Matrix Calculation

[Ujjawal]

Dear SPSS Experts,

I am trying to compute a partial correlation matrix from a correlation matrix.

Equation : This is based on matrix inversion method :

Partial correlation in cell (i, j) = inverse in correlation matrix (i, j) ÷ (-1 × inverse in correlation matrix (i, i) × inverse in correlation matrix (j, j)).

To obtain the matrix using SPPS , i wrote the following code :

GET FILE='C:\Program Files\SPSS\Employee data.sav'.

CORRELATIONS
 /MATRIX OUT (*)
/MISSING LISTWISE
/VARIABLES=salary salbegin jobtime prevexp.

Select if ROWTYPE_ = 'CORR'.
EXECUTE .

MATRIX.

MGET / FILE = *
 / TYPE = CORR.

COMPUTE INVT= INV(CR). /*** Computing Inverse of correlation matrix***/
PRINT INVT.

LOOP A= 1 TO NCOL(INVT).
LOOP B= 1 TO NCOL(INVT).

COMPUTE  PCORR = INVT(A,B) / (-1 * INVT(A,A) * INVT(B,B)).
PRINT PCORR.

END LOOP.
END LOOP.

END MATRIX .

The problem with the above code lies in LOOP-END LOOP. It failed to command SPSS to calculate this equation: inverse in cell (i, j) ÷ (-1 × inverse in cell (i, i) × inverse in cell(j, j)). And it didn't create a matrix.

Any help would be highly appreciated!!

Thanks and Regards
Ujjawal Bhandari

[Bruce Weaver]

Does this do what you want?  

MATRIX.

MGET / FILE = *
 / TYPE = CORR.

COMPUTE INVT= INV(CR). /*** Computing Inverse of correlation matrix***/
PRINT INVT.

* Create the PCORR matrix before looping.

COMPUTE PCORR=MAKE(NCOL(INVT),NCOL(INVT),1).

LOOP A= 1 TO NCOL(INVT).
LOOP B= 1 TO NCOL(INVT).

COMPUTE  PCORR(A,B) = INVT(A,B) / (-1 * INVT(A,A) * INVT(B,B)).

END LOOP.
END LOOP.

* Don't PRINT PCORR until the looping is done.

PRINT PCORR.

END MATRIX .

Ujjawal wrote

Dear SPSS Experts,

I am trying to compute a partial correlation matrix from a correlation matrix.

Equation : This is based on matrix inversion method :

Partial correlation in cell (i, j) = inverse in correlation matrix (i, j) ÷ (-1 × inverse in correlation matrix (i, i) × inverse in correlation matrix (j, j)).

To obtain the matrix using SPPS , i wrote the following code :

GET FILE='C:\Program Files\SPSS\Employee data.sav'.

CORRELATIONS
 /MATRIX OUT (*)
/MISSING LISTWISE
/VARIABLES=salary salbegin jobtime prevexp.

Select if ROWTYPE_ = 'CORR'.
EXECUTE .

MATRIX.

MGET / FILE = *
 / TYPE = CORR.

COMPUTE INVT= INV(CR). /*** Computing Inverse of correlation matrix***/
PRINT INVT.

LOOP A= 1 TO NCOL(INVT).
LOOP B= 1 TO NCOL(INVT).

COMPUTE  PCORR = INVT(A,B) / (-1 * INVT(A,A) * INVT(B,B)).
PRINT PCORR.

END LOOP.
END LOOP.

END MATRIX .

The problem with the above code lies in LOOP-END LOOP. It failed to command SPSS to calculate this equation: inverse in cell (i, j) ÷ (-1 × inverse in cell (i, i) × inverse in cell(j, j)). And it didn't create a matrix.

Any help would be highly appreciated!!

Thanks and Regards
Ujjawal Bhandari

[David Marso]

Bouncing off Bruce:
Note the denominator is a simple function of outer product of the DIAG of the INV(R).

MATRIX.
MGET / FILE = */ TYPE = CORR.
COMPUTE INVT= INV(CR). /*** Computing Inverse of correlation matrix***/
COMPUTE PCORR=INVT &/ (1/-1 * DIAG(INVT) * T(DIAG(INVT) )).
PRINT INVT.
PRINT PCORR.
END MATRIX.

Bruce Weaver wrote

Does this do what you want?  

MATRIX.

MGET / FILE = *
 / TYPE = CORR.

COMPUTE INVT= INV(CR). /*** Computing Inverse of correlation matrix***/
PRINT INVT.

* Create the PCORR matrix before looping.

COMPUTE PCORR=MAKE(NCOL(INVT),NCOL(INVT),1).

LOOP A= 1 TO NCOL(INVT).
LOOP B= 1 TO NCOL(INVT).

COMPUTE  PCORR(A,B) = INVT(A,B) / (-1 * INVT(A,A) * INVT(B,B)).

END LOOP.
END LOOP.

* Don't PRINT PCORR until the looping is done.

PRINT PCORR.

END MATRIX .

Ujjawal wrote

Dear SPSS Experts,

I am trying to compute a partial correlation matrix from a correlation matrix.

Equation : This is based on matrix inversion method :

Partial correlation in cell (i, j) = inverse in correlation matrix (i, j) ÷ (-1 × inverse in correlation matrix (i, i) × inverse in correlation matrix (j, j)).

To obtain the matrix using SPPS , i wrote the following code :

GET FILE='C:\Program Files\SPSS\Employee data.sav'.

CORRELATIONS
 /MATRIX OUT (*)
/MISSING LISTWISE
/VARIABLES=salary salbegin jobtime prevexp.

Select if ROWTYPE_ = 'CORR'.
EXECUTE .

MATRIX.

MGET / FILE = *
 / TYPE = CORR.

COMPUTE INVT= INV(CR). /*** Computing Inverse of correlation matrix***/
PRINT INVT.

LOOP A= 1 TO NCOL(INVT).
LOOP B= 1 TO NCOL(INVT).

COMPUTE  PCORR = INVT(A,B) / (-1 * INVT(A,A) * INVT(B,B)).
PRINT PCORR.

END LOOP.
END LOOP.

END MATRIX .

The problem with the above code lies in LOOP-END LOOP. It failed to command SPSS to calculate this equation: inverse in cell (i, j) ÷ (-1 × inverse in cell (i, i) × inverse in cell(j, j)). And it didn't create a matrix.

Any help would be highly appreciated!!

Thanks and Regards
Ujjawal Bhandari

[Ujjawal]

Thank you Mr God :))

[Bruce Weaver]

Once again, David sent me to the FM.  ;-)  From the Arithmetic Operators section under MATRIX - END MATRIX:

&/    Elementwise division.  Each element of the matrix is divided by the corresponding element of the second matrix. The matrices must have the same dimensions, or one must be a scalar.

David Marso wrote

Bouncing off Bruce:
Note the denominator is a simple function of outer product of the DIAG of the INV(R).

MATRIX.
MGET / FILE = */ TYPE = CORR.
COMPUTE INVT= INV(CR). /*** Computing Inverse of correlation matrix***/
COMPUTE PCORR=INVT &/ (1/-1 * DIAG(INVT) * T(DIAG(INVT) )).
PRINT INVT.
PRINT PCORR.
END MATRIX.

Bruce Weaver wrote

Does this do what you want?  

MATRIX.

MGET / FILE = *
 / TYPE = CORR.

COMPUTE INVT= INV(CR). /*** Computing Inverse of correlation matrix***/
PRINT INVT.

* Create the PCORR matrix before looping.

COMPUTE PCORR=MAKE(NCOL(INVT),NCOL(INVT),1).

LOOP A= 1 TO NCOL(INVT).
LOOP B= 1 TO NCOL(INVT).

COMPUTE  PCORR(A,B) = INVT(A,B) / (-1 * INVT(A,A) * INVT(B,B)).

END LOOP.
END LOOP.

* Don't PRINT PCORR until the looping is done.

PRINT PCORR.

END MATRIX .

Ujjawal wrote

Dear SPSS Experts,

I am trying to compute a partial correlation matrix from a correlation matrix.

Equation : This is based on matrix inversion method :

Partial correlation in cell (i, j) = inverse in correlation matrix (i, j) ÷ (-1 × inverse in correlation matrix (i, i) × inverse in correlation matrix (j, j)).

To obtain the matrix using SPPS , i wrote the following code :

GET FILE='C:\Program Files\SPSS\Employee data.sav'.

CORRELATIONS
 /MATRIX OUT (*)
/MISSING LISTWISE
/VARIABLES=salary salbegin jobtime prevexp.

Select if ROWTYPE_ = 'CORR'.
EXECUTE .

MATRIX.

MGET / FILE = *
 / TYPE = CORR.

COMPUTE INVT= INV(CR). /*** Computing Inverse of correlation matrix***/
PRINT INVT.

LOOP A= 1 TO NCOL(INVT).
LOOP B= 1 TO NCOL(INVT).

COMPUTE  PCORR = INVT(A,B) / (-1 * INVT(A,A) * INVT(B,B)).
PRINT PCORR.

END LOOP.
END LOOP.

END MATRIX .

The problem with the above code lies in LOOP-END LOOP. It failed to command SPSS to calculate this equation: inverse in cell (i, j) ÷ (-1 × inverse in cell (i, i) × inverse in cell(j, j)). And it didn't create a matrix.

Any help would be highly appreciated!!

Thanks and Regards
Ujjawal Bhandari

[David Marso]

Not only syntactically more efficient, but DRAMATIC performance differences.
**MUST BE VERY CAREFUL to ensure that denominator matrix does NOT contain 0's **.
Similar performance with the other & MATRIX operators.
Also MSUM vs LOOPS to SUM matrices or submatrices.
--------------------------------------------------------------------
* Processor Time  00:00:05.01 * Elapsed Time    00:00:05.68 *.
MATRIX.
COMPUTE R1=UNIFORM(1000,1000).
COMPUTE R2=UNIFORM(1000,1000).
COMPUTE R3=MAKE(1000,1000,0).
LOOP #=1 TO 1000.
LOOP ##=1 TO 1000.
COMPUTE R3(#,##)=R1(#,##)/R2(#,##).
END LOOP.
END LOOP.
END MATRIX.

* Processor Time  00:00:00.17 * Elapsed Time    00:00:00.19 *.

MATRIX.
COMPUTE R1=UNIFORM(1000,1000).
COMPUTE R2=UNIFORM(1000,1000).
COMPUTE R3=R1 &/ R2.
END MATRIX.

*Profile: MSUM*.
*****************.
** Program 1.  **.
*********************************************************************.
** Calculate the sum of the values in an array using MSUM function **.
*********************************************************************.
MATRIX.
COMPUTE V=UNIFORM(1000,1000).
COMPUTE X=MSUM(V) .
PRINT X  / FORMAT "F10.5".
END MATRIX.
********************************************************************.
**************  Processor time: 00:00:00.05   **********************.
**************  Elapsed time  : 00:00:00.04   **********************.
*****************************  END PROGRAM 1  **********************.
********************************************************************.

*****************.
** Program 2.  **.
**********************************************************************.
** Calculate the sum of the values in an array using painfully slow **.
** and tedious element by element addition                          **.
**********************************************************************.
SET MXLOOPS 1000000.
MATRIX.
COMPUTE V=UNIFORM(1000,1000).
COMPUTE X=0.
LOOP #=1 TO NROW(V).
LOOP ##=1 TO NCOL(V).
COMPUTE X=X+V(#,##).
PRINT X.
END LOOP.
END LOOP.
END MATRIX.
********************************************************************.
**************  Processor time: 00:00:17.93 ************************.
**************  Elapsed time  : 00:00:14.25 ************************.
*****************************  END PROGRAM 2  **********************.
********************************************************************.

Bruce Weaver wrote

Once again, David sent me to the FM.  ;-)  From the Arithmetic Operators section under MATRIX - END MATRIX:

&/    Elementwise division.  Each element of the matrix is divided by the corresponding element of the second matrix. The matrices must have the same dimensions, or one must be a scalar.

David Marso wrote

Bouncing off Bruce:
Note the denominator is a simple function of outer product of the DIAG of the INV(R).

MATRIX.
MGET / FILE = */ TYPE = CORR.
COMPUTE INVT= INV(CR). /*** Computing Inverse of correlation matrix***/
COMPUTE PCORR=INVT &/ (1/-1 * DIAG(INVT) * T(DIAG(INVT) )).
PRINT INVT.
PRINT PCORR.
END MATRIX.

Bruce Weaver wrote

Does this do what you want?  

MATRIX.

MGET / FILE = *
 / TYPE = CORR.

COMPUTE INVT= INV(CR). /*** Computing Inverse of correlation matrix***/
PRINT INVT.

* Create the PCORR matrix before looping.

COMPUTE PCORR=MAKE(NCOL(INVT),NCOL(INVT),1).

LOOP A= 1 TO NCOL(INVT).
LOOP B= 1 TO NCOL(INVT).

COMPUTE  PCORR(A,B) = INVT(A,B) / (-1 * INVT(A,A) * INVT(B,B)).

END LOOP.
END LOOP.

* Don't PRINT PCORR until the looping is done.

PRINT PCORR.

END MATRIX .

Ujjawal wrote

Dear SPSS Experts,

I am trying to compute a partial correlation matrix from a correlation matrix.

Equation : This is based on matrix inversion method :

Partial correlation in cell (i, j) = inverse in correlation matrix (i, j) ÷ (-1 × inverse in correlation matrix (i, i) × inverse in correlation matrix (j, j)).

To obtain the matrix using SPPS , i wrote the following code :

GET FILE='C:\Program Files\SPSS\Employee data.sav'.

CORRELATIONS
 /MATRIX OUT (*)
/MISSING LISTWISE
/VARIABLES=salary salbegin jobtime prevexp.

Select if ROWTYPE_ = 'CORR'.
EXECUTE .

MATRIX.

MGET / FILE = *
 / TYPE = CORR.

COMPUTE INVT= INV(CR). /*** Computing Inverse of correlation matrix***/
PRINT INVT.

LOOP A= 1 TO NCOL(INVT).
LOOP B= 1 TO NCOL(INVT).

COMPUTE  PCORR = INVT(A,B) / (-1 * INVT(A,A) * INVT(B,B)).
PRINT PCORR.

END LOOP.
END LOOP.

END MATRIX .

The problem with the above code lies in LOOP-END LOOP. It failed to command SPSS to calculate this equation: inverse in cell (i, j) ÷ (-1 × inverse in cell (i, i) × inverse in cell(j, j)). And it didn't create a matrix.

Any help would be highly appreciated!!

Thanks and Regards
Ujjawal Bhandari

[Ujjawal]

Thank you for the detailed explanation. This is a great learning for me :)

[Art Kendall]

Why not use /Matrix = IN?

PARTIAL CORR

PARTIAL CORR is available in the Statistics Base option.

PARTIAL CORR VARIABLES= varlist [WITH varlist]
    BY varlist [(levels)]

 [/SIGNIFICANCE={TWOTAIL**}] 
                {ONETAIL  }

 [/STATISTICS=[NONE**] [CORR] [DESCRIPTIVES] [BADCORR] [ALL]] 

 [/FORMAT={MATRIX** }] 
          {SERIAL   }
          {CONDENSED}

 [/MISSING=[{LISTWISE**}]  [{EXCLUDE**}]] 
            {ANALYSIS  }    {INCLUDE  }

 [/MATRIX= [IN({*                  })] [OUT({*                  })]]
               {'savfile'|'dataset'}        {'savfile'|'dataset'}

On 3/28/2013 11:09 AM, Ujjawal [via SPSSX Discussion] wrote:

Thank you for the detailed explanation. This is a great learning for me :)

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NAML

[David Marso]

Art,  
If you have been following recent discussions, it appears that Ujjawal is an aspiring MacroPhiliac (despite my warnings of potential irreversible brain damage and hair loss a few weeks ago).  In addition a mild case of MATRIXitosis appears imminent.  Keep storming up that rocky mountain Ujjawal.  You know you are expected to report back in a couple months and help the fledglings sort their various issues!!!
You can probably relate Art.  Find new toys, beat the crap out of them!
-------------------------------------------------------------------------------------

Art Kendall wrote

Why not use /Matrix
      = IN?
      PARTIAL CORR
     
        PARTIAL CORR is
        available in the Statistics Base option.
      PARTIAL CORR VARIABLES= varlist [WITH varlist]
    BY varlist [(levels)]

 [/SIGNIFICANCE={TWOTAIL**}]
                {ONETAIL  }

 [/STATISTICS=[NONE**] [CORR] [DESCRIPTIVES] [BADCORR] [ALL]]

 [/FORMAT={MATRIX** }]
          {SERIAL   }
          {CONDENSED}

 [/MISSING=[{LISTWISE**}]  [{EXCLUDE**}]]
            {ANALYSIS  }    {INCLUDE  }

 [/MATRIX= [IN({*                  })] [OUT({*                  })]]
               {'savfile'|'dataset'}        {'savfile'|'dataset'}
     
      Art Kendall
Social Research Consultants
      On 3/28/2013 11:09 AM, Ujjawal [via SPSSX Discussion] wrote:
   
     Thank you for the detailed explanation. This is a
      great learning for me :)
     
     
     
        If you reply to this email, your
          message will be added to the discussion below:
        http://spssx-discussion.1045642.n5.nabble.com/Matrix-Calculation-tp5719107p5719141.html 
     
     
        To start a new topic under SPSSX Discussion, email
        [hidden email] 
        To unsubscribe from SPSSX Discussion, click
          here .
        NAML

[Ujjawal]

@ Art :  Thank you for your response.

Correct me if i am wrong :

The problem with the PARTIAL CORR command is that it doesn't allow to create a partial correlation matrix . Lets say, you have 50 variables . You wish to calculate a correlation between every two variables controlling the other 48 variables in one run.

@ David : Thank You for the trust that you have placed in me. I will be glad to be of help the fledglings sort their issues.

[Art Kendall]

You are correct PARTIAL CORR only outputs the full correlation matrix.

It is some years since I used that procedure.  Even before there were PCs, I had seen requests that PARTIAL CORR output the partial correlation matrix.

Lets say, you have 50 variables . You wish to calculate a correlation between every two variables controlling the other 48 variables in one run.

I think I understand what you are trying to do.  I find it hard to think of why you would want to do that.  You must have a huge number of cases to have correlations that would mean anything after partialling out 48 effects.

I could see where you might have 50 variables and want to see a 48 * 48 controlling for 2 variables.

On 3/28/2013 2:36 PM, Ujjawal [via SPSSX Discussion] wrote:

@ Art :  Thank you for your response.

Correct me if i am wrong :

The problem with the PARTIAL CORR command is that it doesn't allow to create a partial correlation matrix . Lets say, you have 50 variables . You wish to calculate a correlation between every two variables controlling the other 48 variables in one run.

@ David : Thank You for the trust that you have placed in me. I will be glad to be of help the fledglings sort their issues.

---

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[David Marso]

You set off some bells from my grad school days.
You might want to look at Image Factoring.
However compare the keystrokes and all the other output.
This gave me a chance to play with OMS!
Very powerful.  
OTOH, I'll probably only use it when I can't roll my own with 4 lines of code ;-))) -smirk-
----------------------------------------------------------------------------------------------------
GET FILE='C:\Program Files\SPSS\Employee data.sav'.
DATASET NAME emp.
CORRELATIONS
   /MATRIX OUT (*)/MISSING LISTWISE
   /VARIABLES=salary salbegin jobtime prevexp.

SELECT IF ROWTYPE_ = 'CORR'.
MATRIX.
MGET / FILE = */ TYPE = CORR.
COMPUTE INVT= INV(CR). /***Inverse of correlation matrix***/.
COMPUTE PCORR=INVT &/ (1/-1 * DIAG(INVT) * T(DIAG(INVT) )).
PRINT PCORR / FORMAT "F10.7".
END MATRIX.

**OR**.
DATASET DECLARE OhYeah.
MATRIX.
MGET / FILE = */ TYPE = CORR.
COMPUTE INVT= INV(CR). /***Inverse of correlation matrix***/.
SAVE (INVT &/ (1/-1 * DIAG(INVT) * T(DIAG(INVT) ))) / OUTFILE Ohyeah.
END MATRIX.
********************************************************.
PRESERVE.
SET TVars=Names.
DATASET ACTIVATE emp.
DATASET DECLARE  AntiImageCovariances.
OMS
  /SELECT TABLES
  /IF COMMANDS=['Factor Analysis'] SUBTYPES=['Anti image Matrices']
  /DESTINATION FORMAT=SAV NUMBERED=TableNumber_
   OUTFILE='AntiImageCovariances'.
FACTOR
  /VARIABLES salary salbegin jobtime prevexp /PRINT AIC /EXTRACTION IMAGE.
OMSEND.
RESTORE.
DATASET ACTIVATE AntiImageCovariances.
SELECT IF Var1 EQ 'Anti-image Covariance'.
FORMATS salary salbegin jobtime prevexp (F10.7).
DO REPEAT v= salary salbegin jobtime prevexp.
COMPUTE V=-1*v.
END REPEAT.
LIST Var2 to prevexp.

Run MATRIX procedure:

MGET created matrix CR.
The matrix has 4 rows and 4 columns.
The matrix was read from the record(s) of row type CORR.

PCORR
  -.1961231   .1767408   .0968679  -.1254512
   .1767408  -.1989526  -.0910597   .1212550
   .0968679  -.0910597  -.9492108   .0653126
  -.1254512   .1212550   .0653126  -.9099412

------ END MATRIX -----



** FROM IMAGE FACTORING/OMS **

Var2         salary   salbegin    jobtime    prevexp

salary    -.1961231   .1767408   .0968679  -.1254512
salbegin   .1767408  -.1989526  -.0910597   .1212550
jobtime    .0968679  -.0910597  -.9492108   .0653126
prevexp   -.1254512   .1212550   .0653126  -.9099412


Number of cases read:  4    Number of cases listed:  4

Ujjawal wrote

@ Art :  Thank you for your response.

Correct me if i am wrong :

The problem with the PARTIAL CORR command is that it doesn't allow to create a partial correlation matrix . Lets say, you have 50 variables . You wish to calculate a correlation between every two variables controlling the other 48 variables in one run.

@ David : Thank You for the trust that you have placed in me. I will be glad to be of help the fledglings sort their issues.

[David Marso]

Image Factoring is a bit difficult to get info on.
After some Googling I located one by a pioneer in FA and CFA
http://link.springer.com/article/10.1007%2FBF02290173?LI=true
-------
In case some of you wonder why I'm sometimes a crabby old fart, take a look at pic 2!!!

[Ujjawal]

Super cool :)) I can clearly see FACTOR and OMS combined has the edge over MATRIX for calculating the partial correlation matrix because they labels the matrix without defining the labels.