/* SAS example of factor analysis */

/* Creating a SAS data set for the data for the life expectancy example */

DATA life;
INPUT Country $ 1-21  m0 m25 m50 m75 w0 w25 w50 w75;
cards;
Algeria              63  51  30  13 67  54  34  15
Cameroon             34  29  13   5 38  32  17   6
Madagascar           38  30  17   7 38  34  20   7
Mauritius            59  42  20   6 64  46  25   8
Reunion              56  38  18   7 62  46  25  10
Seychelles           62  44  24   7 69  50  28  14
South Africa(C)      50  39  20   7 55  43  23   8
South Africa(W)      65  44  22   7 72  50  27   9
Tunisia              56  46  24  11 63  54  33  19
Canada               69  47  24   8 75  53  29  10
CostaRica            65  48  26   9 68  50  27  10
Dominican Rep        64  50  28  11 66  51  29  11
El Salvador          56  44  25  10 61  48  27  12
Greenland            60  44  22   6 65  45  25   9
Grenada              61  45  22   8 65  49  27  10
Guatemala            49  40  22   9 51  41  23   8
Honduras             59  42  22   6 61  43  22   7
Jamaica              63  44  23   8 67  48  26   9
Mexico               59  44  24   8 63  46  25   8
Nicaragua            65  48  28  14 68  51  29  13
Panama               65  48  26   9 67  49  27  10
Trinidad(62)         64  63  21   7 68  47  25   9
Trinidad (67)        64  43  21   6 68  47  24   8
United States (66)   67  45  23   8 74  51  28  10
United States (NW66) 61  40  21  10 67  46  25  11
United States (W66)  68  46  23   8 75  52  29  10
United States (67)   67  45  23   8 74  51  28  10
Argentina            65  46  24   9 71  51  28  10
Chile                59  43  23  10 66  49  27  12
Columbia             58  44  24   9 62  47  25  10
Ecuador              57  46  28   9 60  49  28  11
;
run;

/* ML factor analysis with a varimax rotation */

PROC FACTOR DATA=life
HEY
METHOD=ML       /* Change this to METHOD=PRIN for a principal factor solution */
PRIORS=MAX
ROTATE=VARIMAX  /* Change this to ROTATE=NONE for an unrotated solution */
NFACT=3         /* Specifies the number of factors desired */
RESIDUALS
OUTSTAT=factout;
VAR m0 m25 m50 m75 w0 w25 w50 w75;
RUN; 


/* ******* Some diagnostic plots ******** */

/* Just copy all this into SAS */

DATA tempc; SET factout ;
vtemp=_NAME_; KEEP vtemp _NUMERIC_;
WHERE _TYPE_="CORR"; RUN;
DATA tempr; SET factout ;
vtemp=_NAME_; KEEP vtemp _NUMERIC_;
WHERE _TYPE_="RESIDUAL"; RUN;
PROC TRANSPOSE DATA=tempc 
OUT=tempc2; VAR _NUMERIC_; BY vtemp; RUN;
PROC TRANSPOSE DATA=tempr
OUT=tempr2; VAR _NUMERIC_; BY vtemp; RUN;
DATA tempc3; SET tempc2;
pair=trim(vtemp)||trim(_NAME_); original=COL1;
KEEP pair original; WHERE vtemp>_NAME_; RUN;
DATA tempr3; SET tempr2;
pair=trim(vtemp)||trim(_NAME_); residual=COL1;
KEEP pair residual; WHERE vtemp>_NAME_; RUN;
DATA fitdata; MERGE tempc3 tempr3; BY pair;
predicted=original-residual; RUN; 


/* Predicted correlations vs. original correlations */

PROC GPLOT DATA=fitdata;
PLOT predicted*original;
run;

/* Residual correlations vs. Predicted correlations */

PROC GPLOT DATA=fitdata;
PLOT residual*predicted / vref=0;
run;

/* Histogram, Stem-and-leaf plot, and summary statistics for the residuals */

PROC UNIVARIATE DATA=fitdata PLOT;
VAR residual;
HISTOGRAM residual;
run;

/* ************************************************************************* */

/* SAS factor analysis example on a correlation matrix */
/* rather than the raw data:                           */

DATA WAIS(TYPE=CORR);
INPUT _NAME_ $ _TYPE_ $ X1-X13;
LABEL
X1 = 'Information'
X2 = 'Comprehension'
X3 = 'Arithmetic'
X4 = 'Similarities' 
X5 = 'Digit.span'
X6 = 'Vocabulary'
X7 = 'Digit.symbol' 
X8 = 'Picture.completion' 
X9 = 'Block.design'
X10 = 'Picture.arrangement' 
X11 = 'Object.assembly'
X12 = 'Age'
X13 = 'Education'
;
CARDS;
N       N      933 933 933 933 933 933 933 933 933 933 933 933 933
X1	CORR  1.00  0.67  0.62  0.66  0.47  0.81  0.47  0.60  0.49  0.51  0.41 -0.07  0.66
X2	CORR  0.67  1.00  0.54  0.60  0.39  0.72  0.40  0.54  0.45  0.49  0.38 -0.08  0.52
X3	CORR  0.62  0.54  1.00  0.51  0.51  0.58  0.41  0.46  0.48  0.43  0.37 -0.08  0.49
X4	CORR  0.66  0.60  0.51  1.00  0.41  0.68  0.49  0.56  0.50  0.50  0.41 -0.19  0.55
X5	CORR  0.47  0.39  0.51  0.41  1.00  0.45  0.45  0.42  0.39  0.42  0.31 -0.19  0.43
X6	CORR  0.81  0.72  0.58  0.68  0.45  1.00  0.49  0.57  0.46  0.52  0.40 -0.02  0.62
X7	CORR  0.47  0.40  0.41  0.49  0.45  0.49  1.00  0.50  0.50  0.52  0.46 -0.46  0.57
X8	CORR  0.60  0.54  0.46  0.56  0.42  0.57  0.50  1.00  0.61  0.59  0.51 -0.28  0.48
X9	CORR  0.49  0.45  0.48  0.50  0.39  0.46  0.50  0.61  1.00  0.54  0.59 -0.32  0.44
X10	CORR  0.51  0.49  0.43  0.50  0.42  0.52  0.52  0.59  0.54  1.00  0.46 -0.37  0.49
X11	CORR  0.41  0.38  0.37  0.41  0.31  0.40  0.46  0.51  0.59  0.46  1.00 -0.28  0.40
X12	CORR -0.07 -0.08 -0.08 -0.19 -0.19 -0.02 -0.46 -0.28 -0.32 -0.37 -0.28  1.00 -0.29
X13	CORR  0.66  0.52  0.49  0.55  0.43  0.62  0.57  0.48  0.44  0.49  0.40 -0.29  1.00
;

PROC FACTOR DATA=WAIS
HEY
METHOD=ML
PRIORS=MAX
ROTATE=VARIMAX
NFACT=6
RESIDUALS
OUTSTAT=factout;
VAR X1-X13;
RUN; 

/* SAS automatically recognizes that the "data" form a correlation matrix, not actual raw data. */