .
>>>> compute jk24_hm25 = .
>>>> compute jk25_hm25 = .
>>>> compute jk26_hm25 = .
>>>> compute jk34_hm25 = .
>>>> compute jk35_hm25 = .
>>>> compute jk36_hm25 = .
>>>>
>>>> compute jk14_hm26 = .
>>>> compute jk15_hm26 = .
>>>> compute jk16_hm26 = .
>>>> compute jk24_hm26 = .
>>>> compute jk25_hm26 = .
>>>> compute jk26_hm26 = .
>>>> compute jk34_hm26 = .
>>>> compute jk35_hm26 = .
>>>> compute jk36_hm26 = .
>>>>
>>>> compute jk14_hm35 = .
>>>> compute jk15_hm35 = .
>>>> compute jk16_hm35 = .
>>>> compute jk24_hm35 = .
>>>> compute jk25_hm35 = .
>>>> compute jk26_hm35 = .
>>>> compute jk34_hm35 = .
>>>> compute jk35_hm35 = .
>>>> compute jk36_hm35 = .
>>>>
>>>> compute jk14_hm36 = .
>>>> compute jk15_hm36 = .
>>>> compute jk16_hm36 = .
>>>> compute jk24_hm36 = .
>>>> compute jk25_hm36 = .
>>>> compute jk26_hm36 = .
>>>> compute jk34_hm36 = .
>>>> compute jk35_hm36 = .
>>>> compute jk36_hm36 = .
>>>>
>>>> and then sum the 81 terms and multiply by Sqrt[(.5/(N-1)).
>>>>
>>>> Any tips would be most appreciated.
>>>>
>>>> Thanks,
>>>>
>>>> Ryan
>>>>
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>
>
> -----
> --
> Bruce Weaver
>
[hidden email]
>
http://sites.google.com/a/lakeheadu.ca/bweaver/>
> "When all else fails, RTFM."
>
> NOTE: My Hotmail account is not monitored regularly.
> To send me an e-mail, please use the address shown above.
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