1月 042011
 
The book "Bayesian Computation with R" by Jim Albert is an easy to read entry level book on applied Bayesian Statistics. While the book was written for R users, it is not difficult to translate the languages between R and SAS and I believe it is a good way to show Bayesian capability of SAS. In the next several months, I am going to translate all R code in the book into SAS. Readers are encouraged to buy this book to understand what's behind the code. The posts here will only spend minimum effects to explain the statistics underlying while most resource will still be denoted to SAS coding.

This post will cover Chapter 1.

We first follow section 1.2.2, using PROC IMPORT to read in TAB deliminated file, which corresponds to read.table(file, sep='\t', header=T)  in R. We also designated PDF as Output Destination.

/* Chapter 1 of Bayesian Computation with R */

%let folder=C:\Documents\SAS for Bayesian Compu with R;
%let datafolder=&folder\data;

libname data "&datafolder";
options missing='.' formchar = "|----|+|---+=|-/\<>*" errors=2 fullstimer;

/*@@@@@@ Section 1.2.2 @@@@@*/
/*--> Read Tab Deliminated Data into SAS */
proc import datafile="&datafolder/studentdata.txt" out=student dbms=dlm replace;
datarow=2; /* redundent with GETNAMES= statement */
guessingrows=2; /* Only use first 2 rows of data to guess the type of data */
delimiter='09'x; /* this is redudent if we specify DBMS=TAB in PROC IMPORT option */
getnames=YES; /* This is the same as 'header=True' in R's table.read function */
run;

ods pdf file="&folder/Chapter1.pdf";
/*--> To see Variable Names and print first row of this data
Use SPLIT="*" to specify the split character being "*", which controls
line breaks in column headings
*/
proc print data=student(obs=1) split="*"; run;

SAS output looks like:
Section 1.2.3, summarize frequency tables and use Barplot to visualize the counts.

PROC FREQ directly corresponds to table() function in R, but provides much richer functionality. PROC GBARLINE is used to answer what barplot() does in R. The LABEL= statement in SAS is a very handy tool for annotation purpose for PRINT or GRAPH.

PROC MEANS somehow corresponds to summary() function to obtain summary statistics for quantitative variables. You can sepecify MAXDEC= to keep desired number of decimals in print out.
Histogram can be obtained in SAS via either PROC UNIVARIATE or newly introduced PROC SGPLOT. PROC UNIVARIATE provides more control though. As shown below, you can specify desired mid-points while you can't do so in SGPLOT. On the other hand, SGPLOT is very convenient if you want to overlay density curve, either a normal fit or kernel one.


/*@@@@ section 1.2.3 @@@*/
/*--> To summarize and graph a single Batch */
proc freq data=student;
table Drink;
run;

/*--> Barplot on single variable */
title "Original idea, summarize and plot";
proc freq data=student noprint;
table Drink /out=t;
run;
goptions reset=all noborder;
proc gbarline data=t;
bar Drink /discrete space=4 sumvar=count;
run;quit;
title;
/*--> Actually, in SAS, it is better to directly use
PROC GBARLINE */
goptions reset=all noborder;
title "In SAS, PROC GBARLINE directly summarize";
proc gbarline data=student;
bar Drink /discrete space=3 ;
run;quit;
title;

data student;
set student;
hours_of_sleep=WakeUp-ToSleep;
/* Label can be useful for annotation purpose */
label hours_of_sleep="Hours Of Sleep";
run;

proc means data=student
/* Request same statistics as in the book */
min q1 median q3 max nmiss
/* MAXDEC= specifies keeping 2 decimals */
maxdec=2;
var hours_of_sleep;
run;

/*--> Histogram using PROC UNIVARIATE */
proc univariate data=student noprint;
var hours_of_sleep;
histogram /midpoints=2.5 to 12.5 by 1;
run;

/* new SGPLOT is a handy way to draw histogram and density */
proc sgplot data=student;
histogram hours_of_sleep/scale=count;
density hours_of_sleep/scale=count type=normal;
run;

Compare SAS outputs:





Boxplot to visualize distribution of  quantitative variables by some classification variable. Here, formula such as var1*var2 style corresponds to var1~var2 style in R.


/*@@@ section 1.2.4 @@@@*/
/*---> Compare Batches using Boxplot */
proc sort data=student out=studentsorted; by Gender; run;
proc boxplot data=studentsorted;
plot hours_of_sleep*Gender;
run;

proc means data=student
min q1 median q3 max nmiss
nway maxdec=2;
class Gender;
var Haircut;
run;

SAS output looks like:




R has built-in jitter function, however, we have to make our own in SAS. This verision doesn't apply Fuzzy yet, only for demo purpose.


%macro jitter(var, newname, data=last, factor=1, amount=);
/* follow the JITTER function in R, no fuzzy applied yet .
if amount is given, then use this value for disturbance
else if amount is 0, then use the range of &var for disturbance
else if amount is NULL, then use the smallest difference among
distinct values of &var for disturbance. if all values are
the same, then use the value obtained from range

if range of &var is 0, then use the lower range for disturbance
otherwise
*/
%let blank=%str( );
%if &data=' ' %then %let data=last;
%local fid;

data _null_;
fid=round(ranuni(0)*10000, 1);
call symput('fid', compress(fid));
run;
proc means data=&data noprint;
var &var;
output out=_util&fid
range(&var)=range
min(&var)=min
max(&var)=max;
run;
data _util&fid;
set _util&fid;
if range^=0 then z=range; else z=min;
if z=0 then z=1;
run;

%if %eval(&amount=&blank) %then %do;
proc sort data=&data.(keep=&var where=(&var^=.))
out=_xuti&fid nodupkey;
by &var;
run;
data _duti&fid;
set _xuti&fid nobs=ntotal end=eof;
array _x{2} _temporary_;
if ntotal=1 then do;
amount=&factor/50*abs(&var);
keep amount;
output;
stop;
end;
else do;
if _n_=1 then do;
_x[1]=&var; _x[2]=constant('BIG');
end;
else do;
_x[2]=min(_x[2], &var - _x[1]);
_x[1]=&var;
if eof then do;
amount=&factor/5*abs(_x[2]);
keep amount;
output;
end;
end;
end;
run;

%end;
%else %if %eval(&amount=0) %then %do;
data _duti&fid;
set _util&fid;
amount=&factor*z/50;
keep amount;
output;
run;
%end;
%else %do;
data _duti&fid;
amount=&amount;
keep amount;
output;
run;
%end;

proc sql noprint;
select name into :keepvars separated by ' '
from sashelp.vcolumn
where libname='WORK'
and memname=%upcase("&data")
and memtype="DATA"
;
quit;
data &data;
array _x{1} _temporary_;
if _n_=1 then do;
set _duti&fid;
_x[1]=amount;
end;
set &data;
&newname=&var + ranuni(0)*(2*_x[1])-_x[1];
label &newname="jitter(&var)";
keep &keepvars &newname;
run;
proc datasets library=work nolist;
delete _duti&fid _xuti&fid _util&fid;
run;quit;
%mend;


Now we can apply jitter function to the two variables studied in the book and check them out. For graphics, we use axis statement to define how we want the two axes to appear in print out, and use symbol statement to define the appearance of symbols for data. Here we ask for black circles, not connected (interpol=none).


%jitter(hours_of_sleep, xhos, data=student, factor=1, amount=);
%jitter(ToSleep, xts, data=student, factor=1, amount=);

goptions border reset=all;
axis1 label=("jitter(ToSleep)")
major=(height=2 number=5) minor=none;
axis2 label=(angle=90 "jitter(Hours of Sleep")
major=(height=2 number=5) minor=none;
symbol1 value=circle interpol=none color=black;
proc gplot data=student;
plot xhos*xts/haxis=axis1 vaxis=axis2;
run;quit;


In order to overlay a fitted regression line, we have multiple ways to do it in SAS, and the Statistical Plot procedures are particularly handy to generate this type of figures. Compare the code and corresponding figures (in the same order of LINEPRINTER, ODS GRAPHICS, Manually Drawn, SGPLOT). For manually drawn figures, since we ask for connected dots in order to obtain a line overlay on circles, we have to sort the data by X-axis variable to make the line as straight as possible. The manually drawn figure is also the one closest to the R figure in the book.



/* old school LINEPRINTER option*/
proc reg data=student lineprinter;
title "Line Printer Style";
model Hours_of_Sleep=ToSleep /noprint;
var xhos xts;
plot pred.*xts='X' xhos*xts/overlay symbol='o';
run;quit;
title;

/* Using ODS GRAPHICS */
ods select none; /* to suppress PROC REG output */
title "ODS Graphics";
ods graphics on;
proc reg data=student ;
model Hours_of_Sleep=ToSleep;
var xhos xts;
output out=student pred=p;
ods select FitPlot;
run;quit;
ods graphics off;
title;
ods select all;

/* Following standard R approach, tedious in SAS */
proc sort data=student out=studentsorted;
by ToSleep;
run;
goptions border reset=all;
axis1 label=("jitter(ToSleep)") order=(-2 to 6 by 2) major=(height=2 number=5) minor=none;
axis2 label=(angle=90 "jitter(Hours of Sleep") offset=(, 2 pct) major=(height=2 number=5) minor=none;
symbol1 value=circle interpol=none color=black;
symbol2 value=none interpol=line color=black;
proc gplot data=studentsorted;
plot xhos*xts p*xts/overlay haxis=axis1 vaxis=axis2;
run;quit;

/* Using build-in REGRESSION capability of GPLOT by specifying
INTERPOL=R<><0><> option in SYMBOL statement.
In the first <>, you identify the type of regression:
L=linear, Q=quadratic, C=cubic
In the second <>, you specify if intercept is omitted;
In the third <>, you specify type of CI:
CLM=CI of mean predicted value;
CLI=CI of individual points;
*/
goptions border reset=all;
axis1 label=("jitter(ToSleep)") order=(-2 to 6 by 2) major=(height=2 number=5) minor=none;
axis2 label=(angle=90 "jitter(Hours of Sleep") offset=(, 2 pct) major=(height=2 number=5) minor=none;
symbol1 value=circle interpol=rlclm95 color=black ci=blue co=blue;
proc gplot data=student;
plot xhos*xts/regeqn /* haxis=axis1 vaxis=axis2*/;
run;quit;

/* New SGPLOT has build in regression line capability: REG, SPLINE, LOESS */
proc sgplot data=student;
scatter x=xts y=xhos;
reg x=ToSleep y=Hours_of_Sleep;
run;




Now, to study the robustness of T-Statistics which relies on several assumptions, such as normality, homoskedasticity, etc. First, we need to define a "function" to calculate T-statistics like in the book.


/* section 1.3 Robustness of T-Statistics */
/* section 1.3.2 Write a function to compute T-Statistics */
%macro tstatistics(vars, dsn=last, outdsn=, class=);
%if &class='' %then %let classstmt=;
%else %let classstmt=class &class;

%let nvars=%sysfunc(count(&vars, ' '));

%let var1=%scan(&vars, 1, ' ');
%let var2=%scan(&vars, 2, ' ');
proc means data=&dsn noprint nway;
&classstmt;
var &vars;
output out=tdata(where=(_STAT_ in ('STD', 'MEAN', 'N')));
run;
data &outdsn;
set tdata; by &class _TYPE_;
retain m n mean1 mean2 std:;
select(compress(_STAT_));
when('N') do;
m=&var1;
n=&var2;
end;
when('MEAN') do;
mean1=&var1;
mean2=&var2;
end;
when('STD') do;
std1=&var1;
std2=&var2;
end;
otherwise;
end;
if last._TYPE_ then do;
sp=sqrt(((m-1)*std1**2 + (n-1)*std2**2)/(m+n-2));
t= (mean1-mean2)/(sp * sqrt(1/m + 1/n));
keep &class _TYPE_ m n std: mean: sp t;
output;
end;
run;
%mend;

Just like the "source(file)" command in R, in SAS, we have a counterpart called %include(or in abv. %inc). Suppose you have a SAS file called "tstatistics.sas" in some folder &folder, the following statement will read in the source code from this file. Since this is a SAS file, suffix ".sas" is not necessary.


filename BCR "&folder";
%inc BCR(tstatistics);

The following code pieces conduct the four simulate scenarios illustrated in the book and draw the last figure.

data test;
input x y;
cards;
1 5
4 4
3 7
6 6
5 10
;
run;

%tstatistics(x y, dsn=test, outdsn=tdata2, class=);

/* section 1.3.3 Monte Carlo study on the Robustness of T-Statistics */
%let alpha=0.1;
%let m=10;
%let n=10;
%let Niter=10000;
data test;
retain seed1 99787 seed2 76568;
do iter=1 to &Niter;
do j=1 to max(&n, &m);
if j<=&m then call rannor(seed1, x); else x=.;
if j<=&n then call rannor(seed2, y); else y=.;
keep iter x y;
output;
end;
end;
run;

%tstatistics(x y, dsn=test, outdsn=tdata2, class=iter);

data _null_;
set tdata2 end=eof;
retain n_reject 0;
if abs(t)>quantile('T', 1-&alpha/2, n+m-2) then n_reject+1;
if eof then do;
call symput('n_reject', n_reject/_n_);
end;
run;
%put &n_reject;


/* section 1.3.4 Study the robustness of T-Statistics */

%let alpha=0.1;
%let m=10;
%let n=10;
%let Niter=10000;
data test;
retain seed1 987687 seed2 76568;
array x[4];
array y[4];
do iter=1 to &Niter;
do j=1 to max(&n, &m);
do k=1 to 4;
select (k);
when(1) do;
if j<=&m then call rannor(seed1, x[k]); else x[k]=.;
if j<=&n then call rannor(seed2, y[k]); else y[k]=.;
end;
when(2) do;
if j<=&m then call rannor(seed1, x[k]); else x[k]=.;
if j<=&n then call rannor(seed2, y[k]); else y[k]=.;
y[k]=y[k]*10;
end;
when(3) do;
if j<=&m then x[k]=rand('T', 4); else x[k]=.;
if j<=&n then y[k]=rand('T', 4); else y[k]=.;
end;
otherwise do;
if j<=&m then call rannor(seed1, x[k]); else x[k]=.;
if j<=&n then call ranexp(seed2, y[k]); else y[k]=.;
x[k]=10+x[k]*2; y[k]=y[k]/0.1;
end;
end;
end;
keep iter x1-x4 y1-y4;
output;
end;
end;
run;

%tstatistics(x1 y1, dsn=test, outdsn=tdata1, class=iter);

%tstatistics(x2 y2, dsn=test, outdsn=tdata2, class=iter);

%tstatistics(x3 y3, dsn=test, outdsn=tdata3, class=iter);

%tstatistics(x4 y4, dsn=test, outdsn=tdata4, class=iter);

data _null_;
n_reject=0;
do until (eof1);
set tdata1 end=eof1 nobs=n1;
retain n_reject 0;
if abs(t)>quantile('T', 1-&alpha/2, n+m-2) then n_reject+1;
if eof1 then do;
*call symput('n_reject', n_reject/_n_);
p_reject=n_reject/n1;
put "NOTE>> Prob(Rejection)=" p_reject 8.4;
end;
end;
n_reject=0;
do until (eof2);
set tdata2 end=eof2 nobs=n2;
retain n_reject 0;
if abs(t)>quantile('T', 1-&alpha/2, n+m-2) then n_reject+1;
if eof2 then do;
*call symput('n_reject', n_reject/_n_);
p_reject=n_reject/n2;
put "NOTE>> Prob(Rejection)=" p_reject 8.4;
end;
end;

do until (eof3);
set tdata3 end=eof3 nobs=n3;
retain n_reject 0;
if abs(t)>quantile('T', 1-&alpha/2, n+m-2) then n_reject+1;
if eof3 then do;
*call symput('n_reject', n_reject/_n_);
p_reject=n_reject/n3;
put "NOTE>> Prob(Rejection)=" p_reject 8.4;
end;
end;

do until (eof4);
set tdata4 end=eof4 nobs=n4;
retain n_reject 0;
if abs(t)>quantile('T', 1-&alpha/2, n+m-2) then n_reject+1;
if eof4 then do;
*call symput('n_reject', n_reject/_n_);
p_reject=n_reject/n4;
put "NOTE>> Prob(Rejection)=" p_reject 8.4;
end;
end;
run;

/* draw the overlay density curves of empirical T-statistics and T-distribution */
proc sort data=tdata2;
by t;
run;
data tdata2;
set tdata2;
dt=pdf('T', t, 18);
run;

ods select none;
ods output Controls=Controls;
ods output UnivariateStatistics=UniStat;
proc kde data=tdata2 ;
univar t /out=density method=snr unistats;
run;
ods select all;

data density;
set density;
dt=pdf('T', value, 18);
run;

data _null_;
set UniStat;
if Descr='Bandwidth' then call symput ('bw', compress(round(t, 0.0001)));
run;

goptions reset=all border;

title "Comparing Empirical and Theoretical Densities";
legend label=none position=(top right inside) mode=share;
axis1 label=("N=&Niter Bandwidth=&bw")
order=(-4 to 8 by 2) offset=(1,1)
major=(height=2) minor=none;
axis2 label=(angle=90 "Density")
order=(0 to 0.4 by 0.1) offset=(0, 0.1)
major=(height=2) minor=none;
symbol1 interpol=join color=black value=none width=3;
symbol2 interpol=join color=grey value=none width=1;
proc gplot data=density;
plot density*value dt*value/overlay legend=legend
haxis=axis1 vaxis=axis2 ;
label dt='t(18)' density='Exact';
run;quit;

ods pdf close;

Key Points Summary: 

0. We can use FORMCHAR option to eliminate  weird characters

1. We can use PROC IMPORT to import deliminated data and it provided flexible options to control the output;

2. We can use PROC FREQ to summarize categorical data

3. We can use PROC MEANS and PROC UNIVARIATE to generate descriptive statistics for numerical data

4. We can study the dispersion of numerical variable by categorical variable using BOXPLOT

5. We provided a JITTER function for better graphical presentation of heavily overlapped data

6. We showed that there are multiple ways to visualize scatter plots together with fitted regression lines:

  • 6.1 LINEPRINTER in PROC REG 
  • 6.2 Using PROC REG to obtain regression line and overlay it on the scatter plot 
  • 6.3 Using ODS Graphics in PROC REG 
  • 6.4 Using INTERPOL=R<><><> option in SYMBOL statement 
  • 6.5 Using PROC SGPLOT 
7. We demonstrated how to conduct robust T-test in SAS following the code in the book.
Bayesian Computation with R (Use R)
 Posted by at 8:18 下午

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