SPSSX Discussion - Re: Solving Two Equations using MATRIX

Re: Solving Two Equations using MATRIX

Posted by Ryan on Jul 21, 2015; 8:53pm
URL: http://spssx-discussion.165.s1.nabble.com/Solving-Two-Equations-using-MATRIX-tp5730174p5730213.html

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 <[hidden email]> 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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