Categorical Conjoint Measurement Macro
/****************************************************************/
/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: CANCORR2 */
/* TITLE: Categorical Conjoint Measurement Macro */
/* PRODUCT: IML */
/* SYSTEM: ALL */
/* KEYS: MULTIV REGR */
/* PROCS: CANCORR IML PRINT */
/* DATA: */
/* */
/* SUPPORT: WEW UPDATE: 06SEP1989 */
/* REF: */
/* MISC: TRANSLATED FROM MATRIX TO IML USING MATIML */
/* */
/****************************************************************/
%MACRO CCM;
*------------------CATEGORICAL CONJOINT MEASUREMENT---------------+
| |
| THE PURPOSE OF CATEGORICAL CONJOINT MEASUREMENT IS TO ASSIGN |
| NUMERIC VALUES TO EACH CATEGORY OF A CONTINGENCY TABLE SO AS TO |
| MAXIMIZE THE CORRELATION BETWEEN THE RESULTING ROW AND COLUMN |
| VARIABLES. THIS IS ACCOMPLISHED BY CANONICAL CORRELATION ON |
| DUMMY VARIABLES. THE VALUES ARE GIVEN BY THE RAW COEFFICIENTS |
| FOR THE FIRST CANONICAL VARIABLES. |
| |
| THE MACRO ASSUMES THAT YOU HAVE PROVIDED THE CONTINGENCY |
| TABLE IN THE FORM OF A MATRIX "RC". THE MACRO COMPUTES A |
| CORRECTED SSCP MATRIX AND CREATES A DATASET SUITABLE FOR INPUT |
| TO PROC CANCORR. YOU MUST ALSO PROVIDE A MATRIX "NAME" |
| CONTAINING NAMES FOR THE ROW AND COLUMN DUMMY VARIABLES. |
| |
| CATEGORICAL CONJOINT MEASUREMENT IS A SPECIAL CASE OF |
| CORRESPONDENCE ANALYSIS AND IS CLOSELY RELATED TO THE METHOD |
| OF RECIPROCAL AVERAGES. |
| |
| SEE PP. 290-293 OF MARDIA, KENT & BIBBY: MULTIVARIATE ANALYSIS |
| |
+-----------------------------------------------------------------;
PRINT RC;
*------COMPUTE CORRECTED SSCP MATRIX FROM CONTINGENCY TABLE-----;
R = RC[,+];
C = RC[+,];
N = R[+,];
RR = DIAG(R) - (R*R`)/N;
CC = DIAG(C) - (C`*C)/N;
RC = RC - (R*C)/N;
sscp = (RR || RC) // (RC` || CC);
* THE SSCP MATRIX IS NOW: | RR RC |
| RC` CC | ;
*------CREATE AN OUTPUT DATA SET WITH NO. OF OBSERVATIONS AND
THE CORRECTED SSCP MATRIX--------------------------------;
NRC = NROW(sscp);
int = J({1},NRC,0);
sscp=(n||int)//(int`||sscp);
Nobs = J({1},ncol(sscp),N);
X = Nobs // sscp;
NAME={ 'INTERCEP'} || NAME;
RNAME = { ' '} || NAME;
CREATE CCMDATA (RENAME=(RNAME =_NAME_ ))
FROM X [ROWNAME=RNAME COLNAME=NAME ];
APPEND FROM X [ROWNAME=RNAME];
QUIT;
DATA CCMDATA(TYPE=SSCP); SET CCMDATA;
IF _N_ = 1 THEN _TYPE_ = 'N ';
ELSE _TYPE_ = 'SSCP';
run;
PROC PRINT; run;
%mend;
*----------------------------------------------------------------+
| DATA FROM GLASS(1954), SOCIAL MOBILITY IN BRITAIN, |
| ROUTLEDGE & KEGAN |
| ROW CATEGORIES ARE FATHER'S SOCIAL STATUS. |
| COLUMN CATEGORIES ARE SON'S SOCIAL STATUS. |
+----------------------------------------------------------------;
PROC IML;
TITLE 'CATEGORICAL CONJOINT MEASUREMENT BY CANONICAL CORRELATION';
TITLE2 'EXAMPLE 1';
RESET AUTONAME ;
*------SET UP CONTINGENCY TABLE------;
RC ={ 50 45 8 18 8,
28 174 84 154 55,
11 78 110 223 96,
14 150 185 714 447,
0 42 72 320 411};
NAME ={ 'F1' 'F2' 'F3' 'F4' 'F5' 'S1' 'S2' 'S3' 'S4' 'S5'};
%CCM
*------THE CATEGORIES ARE SCALED BY OBTAINING THE CANONICAL
COEFFICIENTS FOR THE FIRST CANONICAL VARIABLE-------------;
PROC CANCORR DATA=CCMDATA NCAN=1 SIMPLE CORR outstat=outst
VNAME = 'DUMMY VARIABLES FOR FATHER''S STATUS'
WNAME = 'DUMMY VARIABLES FOR SON''S STATUS'
;
VAR F2 F3 F4 F5 F1;
WITH S2 S3 S4 S5 S1;
run;
proc print data=outst;
where _TYPE_ = 'RAWSCORE';
run;
*---------------------------------------------------------------;
PROC IML;
TITLE2 'EXAMPLE 2';
RESET AUTONAME ;
RC ={ 8 4 2 1 0 0,
4 8 4 2 1 0,
2 4 8 4 2 1,
1 2 4 8 4 2,
0 1 2 4 8 4,
0 0 1 2 4 8};
NAME ={ 'R1' 'R2' 'R3' 'R4' 'R5' 'R6'
'C1' 'C2' 'C3' 'C4' 'C5' 'C6'};
%CCM
PROC CANCORR DATA=CCMDATA NCAN=1 SIMPLE CORR outstat=outst
;
VAR R1-R6;
WITH C1-C6;
run;
proc print data=outst;
where _TYPE_ = 'RAWSCORE';
run;
*;
*-------------ANOTHER METHOD------------------------------------;
%MACRO CCM2;
*---CATEGORICAL CONJOINT MEASUREMENT NO. 2--------------;
*** NOTE: A FREQ statement must be used with PROC CANCORR,
i.e, FREQ freq;
PRINT RC;
NR = NROW(RC);
NC = NCOL(RC);
X = SHAPE(RC,0,{1}) || DESIGN( ({1}:NC)`@ J(NR,{1},{1}))
|| DESIGN( J(NC,{1},{1})@({1}:NR)`);
CNAME ={ 'FREQ'};
CNAME = CNAME || NAME;
_TMP_ROW = 'ROW1 ' : compress('ROW'+char(nrow(X)));
CREATE CCMDATA ( RENAME=(_TMP_ROW=ROW ))
FROM X [ROWNAME=_TMP_ROW COLNAME=CNAME ];
APPEND FROM X [ROWNAME=_TMP_ROW];
QUIT;
PROC PRINT;
RUN;
%MEND;
PROC IML;
TITLE 'CATEGORICAL CONJOINT MEASUREMENT BY CANONICAL CORRELATION';
TITLE2 'EXAMPLE 1: ANOTHER METHOD';
RESET AUTONAME ;
*------SET UP CONTINGENCY TABLE------;
RC ={ 50 45 8 18 8,
28 174 84 154 55,
11 78 110 223 96,
14 150 185 714 447,
0 42 72 320 411};
NAME ={ 'F1' 'F2' 'F3' 'F4' 'F5' 'S1' 'S2' 'S3' 'S4' 'S5'};
%CCM2
*------THE CATEGORIES ARE SCALED BY OBTAINING THE CANONICAL
COEFFICIENTS FOR THE FIRST CANONICAL VARIABLE-------------;
PROC CANCORR DATA=CCMDATA NCAN=1 SIMPLE CORR outstat=outst
VNAME = 'DUMMY VARIABLES FOR FATHER''S STATUS'
WNAME = 'DUMMY VARIABLES FOR SON''S STATUS'
;
VAR F2 F3 F4 F5 F1;
WITH S2 S3 S4 S5 S1;
FREQ freq;
run;
proc print data=outst;
where _TYPE_ = 'RAWSCORE';
run;
title;title2;
