Regression discontinuity

whs278 — Mon, 03 Feb 2020 19:30:59 GMT

Hi,

I was wondering if SAS had any automated feature for creating a Regression Discontinuity plot. What I want is a function that will split the running variable by a given binwidth and then create a binned scatterplot. The bins should be counted from the point of discontinuity so that each bin contains either all treatment or all control observations.

For example, in the plot below, X is the running variable. There is a threshold for treatment assignment at 120 represented by a red, dashed vertical line. The binwidth is equal to 10. Consequently, the bins are counted to the right and to the left of the threshold (e.g. 110-120, 100-110,... on the left and 120-130, 130-140... on the right. The observations are binned into these categories and then plotted as points. The y-value is determined by the mean for each bin. As you can see from this example, ideally if a treatment is effective, we should see a discontinuity at the threshold, which we do in this case.

I created the above plot using this code. However, I was wondering whether or not there was a procedure in SAS that does the same thing. I believe there are functions in R and Stata that create similar plots.

%MACRO BINSCATTER_TEST(DATA, X, Y, CENTER = 0.5, BINSIZE =10,
HIST = 1, BINSCATTER = 1,
X_TICK = 50, PRINT = 0);

/*FIND THE RANK FARTHEST AWAY FROM CUT SCORE*/
/*NOTE: PROBABLY CAN FIND WAY TO DO THIS INSIDE PROC IML STEP*/
PROC SQL NOPRINT;

SELECT MAX(ABS( &CENTER - MIN_&X), (MAX_&X - &CENTER)) INTO :FARTHEST_RNK
FROM (SELECT MIN(&X) AS MIN_&X,
MAX(&X) AS MAX_&X
FROM &DATA);
QUIT;
%PUT &=FARTHEST_RNK;

PROC IML;

/*MATRICES CREATED INSIDE PROC IML: */
/*NEG, POS, NEG_REV, CUTS, MIN_CUT, MAX_CUT, B, START_MIDS, END_MIDS, MIDS*/

USE &DATA;
READ ALL VAR {&X} INTO X;

CLOSE &DATA;

%LET MID_BIN = &BINSIZE / 2;

POS = DO(&CENTER, &CENTER + &FARTHEST_RNK + &BINSIZE, &BINSIZE);
NEG = DO(&CENTER, &CENTER -&FARTHEST_RNK - &BINSIZE, -&BINSIZE);

/*NOTE: NEED TO DROP CUT SCORE FROM ONE OF THESE VECTORS TO PREVENT OVERLAP*/
NEG = NEG[ , 2:NCOL(NEG)];

/*CREATE 'MINI-FUNCTION' TO REVERSE NEG VECTOR*/
START FLIPLR(A);
RETURN A[, NCOL(A):1];
FINISH;

NEG_REV = FLIPLR(NEG);

/*CONCATENATE REVESED NEG AND POS INTO ONE VECTOR CONTAINING ALL CUTPOINTS*/
CUTS = NEG_REV||POS;

/*CREATE VECTOR CONTAINING BIN ASSIGNMENT FOR EACH OBSERVATION IN DATASET*/
B = BIN(X, CUTS);

/*FIND MIDPOINTS OF BINS TO PLOT POINTS INTO SCATTER PLOTS*/
START_MIDS = MIN(CUTS) + (&MID_BIN);
END_MIDS = MAX(CUTS) - (&MID_BIN);
MIDS = DO(START_MIDS, END_MIDS, &BINSIZE);

/*CREATE MACRO VARIABLES FOR PROCS GRAPHICS*/
CALL SYMPUTX("MIN_CUT", MIN(CUTS));
CALL SYMPUTX("MAX_CUT", MAX(CUTS));
CALL SYMPUTX("BIN_START", &MIN_CUT - &MID_BIN);
CALL SYMPUTX("XMIN", &X_TICK*FLOOR(&MIN_CUT / &X_TICK));
CALL SYMPUTX("XMAX", &X_TICK*CEIL(&MAX_CUT / &X_TICK));

/*OUTPUT DATASET CONTAINING EACH OBSERVATION OF X AND B*/
CREATE BINNED_IML VAR {X B};
APPEND;
CLOSE BINNED_IML;

/*OUTPUT DATASET CONTAINING THE MIDPOINTS FOR EACH BIN*/
CREATE MID_PTS VAR {MIDS CUTS};
APPEND;
CLOSE;

QUIT;

/*APPEND BINNED_IML TO ORIGINAL DATASET (CBIND)*/
DATA DATA_BINNED_IML;
SET &DATA;
SET BINNED_IML;
RUN;

ODS GRAPHICS ON / WIDTH=6IN HEIGHT=4IN NOBORDER;

/*-------------- PRODUCE GRAPHIC FOR EACH X VARIABLE ------------*/

/*--- HISTOGRAM ---*/
%IF &HIST = 1 %THEN %DO;
PROC SGPLOT DATA = &DATA;
HISTOGRAM &X / BINSTART = &BIN_START
BINWIDTH = &BINSIZE
SCALE = COUNT;
XAXIS MAX=&MAX_CUT MIN= &MIN_CUT;
REFLINE &CENTER / AXIS = X LINEATTRS=(COLOR = RED PATTERN = DASH);
XAXIS VALUES=(&XMIN TO &XMAX BY &X_TICK) ;
RUN;
%END;

/*-------------- PRODUCE GRAPHICS FOR EACH Y VARIABLE ------------*/
%DO I=1 %TO %SYSFUNC(COUNTW(&Y));

%LET Y_I = %SCAN(&Y, &I);

/*--- CALCULATE MEAN OF Y VARIABLE FOR EACH BIN ---*/
PROC MEANS DATA = DATA_BINNED_IML NOPRINT;
CLASS B;
VAR &Y_I ;
OUTPUT OUT = BIN_MEANS(WHERE=(_TYPE_=1)) MEAN=;

RUN;

/*--- MERGE MID_PTS WITH BIN_MEANS BY B ---*/
/*NOTE: WE NEED THIS STEP IN CASE SOME BINS HAVE ZERO OBS*/
DATA MID_PTS;
SET MID_PTS;
B = _N_;
RUN;

PROC SORT DATA= MID_PTS;
BY B;
RUN;

PROC SORT DATA= BIN_MEANS;
BY B;
RUN;

DATA BINNED(RENAME=(MIDS = &X));
MERGE BIN_MEANS(RENAME =(_FREQ_=N) DROP=_TYPE_) MID_PTS;
BY B;

RUN;

/*--- BINNED SCATTER PLOT ---*/
%IF &BINSCATTER = 1 %THEN %DO;
PROC SGPLOT DATA = BINNED;
SCATTER X = &X Y = &Y_I ;
REFLINE &CENTER / AXIS = X LINEATTRS=(COLOR = RED PATTERN = DASH);
XAXIS VALUES=(&XMIN TO &XMAX BY &X_TICK) ;
RUN;
%END;

%END;

ODS GRAPHICS OFF;

/*CHECK: MAKE SURE BIN CATEGORIES ARE CORRECT*/
%IF &PRINT = 1 %THEN %DO;
PROC PRINT DATA = MID_PTS;
RUN;

PROC SORT DATA= DATA_BINNED_IML;
BY B;
RUN;

PROC PRINT DATA = DATA_BINNED_IML;
BY B;
VAR B TREAT X Y;
RUN;

PROC PRINT DATA = BIN_MEANS;
RUN;

PROC PRINT DATA = BINNED;
RUN;
%END;

%MEND BINSCATTER_TEST;

/*----------------------------------------------------------------------------------------*/
/*-------------------------------------- FAKE DATA ---------------------------------------*/
/*----------------------------------------------------------------------------------------*/

DATA FAKE;
DO STUDENT_ID =1 TO 1000;

X = RAND("NORMAL", 120, 20);

IF X GE 120 THEN DO;
TREAT = 1;
Y = X + 40 + RAND("NORMAL", 0, 5);
END;
ELSE DO; ;
TREAT = 0;
Y = X + RAND("NORMAL", 0, 5);
END;
OUTPUT;
END;

RUN;

%BINSCATTER_TEST(FAKE, X, Y, CENTER=120, BINSIZE = 10, X_TICK = 10, PRINT = 0);

Re: Regression discontinuity

Ksharp — Tue, 04 Feb 2020 04:39:15 GMT

I think you could try PROC LOESS non-parameter regression .

@Rick_SAS has written several blog about regression .

Re: Regression discontinuity

Rick_SAS — Fri, 07 Feb 2020 17:11:28 GMT

> I was wondering if SAS had any automated feature for creating a Regression Discontinuity plot. ...

> I was wondering whether or not there was a procedure in SAS that does the same thing.

No. I don't think so.

Your program uses the BIN function in SAS/IML, which is a good choice.

Re: Regression discontinuity

whs278 — Fri, 07 Feb 2020 20:11:02 GMT

Hi Rick,

Thank you for the response. I was trying to see if there was a canned procedures so that I could check my macro, but it appears that there isn't one in SAS as of now.

By the way, I found your blog post very helpful when working on that macro. Coming from a background in R, I am glad that SAS has PROC IML to do things like that.

Blog Entry on Bin Observations using Custom Cut Points

https://blogs.sas.com/content/iml/2013/07/15/cut-pts-and-uneven-bins.html.

topic Regression discontinuity in Statistical Procedures

Regression discontinuity

Re: Regression discontinuity

Re: Regression discontinuity

Re: Regression discontinuity