A Robust Histogram

I wanted to create a robust histogram to display the response time of a web site. To make a histogram you need to create your own statgraph using the Graphic Template Language (GTL). This requires a lot of research to see what is needed to make it all happen. Below is an image of the end result.

I received some excellent assistance from Lelia at SAS technical support to add the percent sign (%) on the Y axis. This was accomplished by creating a custom format then assigning it to tickvalueformat= option inside linearopts=().

You will see within the proc template code that I am using a vertical reference line to denote the 2.5 second boundary. Each of the bars cover an area between 0.5 above and below the center point. For example, the value 2 has a range of 1.5 to 2.5.

A bunch of summary statistics are handled in GTL by using the eval() function. Below the histogram is a fringeplot that shows the activity of hits by time period. A normal distribution curve was added using the densityplot syntax. Under the fringeplot is a horizontal boxplot that shows the spread of the data in a different fashion than the histogram.

The frequency procedure was used to obtain the percentages for each bar in the display. Here is the SAS data set that was created from the proc freq call.

The final piece I wanted was to display the actual bin values above the bars in the histogram. There are no options to do this using GTL but SAS does support the inclusion of an annotated (sganno) data set. With help from SAS tech support I was able to accomplish that last wish list item resulting in what I call a very robust histogram.

I used a random function (call streaminit with rand()) to create simulated data and suppressed values that exceeded 1.75. The rounded duration value was used with proc freq to drive the annoated data set to populate the values above the bars and the reference line.

The proc template code is very much reusable and is used by proc sgrender to create the output. You will notice that I am writing to the WORK folder via ODS HTML5.

proc format;
   picture mypct (round)
   low - high='009%';
run;

proc template;
  define statgraph distribution;
    dynamic
      VAR
      VARLABEL
      TITLE
      NORMAL
      fmt
    ;
    mvar pct2secs;

    begingraph;
      entrytitle TITLE;
      layout lattice /
        columns         = 1
        rows            = 2
        rowgutter       = 2px
        rowweights      = (.9 .1)
        columndatarange = union
      ;

        columnaxes;
          columnaxis /
            label      = VARLABEL
            display    = (ticks tickvalues label)
            type       = linear
          ;
        endcolumnaxes;    

        layout overlay /
          yaxisopts = (
            offsetmin   = .035
            offsetmax   = .065
            griddisplay = on
            linearopts = (tickvalueformat = mypct4.)
          )

          xaxisopts = (label = "Duration in Seconds");
          referenceline x = 2.5 /
            lineattrs          = (color = red pattern = dash) 
            curvelabel         = pct2secs
            curvelabellocation = outside
          ;

          layout gridded /
            columns   = 2
            border    = true
            autoalign = (topleft topright)
          ;
            entry halign = left "Nobs";
            entry halign = right eval(strip(put(n(VAR), comma12.)));
            entry halign = left "Min";
            entry halign = right eval(strip(putn(min(VAR), '12.3')));
            entry halign = left "Q1";
            entry halign = right eval(strip(putn(q1(VAR), '12.3')));
            entry halign = left "Median";
            entry halign = right eval(strip(putn(median(VAR), '12.3')));
            entry halign = left "Mean";
            entry halign = right eval(strip(putn(mean(VAR), '12.3')));
            entry halign = left "Q3";
            entry halign = right eval(strip(putn(q3(VAR), '12.3')));
            entry halign = left "Max";
            entry halign = right eval(strip(putn(max(VAR), '12.3')));
            entry halign = left "StdDev";
            entry halign = right eval(strip(putn(stddev(VAR), '12.3')));
            entry halign = left "IQR";
            entry halign = right eval(strip(putn(qrange(VAR), '12.3')));
          endlayout;
 
          histogram VAR /
            scale     = percent
            binwidth  = 1
            dataskin  = gloss
          ;
          annotate / id='label';
 
          if (exists(NORMAL))
            densityplot VAR /
              normal()
              name        = 'norm'
              legendlabel = 'Normal'
            ;
          endif;

          fringeplot VAR / datatransparency = .7;

          discretelegend "norm" "kern" /
            location  = inside
            across    = 1
            autoalign = (topright topleft)
            opaque    = true
          ;
        endlayout;

         boxplot y = VAR / orient = horizontal;
     endlayout;
   endgraph;
  end;
run;

 
data hitsinseconds;
  call streaminit(123);       /* set random number seed */
  do _n_ = 1 to 2000;
    duration = round(7 * rand("Uniform"), .001);
    if duration > 1.75 then do;
      if rand("Uniform") > .05 then continue;
    end;
    Seconds = round(duration, 1);
    output;
  end;
run;

proc freq data = hitsinseconds noprint;
  table seconds / out = hitfreq outcum;
run;

data sganno;
  retain id 'label';
  set hitfreq;
  drawspace = 'datavalue';
  function  = 'text';
  x1        = seconds;
  y1        = percent;
  label     = cats(put(percent, 7.2), '%');
  textcolor = 'black';
  textsize  = 8;
  anchor    = 'bottom';
  if seconds = 2 then call symputx('pct2secs', cats(put(cum_pct, 8.), '%'));
run;

ods listing close;
ods graphics on / width = 640px height = 480px;
ods html5 
  path = "%sysfunc(pathname(work))" 
  file = "histogram.html" 
  style = seaside
;

  title;
  proc sgrender
    data     = hitsinseconds
    template = distribution
    sganno   = sganno
  ;

    dynamic
      var      = "duration"
      varlabel = "Time in Seconds"
      normal   = "yes"
      title    = "&pct2secs of hits were under 2.5 seconds"
    ;
    
    format duration 8.1;
  run;
ods html close; 

When a problem comes along, you must whip it!

While I have used the SAS FIND() function frequently, that is not the case for the similarly named FINDW() (find word) function. Taking advice from the 1980s band Devo, a problem came along and I was ready to whip it, whip it good!

A pangram is a unique sentence that contains all the leters of the alphabet at least once. The name comes from the Greek root words pan, meaning "all," and gram, meaning "something written or recorded". The best-known English pangram is "The quick brown fox jumps over the lazy dog" and that is what I will use to test the issue.

The FIND() function returns the starting position of the substring of characters so it can find both Quick and Qui. It is important to note that the 3rd parameter in FIND that uses an 'i' modifier to ignore the case of the characters - upper and lower are treated the same.

Now that we know how the FIND() function works, you would think that FINDW() would do the same - that is the 3rd parameter just needs a 'i' to ignore the case and it will work on full words not a substring. That is not the case for FINDW(), see the differnce between a_findw and a_findw2 that can find the word 'Quick'.

There are times I want an exact match vs a substring match and now I can see the differences - problem whiped - err solved.

data test; 
  str = "The quick brown fox jumps over the lazy dog";
  a_find = find(str, "Quick", 'i');          /* found at position 5 */
  a_findw = findw(str, "Quick", 'i');        /* not found */
  a_findw2 = findw(str, "Quick", ' ', 'i');  /* found at position 5 */
 
  b_find = find(str, 'Qui', 'i');            /* found at position 5 */
  b_findw2 = findw(str, 'Qui', ' ', 'i');    /* not found - no word named Qui */
run;

Should you think this post has gone to the dogs, please consider just as in SAS there are many ways to solve a problem there too are alternate ways to whip it, whippet good!

If only I had an Array

Modeling data sets often have binary flag variable to indicate if a condition is true or false. Sometimes those indicators need to be collapsed or recoded into a single value based on conditions. See the below code for one technique to handle this.

       if s_del30postscratch_ind  = 1 then curr_delinquency = "D30";
  else if s_del60postscratch_ind  = 1 then curr_delinquency = "D60";
  else if s_del90postscratch_ind  = 1 then curr_delinquency = "D90";
  else if s_del120postscratch_ind = 1 then curr_delinquency = "D120";
  else if s_del150postscratch_ind = 1 then curr_delinquency = "D150";
  else if s_del180postscratch_ind = 1 then curr_delinquency = "D180+";
  else curr_delinquency = "Current";

An alternative way to do the same thing in SAS using two arrays is as follows:

  array avars s_del30postscratch_ind s_del60postscratch_ind s_del90postscratch_ind 
              s_del120postscratch_ind s_del180postscratch_ind;
  array anames[5] $8 _temporary_ ('D30', 'D60', 'D90', 'D120', 'D180+');
  
  do _n_ = 1 to dim(avars);
    if avars[_n_] = 1 then curr_delinquency = anames[_n_];
  end;
  if sum(of avars[*]) = 0 then curr_delinquency = 'Current';

Here is the entire array technique complete with some sample data. The temporary array has the same number of elements so the relative offset matches and makes this a better, more eloquent technique that can be expanded to easily support more if statements if that is what you encounter. Notice the use of the double dash (--) to specify the start and stop columns to process that can be used as a shortcut. Just a different way to do the same thing.

data x;
  length curr_delinquency $8;
  input s_del30postscratch_ind s_del60postscratch_ind s_del90postscratch_ind 
        s_del120postscratch_ind s_del180postscratch_ind;
  array avars s_del30postscratch_ind -- s_del180postscratch_ind;
  array anames[5] $8 _temporary_ ('D30', 'D60', 'D90', 'D120', 'D180+');
  
  do _n_ = 1 to dim(avars);
    if avars[_n_] = 1 then curr_delinquency = anames[_n_];
  end;
  if sum(of avars[*]) = 0 then curr_delinquency = 'Current';
  datalines;
  1 0 0 0 0
  0 1 0 0 0
  0 0 1 0 0
  0 0 0 1 0
  0 0 0 0 1
  1 1 1 1 1 
  0 0 0 0 0
  ;
run;