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

  EXAMPLE 1, CHAPTER 4

  Modified program including use of PROC INSIGHT to make 
  scatterplot matrices.

  Using SAS to obtain sample mean vectors, sample covariance
  matrices, and sample correlation matrices.

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

options ls=80 ps=59 nodate; run;

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

  The data are not in the correct from for use with the SAS procedures
  CORR and DISCRIM we use below.  These procedures require that the
  data be in the form of one record (line) per experimental unit.
  The data in the file dental.dat are in the form of one record per
  observation (so that each child has 4 data records).  

  In particular, the data set looks like

  1 1 8 21 0
  2 1 10 20 0
  3 1 12 21.5 0
  4 1 14 23 0
  5 2 8 21 0
      .
      .
      .

  column 1    observation number
  column 2    child id number
  column 3    age
  column 4    response (distance)
  column 5    gender indicator (0=girl, 1=boy)

  We thus create a new data set such that each record in the data
  set represents all 4 observations on each child plus gender
  identifier.  To do this, we use some data manipulation features
  of the SAS data step.  The second data step does this.

  We redefine the values of AGE so that we may use AGE as an "index"
  in creating the new data set DENT2. The DATA step that creates
  DENT2 demonstrates one way (using the notion of an ARRAY) to
  transform a data set in the form of one observation per record
  (the original form) into a data set in the form of one record per
  individual.  The data must be sorted prior to this operation; we
  invoke PROC SORT for this purpose.

  In the new data set, the observations at ages 8, 10, 12, and 14
  are placed in variables AGE1, AGE2, AGE3, and AGE4, respectively.

  We use PROC PRINT to print out the first 5 records (so data for
  the first 5 children, all girls) using the OBS= feature of the 
  DATA= option.

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

data dent1; 
	infile 'dental.dat';
  	input obsno child age distance gender;
run;
  
data dent1; set dent1;
  if age=8 then age=1;
  if age=10 then age=2;
  if age=12 then age=3;
  if age=14 then age=4;
  drop obsno;
run;

proc sort data=dent1;
  by gender child;
run;

data dent2(keep=age1-age4 gender child);
  array aa{4} age1-age4;
  do age=1 to 4;
  set dent1;
  by gender child;
  aa{age}=distance;
  if last.child then return;
end;
run;

/*  Alternatively, replace the above code with the following using 
    proc transpose (thanks to Laine Elliott for noting this):  */

/*

data dent1; infile 'dental.dat';
  input obsno child age distance gender;
run;

proc transpose data=dent1 out=dent2 prefix=age;
   by gender child notsorted;
   var distance; 
run;

*/

title "TRANSFORMED DATA -- 1 RECORD/INDIVIDUAL";
proc print data=dent2(obs=5); run;

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

  Here, we use PROC CORR to obtain the sample means at each
  age (the means of the variables AGE1,...,AGE4 in DENT2 and to
  calculate the sample covariance matrix and corresponding sample
  correlation matrix separately for each group (girls and boys).
  The COV option in the PROC CORR statement asks for the sample
  covariance to be printed; without it, only the sample correlation
  matrix would appear in the output.  

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

proc sort data=dent2; by gender; run;

title "SAMPLE COVARIANCE AND CORRELATION MATRICES BY GENDER";
proc corr data=dent2 cov;
 by gender; var age1 age2 age3 age4; 
run;

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

  We now obtain the "centered" and "scaled" values 
  that may be used for plotting scatterplot matrices such as that
  in Figure 3.  Here, we call PROC MEANS to calculate the sample
  mean (MAGE1,...,MAGE4) and standard deviation (SDAGE1,...,SDAGE4)
  for each of the variables AGE1,...,AGE4 for each gender.  These 
  are output to the data set DENTSTATS, which has two records, one 
  for each gender (see the output).  We then MERGE this data set 
  with DENT2 BY GENDER, which has the effect of matching up the 
  appropriate gender mean and SD to each child.  We print out the
  first three records of the resulting data set to illustrate.
  We use the NOPRINT option with PROC MEANS to suppress printing of
  its output.

  The variables CSAGE1,...,CSAGE4 contain the centered/scaled values.

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

proc sort data=dent2; by gender child; run;

proc means data=dent2 mean std noprint; by gender;
  var age1 age2 age3 age4;
  output out=dentstats mean=mage1 mage2 mage3 mage4
         std=sdage1 sdage2 sdage3 sdage4;
run;

title "SAMPLE MEANS AND SDS BY GENDER FROM PROC MEANS";
proc print data=dentstats; run;

data dentstats; merge dentstats dent2; by gender;
  csage1=(age1-mage1)/sdage1;
  csage2=(age2-mage2)/sdage2;
  csage3=(age3-mage3)/sdage3;
  csage4=(age4-mage4)/sdage4;
run;

title "INDIVIDUAL DATA MERGED WITH MEANS AND SDS BY GENDER";
proc print data=dentstats(obs=3); run;

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

  The following code is an addition to that at the end of Chapter
  4 of the notes and was contributed by Xiaoyi Gao.

  Here, we first keep in the data set DENTSTATS only the information
  needed to make scatterplot matrices.  SAS PROC INSIGHT is then 
  called to produce the scatterplot matrices.

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

data dentstats;
	set dentstats;
	keep gender csage1 csage2 csage3 csage4;
run;

proc print; run;

proc insight data=dentstats;
	by gender;
	scatter csage1 csage2 csage3 csage4 * csage1 csage2 csage3 csage4;
	window 0 0 50 50;
run;
	
/*******************************************************************

  One straightforward way to have SAS calculate the pooled sample
  covariance matrix and the corresponding estimated correlation matrix
  is using PROC DISCRIM.  This procedure is focused on so-called
  discriminant analysis, which is discussed in a standard text on
  general multivariate analysis.  The data are considered as
  in the form of vectors; here, the elements of a data vector are
  denoted as AGE1,...,AGE4.  

  Here, we only use PROC DISCRIM for its facility to print out the 
  sample covariance matrix and correlation matrix "automatically," 
  and disregard other portions of the output.

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

proc discrim pcov pcorr data=dent2;
  class gender;
  var age1 age2 age3 age4;
run;

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

  Although it is a bit cumbersome, we may use some DATA step
  manipulations and PROC CORR to obtain the values of the autocorrelation
  function  for each gender.  We first drop variables
  no longer needed from the data set DENTSTATS.

  We create then three data sets, LAG1, LAG2, and LAG3, and describe 
  LAG1 here; the other two are similar.  We create two new variables, 
  PAIR1 and PAIR2.  For LAG1, PAIR1 and PAIR2 are the two values in (5.43) 
  for u=1. As there are 4 ages, each child has 3 such pairs.  The output 
  of PROC PRINT for LAG1 shows this for the first 2 children.
  We then sort the data by gender and call PROC CORR to find the
  sample correlation between the two variables for each gender.
  
  The same principle is used to obtain the correlation by gender for
  lags 2 and 3 [u=2,3].

  There are other, more sophisticated ways to obtain the values
  of the autocorrelation function; however, for longitudinal data sets
  where the number of time points is small, the "manual" approach
  we have demonstrated here is easy to implement and understand.  

  PAIR1 versus PAIR2 may be plotted for each lag to obtain visual 
  presentation of the results as in Figure 6.

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

data dentstats; set dentstats;
  drop age1-age4 mage1-mage4 sdage1-sdage4;
run;

data lag1; set dentstats;
  by child;
  pair1=csage1; pair2=csage2; output;
  pair1=csage2; pair2=csage3; output;
  pair1=csage3; pair2=csage4; output;
  if last.child then return;
  drop csage1-csage4;
run;

title "AUTOCORRELATION FUNCTION AT LAG 1";
proc print data=lag1(obs=6); run;
proc sort data=lag1; by gender;

proc corr data=lag1; by gender; 
  var pair1 pair2; 
run;

data lag2; set dentstats;
  by child;
  pair1=csage1; pair2=csage3; output;
  pair1=csage2; pair2=csage4; output;
  if last.child then return;
  drop csage1-csage4;
run;

title "AUTOCORRELATION FUNCTION AT LAG 2";
proc print data=lag2(obs=6); run;
proc sort data=lag2; by gender;

proc corr data=lag2; by gender; 
  var pair1 pair2; 
run;

data lag3; set dentstats;
  by child;
  pair1=csage1; pair2=csage4; output;
  if last.child then return;
  drop csage1-csage4;
run;

title "AUTOCORRELATION FUNCTION AT LAG 3";
proc print data=lag3(obs=6); run;
proc sort data=lag3; by gender;

proc corr data=lag3; by gender; 
  var pair1 pair2; 
run;