/*------------------<--- Start of Description -->--------------------\
| PERFORM POLYNOMIAL REGRESSION ANALYSIS ON XVAR WITH THE OPTION OF |
| FIRST ELIMINATING OUTLIERS. PROVIDE DESCRIPTIVE STATISTICS ON XVAR |
| AND YVAR, AND PERFORM TESTS OF MODELING ASSUMPTIONS. |
|--------------------<--- End of Description -->---------------------|
|--------------------------------------------------------------------|
|--------------<--- Start of Files or Arguments Needed -->-----------|
| PARAMETERS : DSN - INPUT DATA SET NAME. |
| OPT - OUTLIER ELIMINATION OPTION. |
| OFFORD - FLAG OUTLIERS BUT INCLUDE IN |
| ANALYSIS. |
| OBRIEN - FLAG OUTLIERS AND EXCLUDE FROM |
| ANALYSIS (CAUTION: MAY NOT BE |
| APPROPRIATE WITH 'SMALL' |
| DATASETS). |
| XVAR - NAME OF X VARIABLE. |
| YVAR - NAME OF Y VARIABLE. |
| ID - NAME OF ID VARIABLE (I.E. CLINIC). |
| C1 - X INTERVAL CUT-OFF POINTS (I.E. 5 10 15). |
| IF OMITTED, MACRO WILL CHOOSE 4 INTERVALS |
| BASED ON RANGE OF X VALUES. |
| |
| PROCESSING : OUTLIERS - A VALUE IS FLAGGED AS AN OUTLIER IF |
| IT IS MORE THAN ONE STANDARD DEVIATION FROM THE |
| NEXT HIGHEST (LOWEST) VALUE. (AT MOST 5 VALUES |
| ARE CHECKED.) |
| |
| OUTPUT : PAGE 1 - |
| DESCRIPTIVE STATISTICS - |
| EXTREME VALUES WITH OUTLIERS FLAGGED. MEANS & |
| STD DEVS ARE PROVIDED FOR EACH X INTERVAL AND |
| OVERALL. P-VALUES FOR ANOVA & SPEARMAN'S TESTS. |
| POLYNOMIAL REGRESSION ANALYSIS - |
| POLYNOMIAL COEFFICIENTS FOR LINEAR THRU QUINTIC |
| MODELS ALONG WITH R-SQUARE AND P VALUES FOR |
| MODEL COMPARISONS. |
| TESTS OF MODELING ASSUMPTIONS - |
| SKEWNESS, KURTOSIS, NORMALITY, SPEARMAN AND |
| LEVENE TESTS ARE PERFORMED ON EACH OF THE MODELS. |
| PAGE 2 - |
| PLOT OF Y VS. X AND MEAN-Y VS. MEAN-X. |
| |
| ERROR MSG : MESSAGES ARE OUTPUT IF AN INPUT PARAMETER IS |
| MISSING OR OUT OF RANGE. |
|---------------<--- End of Files or Arguments Needed -->------------|
|--------------------------------------------------------------------|
|----------------<--- Start of Example and Usage -->-----------------|
| Usage: %REGRESS(DSN,OPT,XVAR,YVAR,ID,C1); |
\-------------------<--- End of Example and Usage -->---------------*/
%MACRO REGRESS(DSN,OPT,XVAR,YVAR,ID,C1);
/*--------------------------------------------\
| Author: C. D. STERTZ & S. L. DAOOD; |
| Created: 8/26/88 |
| Purpose: POLYNOMIAL REGRESSION ANALYSIS; |
\--------------------------------------------*/
%GLOBAL QUIT I N4 NOBSERV;
OPTIONS DQUOTE;
%IF &DSN= %THEN %DO;
%PUT "ERROR: NO DATASET NAME WAS SUPPLIED IN PARM LIST.";
%GO TO ENDUP;
%END;
%IF &OPT= %THEN %DO;
%PUT "ERROR: NO OPTION (OBRIEN/OFFORD) WAS SUPPLIED.";
%GO TO ENDUP;
%END;
%IF ^(&OPT=OBRIEN | &OPT=OFFORD) %THEN %DO;
%PUT "ERROR: OPTION MUST BE OBRIEN OR OFFORD.";
%GO TO ENDUP;
%END;
%IF &XVAR= %THEN %DO;
%PUT "ERROR: NO X VARIABLE SUPPLIED";
%GO TO ENDUP;
%END;
%IF &YVAR= %THEN %DO;
%PUT "ERROR: NO Y VARIABLE SUPPLIED";
%GO TO ENDUP;
%END;
%LET _TIT= ;
%IF &OPT=OBRIEN %THEN %LET _TIT="OUTLIERS ELIMINATED";
**** COUNT & ELIMINATE MISSINGS ****;
DATA _DSN; SET &DSN END=EOF;
KEEP &ID &XVAR &YVAR;
RETAIN DEL_CNT 0;
IF (&XVAR=. | &YVAR=.) THEN DEL_CNT = DEL_CNT+1;
IF (EOF) THEN DO;
DELC = PUT(DEL_CNT,3.);
CALL SYMPUT('_DELS',DELC);
END;
IF (&XVAR=. | &YVAR=.) THEN DELETE;
%IF &C1= %THEN %DO;
%LET NUM=4;
DATA _NULL_; SET _DSN END=EOF;
RETAIN BOTTOM TOP;
IF (_N_ =1) THEN DO;
BOTTOM=&XVAR; TOP=&XVAR;
END;
IF (&XVARTOP) THEN TOP=&XVAR;
IF (EOF) THEN DO;
INTERVAL=(TOP - BOTTOM)/4;
T1=CEIL(BOTTOM + INTERVAL);
T2=CEIL(T1 + INTERVAL);
T3=CEIL(T2 + INTERVAL);
TT1=' '; TT2=' '; TT3=' ';
TT1=PUT(T1,Z5.);
TT2=PUT(T2,Z5.);
TT3=PUT(T3,Z5.);
NEWVAL=' ';
NEWVAL=TT1 || ' ' || TT2 || ' ' || TT3;
CALL SYMPUT('C1',NEWVAL);
END;
%END;
DATA _DSN(KEEP=&ID GROUP WEIGH X X2 X3 X4 X5 Y);
SET _DSN END=EOF;
RETAIN COUNT 0 DEL_CNT 0;
GROUP=" ";
%LET BE=X;
%LET I=1;
X = &XVAR;
X2 = X*X;
X3 = X2*X;
X4 = X3*X;
X5 = X4*X;
Y = &YVAR;
COUNT = COUNT + 1;
%DO %UNTIL(&BE= );
%LET BI=%SCAN(&C1,&I,' ');
%LET BE=%SCAN(&C1,&I+1,' ');
%IF &I=1 %THEN %DO;
IF &XVAR <&BI THEN DO;
GROUP=" X<&BI";
WEIGH=0;
END;
%END;
%IF &BE^= %THEN %DO;
%IF &BE<&BI %THEN %DO;
PUT "ERROR: NON-INCREASING INTERVALS IN PARM LIST";
%GO TO ENDUP;
%END;
IF &BI <= &XVAR < &BE THEN DO;
GROUP="&BI<=X<&BE";
WEIGH=1;
END;
%END;
%ELSE %DO;
IF &XVAR>=&BI THEN DO;
GROUP="&BI<=X ";
WEIGH=2;
END;
%END;
%LET I=%EVAL(&I+1);
%END;
OUTPUT _DSN;
%LET NUM=%EVAL(&I);
IF EOF THEN DO;
CC = PUT(COUNT,6.);
CALL SYMPUT('QUIT',CC);
END;
DATA _DSN; SET _DSN END=EOF;
%IF &QUIT>=6 %THEN %DO;
RETAIN COUNT 0;
COUNT = COUNT + 1;
ID = &ID;
%LET I=1;
%DO II=1 %TO &NUM;
G&I=0;
%LET I=%EVAL(&I+1);
%END;
%LET BE=X;
%LET I=1;
%DO %UNTIL(&BE= );
%LET BI=%SCAN(&C1,&I,' ');
%LET BE=%SCAN(&C1,&I+1,' ');
%IF &I=1 %THEN %DO;
%LET II=1;
IF X < &BI THEN G&II=1;
%END;
%LET II=%EVAL(&II+1);
%IF &BE^= %THEN %DO;
%IF &BE<=&BI %THEN %DO;
PUT "ERROR: NON-INCREASING INTERVALS IN PARM LIST";
%GO TO ENDUP;
%END;
IF &BI <= X < &BE THEN G&II=1;
%END;
%ELSE %DO;
IF X >= &BI THEN G&II=1;
%END;
%LET I=%EVAL(&I+1);
%END;
IF EOF THEN DO;
NN = PUT(COUNT,Z5.);
DO I=1 TO 5;
IF (SUBSTR(NN,I,1)^='0') THEN DO;
INDEX = I;
I=5;
END;
END;
NNN = SUBSTR(NN,INDEX,5-INDEX+1);
CALL SYMPUT('NOBSERV',NNN);
END;
**** DETERMINE AND THROW OUT OUTLIERS IF REQUESTED ****;
%MACRO STD_DEV;
SM = 0; SM_SQ = 0;
DO I=START TO END;
SM = SM + OBS(I);
SM_SQ = SM_SQ + (OBS(I)**2);
END;
SQ_SM = SM**2 / (END - START + 1);
S2 = (SM_SQ - SQ_SM) / (END - START);
STDEV = SQRT(S2);
%MEND STD_DEV;
%MACRO STD_CHK;
START = 1;
END = &NOBSERV;
%STD_DEV;
IF (&NOBSERV>=2 & ABS(OBS(1) - OBS(2)) > STDEV) THEN DO;
OUTL(1) = '*';
START = 2;
%STD_DEV;
END;
IF (&NOBSERV>=3 & ABS(OBS(2) - OBS(3)) > STDEV) THEN DO;
OUTL(1) = '*';
OUTL(2) = '*';
START = 3;
%STD_DEV;
END;
IF (&NOBSERV>=4 & ABS(OBS(3) - OBS(4)) > STDEV) THEN DO;
OUTL(1) = '*';
OUTL(2) = '*';
OUTL(3) = '*';
START = 4;
%STD_DEV;
END;
IF (&NOBSERV>=5 & ABS(OBS(4) - OBS(5)) > STDEV) THEN DO;
OUTL(1) = '*';
OUTL(2) = '*';
OUTL(3) = '*';
OUTL(4) = '*';
START = 5;
%STD_DEV;
END;
IF (&NOBSERV>=6 & ABS(OBS(5) - OBS(6)) > STDEV) THEN DO;
OUTL(1) = '*';
OUTL(2) = '*';
OUTL(3) = '*';
OUTL(4) = '*';
OUTL(5) = '*';
START = 6;
%STD_DEV;
END;
IF (&NOBSERV>=7 &
ABS(OBS(&NOBSERV) - OBS(&NOBSERV-1)) > STDEV) THEN DO;
OUTL(10) = '*';
END = &NOBSERV - 1;
IF (END > START) THEN DO;
%STD_DEV;
END;
END;
IF (&NOBSERV>=8 &
ABS(OBS(&NOBSERV-1) - OBS(&NOBSERV-2)) > STDEV) THEN DO;
OUTL(10) = '*';
OUTL(9) = '*';
END = &NOBSERV - 2;
IF (END > START) THEN DO;
%STD_DEV;
END;
END;
IF (&NOBSERV>=9 &
ABS(OBS(&NOBSERV-2) - OBS(&NOBSERV-3)) > STDEV) THEN DO;
OUTL(10) = '*';
OUTL(9) = '*';
OUTL(8) = '*';
END = &NOBSERV - 3;
IF (END > START) THEN DO;
%STD_DEV;
END;
END;
IF (&NOBSERV>=10 &
ABS(OBS(&NOBSERV-3) - OBS(&NOBSERV-4)) > STDEV) THEN DO;
OUTL(10) = '*';
OUTL(9) = '*';
OUTL(8) = '*';
OUTL(7) = '*';
END = &NOBSERV - 4;
IF (END > START) THEN DO;
%STD_DEV;
END;
END;
IF (&NOBSERV>=11 &
ABS(OBS(&NOBSERV-4) - OBS(&NOBSERV-5)) > STDEV) THEN DO;
OUTL(10) = '*';
OUTL(9) = '*';
OUTL(8) = '*';
OUTL(7) = '*';
OUTL(6) = '*';
END = &NOBSERV - 5;
IF (END > START) THEN DO;
%STD_DEV;
END;
END;
%MEND STD_CHK;
%MACRO OUTLR(L);
PROC SORT DATA=_DSN; BY DESCENDING &L;
PROC TRANSPOSE DATA=_DSN OUT=_TRANSID PREFIX=ID&L._;
VAR ID;
DATA _TRANSID; SET _TRANSID;
%LET N4 = 6;
%IF (&NOBSERV > 10) %THEN %DO;
%LET N4 = %EVAL(&NOBSERV-4);
%END;
KEEP ID&L._1-ID&L._5 ID&L._&N4-ID&L._&NOBSERV;
PROC TRANSPOSE DATA=_DSN OUT=_TRANS PREFIX=&L._;
VAR &L.;
DATA _OUTL&L; SET _TRANS;
LENGTH OUTL&L._1-OUTL&L._10 $1.;
ARRAY OBS(*) &L._1-&L._&NOBSERV;
ARRAY OUTL(10) OUTL&L._1-OUTL&L._10;
%LET N4 = 6;
%IF (&NOBSERV > 10) %THEN %DO;
%LET N4 = %EVAL(&NOBSERV-4);
%END;
KEEP &L._1-&L._5 &L._&N4-&L._&NOBSERV OUTL&L._1-OUTL&L._10;
%STD_CHK;
DATA _MNMX&L;
IF _N_=1 THEN SET _TRANSID;
SET _OUTL&L;
%MEND OUTLR;
**** REMOVE OUTLYING X ****;
%OUTLR(X);
**** REMOVE OUTLYING Y ****;
%OUTLR(Y);
DATA _T_DAT;
IF _N_=1 THEN DO;
MERGE _MNMXX _MNMXY;
END;
SET _DSN;
KEEP ID X Y WEIGH GROUP X2-X5 G1-G&NUM;
%LET N4 = %EVAL(&NOBSERV-4);
%LET N3 = %EVAL(&NOBSERV-3);
%LET N2 = %EVAL(&NOBSERV-2);
%LET N1 = %EVAL(&NOBSERV-1);
%IF (&OPT = OBRIEN) %THEN %DO;
IF ((X=X_1 & OUTLX_1='*') | (X=X_2 & OUTLX_2='*') |
(X=X_3 & OUTLX_3='*') | (X=X_4 & OUTLX_4='*') |
(X=X_5 & OUTLX_5='*') | (X=X_&N4 & OUTLX_6='*') |
(X=X_&N3 & OUTLX_7='*') | (X=X_&N2 & OUTLX_8='*') |
(X=X_&N1 & OUTLX_9='*') | (X=X_&NOBSERV & OUTLX_10='*') |
(Y=Y_1 & OUTLY_1='*') | (Y=Y_2 & OUTLY_2='*') |
(Y=Y_3 & OUTLY_3='*') | (Y=Y_4 & OUTLY_4='*') |
(Y=Y_5 & OUTLY_5='*') | (Y=Y_&N4 & OUTLY_6='*') |
(Y=Y_&N3 & OUTLY_7='*') | (Y=Y_&N2 & OUTLY_8='*') |
(Y=Y_&N1 & OUTLY_9='*') | (Y=Y_&NOBSERV & OUTLY_10='*'))
THEN DELETE;
%END;
PROC SORT DATA=_T_DAT; BY WEIGH GROUP;
DATA _GRPS; SET _T_DAT END=EOF; BY WEIGH GROUP;
RETAIN G_NUM 0;
KEEP _GRPS;
IF FIRST.GROUP THEN DO;
_GRPS=GROUP;
G_NUM= G_NUM + 1;
OUTPUT;
END;
IF EOF THEN DO;
NN = PUT(G_NUM,Z2.);
DO I=1 TO 2;
IF (SUBSTR(NN,I,1)^='0') THEN DO;
INDEX = I;
I=2;
END;
END;
NNN = SUBSTR(NN,INDEX,2-INDEX+1);
CALL SYMPUT('NUM',NNN);
END;
DATA _GRPS; SET _GRPS END=EOF;
KEEP _GRPS;
OUTPUT;
IF EOF THEN DO;
CT=_N_; _GRPS=" ";
DO WHILE(CT<10);
CT = CT + 1;
OUTPUT;
END;
_GRPS=' TOTAL';
OUTPUT;
END;
DATA _DSN; SET _T_DAT END=EOF;
IF (EOF) THEN DO;
OUTS = &NOBSERV - _N_;
OUTSPUT = PUT(OUTS,3.);
CALL SYMPUT('_OUTS',OUTSPUT);
NN = PUT(_N_,Z5.);
DO I=1 TO 5;
IF (SUBSTR(NN,I,1) ^= '0') THEN DO;
INDEX = I;
I = 5;
END;
END;
NNN = SUBSTR(NN,INDEX,5-INDEX+1);
CALL SYMPUT('NOBSERV',NNN);
END;
%LET KK = %EVAL(&NUM-1);
**** CALCULATE GROUP & TOTAL STATS ****;
PROC SORT DATA=_DSN; BY GROUP WEIGH;
PROC MEANS NOPRINT DATA=_DSN;
BY GROUP WEIGH;
VAR Y X;
OUTPUT OUT=_GRPSTAT MEAN=MN_Y MN_X
STD=STD_Y
N=N;
PROC SORT DATA=_GRPSTAT; BY WEIGH GROUP;
PROC MEANS NOPRINT DATA=_DSN;
VAR Y X;
OUTPUT OUT=_TOTSTAT(KEEP=MN_Y MN_X STD_Y STD_X CSS_Y CSS_X N)
MEAN=MN_Y MN_X
STD=STD_Y STD_X
CSS=CSS_Y CSS_X
N=N;
DATA _NULL_; SET _TOTSTAT;
CALL SYMPUT('MEANX', MN_X);
DATA _MEANS; SET _GRPSTAT(IN=INGP) _TOTSTAT(IN=INSMN);
DROP CT SAVE1-SAVE7;
IF INGP THEN OUTPUT;
IF INSMN THEN DO;
SAVE1=N; SAVE2=MN_Y; SAVE3=MN_X; SAVE4=STD_Y;
SAVE5=STD_X; SAVE6=CSS_Y; SAVE7=CSS_X;
N=.; MN_Y=.; MN_X=.; STD_Y=.; STD_X=.; CSS_Y=.; CSS_X=.;
GROUP=' ';
CT=_N_;
DO WHILE (CT<=10);
OUTPUT;
CT=CT + 1;
END;
GROUP=' TOTAL';
N=SAVE1; MN_Y=SAVE2; MN_X=SAVE3; STD_Y=SAVE4;
STD_X=SAVE5; CSS_Y=SAVE6; CSS_X=SAVE7;
OUTPUT;
END;
**** TRANSFORM X VALUES AROUND MEAN ****;
DATA _DSNSAV; SET _DSN;
DATA _DSN; SET _DSN;
X = X - &MEANX;
X2 = X * X;
X3 = X2 * X;
X4 = X3 * X;
X5 = X4 * X;
**** FIT POLYNOMIAL MODELS - OUTPUT COEFF & RESIDUALS ****;
PROC SORT DATA=_DSN; BY X Y ID;
PROC REG DATA=_DSN NOPRINT;
MEAN: MODEL Y=; OUTPUT OUT=_RES_0 R=R_0;
PROC REG DATA=_DSN NOPRINT OUTEST=_OUTREGR;
LINEAR: MODEL Y=X; OUTPUT OUT=_RES_1 R=R_1;
QUADRATC: MODEL Y=X X2; OUTPUT OUT=_RES_2 R=R_2;
CUBIC: MODEL Y=X X2 X3; OUTPUT OUT=_RES_3 R=R_3;
QUARTIC: MODEL Y=X X2 X3 X4; OUTPUT OUT=_RES_4 R=R_4;
QUINTIC: MODEL Y=X X2 X3 X4 X5; OUTPUT OUT=_RES_5 R=R_5;
**** ANOVA ON Y & MODIFIED LEVENE TEST ****;
DATA _LEV; MERGE _RES_0 _RES_1 _RES_2 _RES_3 _RES_4 _RES_5; BY X Y ID;
PROC UNIVARIATE NOPRINT DATA=_LEV;
VAR R_0 R_1 R_2 R_3 R_4 R_5;
OUTPUT OUT=R_STAT MEDIAN=LMD_0 LMD_1 LMD_2 LMD_3 LMD_4 LMD_5
MEAN = MNR_0 MNR_1 MNR_2 MNR_3 MNR_4 MNR_5
STD = STDR_0 STDR_1 STDR_2 STDR_3 STDR_4 STDR_5;
DATA _LEV;
IF _N_=1 THEN SET R_STAT;
SET _LEV;
LEV_0 = ABS(R_0 - LMD_0);
LEV_1 = ABS(R_1 - LMD_1);
LEV_2 = ABS(R_2 - LMD_2);
LEV_3 = ABS(R_3 - LMD_3);
LEV_4 = ABS(R_4 - LMD_4);
LEV_5 = ABS(R_5 - LMD_5);
IF (&NOBSERV>50) THEN DO;
Z_0 = PROBNORM((R_0 - MNR_0)/STDR_0);
Z_1 = PROBNORM((R_1 - MNR_1)/STDR_1);
Z_2 = PROBNORM((R_2 - MNR_2)/STDR_2);
Z_3 = PROBNORM((R_3 - MNR_3)/STDR_3);
Z_4 = PROBNORM((R_4 - MNR_4)/STDR_4);
Z_5 = PROBNORM((R_5 - MNR_5)/STDR_5);
END;
%MACRO GG;
%DO I=1 %TO &KK;
G&I
%END;
%MEND GG;
PROC RSQUARE NOPRINT DATA=_LEV OUTEST=_OUTRSQ SSE MSE;
MODEL Y = %GG / INCLUDE=&KK;
MODEL LEV_0 = %GG / INCLUDE=&KK;
MODEL LEV_1 = %GG / INCLUDE=&KK;
MODEL LEV_2 = %GG / INCLUDE=&KK;
MODEL LEV_3 = %GG / INCLUDE=&KK;
MODEL LEV_4 = %GG / INCLUDE=&KK;
MODEL LEV_5 = %GG / INCLUDE=&KK;
DATA _AONY _LEV_P; SET _OUTRSQ;
SSR = _RSQ_ * _SSE_ / (1 - _RSQ_);
MSB = SSR / (&NUM-1);
F = MSB / _MSE_;
P = 1 - PROBF(F,&NUM-1,&NOBSERV-&NUM);
IF _N_=1 THEN OUTPUT _AONY;
IF _N_^=1 THEN OUTPUT _LEV_P;
**** NORMALITY ****;
%LET W_P_VAL1 = .753/.687/.686/ .713/.730/.749/.764/.781/
.792/.805/.814/.825/.835/ .844/.851/.858/.863/.868/
.873/.878/.881/.884/.888/ .891/.894/.896/.898/.900/
.902/.904/.906/.908/.910/ .912/.914/.916/.917/.919/
.920/.922/.923/.924/.926/ .927/.928/.929/.929/.930;
%LET W_P_VAL2 = .756/.707/.715/ .743/.760/.778/.791/.806/
.817/.828/.837/.846/.855/ .863/.869/.874/.879/.884/
.888/.892/.895/.898/.901/ .904/.906/.908/.910/.912/
.914/.915/.917/.919/.920/ .922/.924/.925/.927/.928/
.929/.930/.932/.933/.934/ .935/.936/.937/.937/.938;
%LET W_P_VAL3 = .767/.748/.762/ .788/.803/.818/.829/.842/
.850/.859/.866/.874/.881/ .887/.892/.897/.901/.905/
.908/.911/.914/.916/.918/ .920/.923/.924/.926/.927/
.929/.930/.931/.933/.934/ .935/.936/.938/.939/.940/
.941/.942/.943/.944/.945/ .945/.946/.947/.947/.947;
%LET W_P_VAL4 = .789/.792/.806/ .826/.838/.851/.859/.869/
.876/.883/.889/.895/.901/ .906/.910/.914/.917/.920/
.923/.926/.928/.930/.931/ .933/.935/.936/.937/.939/
.940/.941/.942/.943/.944/ .945/.946/.947/.948/.949/
.950/.951/.951/.952/.953/ .953/.954/.954/.955/.955;
%MACRO NORM;
%IF (&NOBSERV<=50) %THEN %DO;
PROC UNIVARIATE NOPRINT DATA=_LEV;
VAR R_0 R_1 R_2 R_3 R_4 R_5;
OUTPUT OUT=_NORML NORMAL=W_0 W_1 W_2 W_3 W_4 W_5;
%MACRO PN;
%DO I=0 %TO 5;
PNORM_&I = ' P>.10';
IF (W_&I <= &W4) THEN PNORM_&I = ' .0550) %THEN %DO;
%DO I=0 %TO 5;
PROC SORT DATA=_LEV; BY Z_&I;
PROC TRANSPOSE DATA=_LEV OUT=_ZTRAN(DROP=_NAME_) PREFIX=Z_;
VAR Z_&I.;
%MACRO A2_CALC;
ARRAY Z(&NOBSERV) Z_1 - Z_&NOBSERV;
A2_&I. = 0;
DO J=1 TO &NOBSERV;
A2_&I = A2_&I +
(2*J-1) * (LOG(Z(J)) + LOG(1 - Z(&NOBSERV-J+1)));
END;
A2_&I = (-1 * A2_&I / &NOBSERV) - &NOBSERV;
A2_&I = A2_&I * (1 + .75/&NOBSERV + 2.25/(&NOBSERV**2));
IF (A2_&I >= 1.035) THEN PNORM_&I = ' P<=.01';
IF (A2_&I < 1.035) THEN PNORM_&I = '.011 THEN DO;
PUT #PN @52 _GRPS $CHAR12. @65 N 6. @73 MN_X 10.2 @85 MN_Y
10.2 @97 STD_Y 10.2 ;
PN=PN+1;
END;
END;
PUT #20 @1 130*"=";
PUT @1 "| POLYNOMIAL REGRESSION ANALYSIS |"/
@2 "--------------------------------" @117 "P-VALUE" /
@43 "COEFFICIENTS" @87"ERROR" @112 "MODEL(I) MODEL(I)"/
@16 65*"-" @83 14*"-" @104 "2" @114 "VS VS"/
@2 "MODEL(I)" @24 "B0" @35 "B1" @46 "B2" @57 "B3" @68 "B4"
@79 "B5" @84 "DF" @92 "RMSE" @103 "R"
@110 "MODEL(I-1) MODEL(0)"/
@2 130*"-";
SET MEAN_PGA;
PUT @2 "MEAN(0)" @16 MN_Y 10.3 @82 EDF_MN 4. @88 RMSE_MN 8.2;
DO I=1 TO 5;
SET _PGANAL(drop=_type_);
IF _MODEL_="LINEAR" THEN _MODEL="LINEAR(1) ";
ELSE IF _MODEL_="QUADRATC" THEN _MODEL="QUADRATIC(2)";
ELSE IF _MODEL_="CUBIC" THEN _MODEL="CUBIC(3)";
ELSE IF _MODEL_="QUARTIC" THEN _MODEL="QUARTIC(4)";
ELSE IF _MODEL_="QUINTIC" THEN _MODEL="QUINTIC(5)";
PUT
@2 _MODEL @16 B0 10.3 @27 B1 10.4 @38 B2 10.4 @49 B3 10.5
@60 B4 10.5 @71 B5 10.5 @82 _EDF_ 4. +2 _RMSE_ 8.2 +2
_RSQ_ 8.3 @112 P_I_1 8.3 +2 P_0 8.3;
END;
PUT @1 130*"=";
PUT @1 "| TEST OF MODELLING ASSUMPTIONS USING RESIDUALS "
@49 "FROM THE FOLLOWING MODELS : |";
PUT @2 75*"-" /
@39 "MEAN LINEAR QUADRATIC CUBIC "
@92 "QUARTIC QUINTIC";
SET _ZP;
PUT @3 "SKEWNESS : COEFFICIENT" @35 SKW_R0 8.2 +6 SKW_R1 8.2
+6 SKW_R2 8.2 +6 SKW_R3 8.2 +6 SKW_R4 8.2 +6 SKW_R5 8.2 /
@18 "Z" @35 Z_SKW_R0 8.2 +6 Z_SKW_R1 8.2 +6 Z_SKW_R2 8.2
+6 Z_SKW_R3 8.2 +6 Z_SKW_R4 8.2 +6 Z_SKW_R5 8.2 //
@3 "KURTOSIS : COEFFICIENT" @35 KRT_R0 8.2 +6 KRT_R1 8.2
+6 KRT_R2 8.2 +6 KRT_R3 8.2 +6 KRT_R4 8.2 +6 KRT_R5 8.2 /
@18 "Z" @35 Z_KRT_R0 8.2 +6 Z_KRT_R1 8.2 +6 Z_KRT_R2 8.2
+6 Z_KRT_R3 8.2 +6 Z_KRT_R4 8.2 +6 Z_KRT_R5 8.2 /;
SET _NORML;
PUT @3 "NORMALITY : P " @32 PNORM_0 $CHAR11. +3
PNORM_1 $CHAR11. +3 PNORM_2 $CHAR11. +3 PNORM_3 $CHAR11.
+3 PNORM_4 $CHAR11. +3 PNORM_5 $CHAR11. //
@3 "COMMON VARIANCE :" ;
SET _P_SPEAR;
PUT @4 "P VALUE FROM SPEARMANS R" @35 P_R0 8.3 +6 P_R1 8.3
+6 P_R2 8.3 +6 P_R3 8.3 +6 P_R4 8.3 +6 P_R5 8.3/
@6 "USING ABSOLUTE RESIDUALS" /;
SET __LEV_P;
PUT @4 "P VALUE USING MODIFIED" @35 LEVP0 8.3 +6 LEVP1 8.3
+6 LEVP2 8.3 +6 LEVP3 8.3 +6 LEVP4 8.3 +6 LEVP5 8.3 /
@6 "LEVENE TEST";
STOP;
DATA _ME; SET _MEANS;
IF GROUP=' ' | GROUP=' TOTAL' THEN DELETE;
DATA _PLOT; MERGE _DSNSAV _ME;
PROC PLOT DATA=_PLOT; PLOT Y*X MN_Y*MN_X="*"/OVERLAY;
LABEL Y=%UNQUOTE(%QUOTE(%'&YVAR%'))
X=%UNQUOTE(%QUOTE(%'&XVAR%'));
%END;
%ELSE %DO;
PUT 'INSUFFICIENT NON-MISSING OBSERVATIONS (N<6)';
%END;
%ENDUP:
OPTIONS NODQUOTE;
%MEND REGRESS;
