how do I identify points on the curve?: where is the slope=0?

[drshashlik]

Hi all,

I have time series data of daily observations for an event.  There is one observation per day, and it is always >=0.

I am using proc loess ad/or proc sgplot with a penalised b spline to fit a smooth curve.

I want to identify the points where the curve turns.  Ideally, I need to see where the slope=0 and where the slope becomes negative.

Any help greatly appreciated!

thank you.

[Ksharp]

Check the current point and previous point, next point 's slope .

If 

(Yt-Yt-1)/(t- t-1)    and  (Yt+1-Yt)/(t+1 - t)

have different sign (+ or -) , then t is the point which have 0 slope .

@Rick_SAS wrote a blog about it before.

[Rick_SAS]

You can use finite-difference approximations to estimate the slope of a nonparametric regression model. See the discussion and example in the article "Compute derivatives for nonparametric regression models."

[PGStats]

Here is an example using proc loess and proc expand to process consecutive time series observations:

proc loess data=sashelp.ENSO plots=none;
   model Pressure=Month;
   score ;
   ods output ScoreResults=sr;
run;

proc expand data=sr out=srd;
convert p_pressure=y / transformout=(dif sign movsum 2 = 0 + 1 lead);
run;

/* Show the locations of the slope changes (where y = 1) on a graph */
data graph;
set srd;
if y then pp_pressure = p_pressure;
run;

title "Slope changes";
proc sgplot data=graph noautolegend;
scatter x=month y=pressure;
series x=month y=p_pressure;
scatter x=month y=pp_pressure / markerattrs=(symbol=circlefilled color=red);
run;

[drshashlik]

Thank you, i think this looks exactly like what I want. BUT, I don't have access to proc expand. (I'm using EG, but even though proc expand comes up in the options, i get the error message that the procedure was not found.
Is there a workaround for this problem?
thanks again!

[Rick_SAS]

The link in my response requires only SAS/STAT and the DATA step. Check out the link.

[drshashlik]

Thank you Rick_SAS. I am working through your method, and get this error from this step:
/* score the model at each time point */
proc plm restore=SplineModel noprint;
score data=ScoreData out=ScoreOut; /* Predicted column contains f(x+h) and f(x-h) */
run;
WARNING: At least one variable used in the model is not present or has incompatible type in the WORK.SCOREDATA score data set. All computed score variables are set to missing in WORK.SCOREOUT.
I can't figure out which step has caused this issue.

[Rick_SAS]

Sorry for the confusion. All I meant is that you don't need to use PROC EXPAND to compute the locations where the derivative of the smoother is zero. I intended for you to use PGStats program, but use a DATA step to compute the derivative. Like this:

data Have;
set Sashelp.Enso;
x = Month;
y = Pressure;
run;

/* Put min and max into macro variables */
proc sql noprint;
  select min(x), max(x) into :min_x, :max_x 
  from Have;
quit;

/* compute derivatives at specified points in interval [min(x), max(x)] */
data ScoreData;
do x = &min_x to &max_x by 0.05;   /* choose the step size wisely */
   output;
end;
run;

ods select none;
proc loess data=Have plots=none;
    model y = x;
    score data=ScoreData;
    ods output ScoreResults=ScoreOut;
run;
ods select all;

/* compute first derivative by using finite difference formula.
  Output locations where the derivative is approximately zero  */
data Deriv0;
set ScoreOut;
Slope = dif(p_y) / dif(x);  /* [f(x) - f(x-dx)] / dx */
SlopePrev = lag(Slope);
if n(SlopePrev) AND sign(SlopePrev) ^= sign(Slope) then output; 
run;

data Combine;
merge Have
      ScoreOut(rename=(x=t p_y=p_t))
      Deriv0(rename=(x=xx p_y=yy));
run;

title "Loess Smoother";
title2 "Values with Zero Derivatives Are Marked";
proc sgplot data=Combine noautolegend;
   scatter x=x y=y;
   series x=t y=P_t / lineattrs=GraphData2;
   scatter x=xx y=yy / markerattrs=(symbol=circlefilled color=red);
   yaxis grid; 
run;

[Rick_SAS]

For more on this topic, including a complete example, see 

"Find points where a regression curve has zero slope."