Find the global optimization for non-linear model (like Excel Solver)

[lienbb2]

Hi everybody!

I have a dataset as attached. The problem is find parameter a, b to minimize weighted error.

I used Excel Solver as illustrated and it worked like a charm. But when I wanted to use PROC HPNLMOD in SAS like below, it stopped at a point in which the error value is very far from the Excel's result. I don't know how to solve the most optimal value from PROC HPNLMOD.

PROC HPNLMOD DATA=TEMP01;

PARAMETERS A=0 B=0 LAMBDA=0;

PRED=EXP(A+B*RANKING);

LL=WEIGHT*ABS(PRED-TARGET);

MODEL Y ~ GENERAL(-LL);

ODS OUTPUT PARAMETERESTIMATES=TEMP_PARAM(KEEP=ESTIMATE);

RUN;

[Rick_SAS · Accepted solution]

Your syntax has a few errors. You should always check the log to see what errors and warnings are present.

With such a small data set, you can use NLMIXED, which performs MLE estiamation. I think the following code is self-explanatory, but I would be happy to clarify any steps that might be confusing:

data Temp01;
input Pct Ranking	ABR Target;
Weight = Pct / 100;
Y = 0;
datalines;
5.74	1	-7.080829537	0.01
7.32	2	-6.224511583	0.04
8.01	3	-5.368193629	0.07
11.15	4	-4.511875675	0.06
13.57	5	-3.655557721	0.10
13.43	6	-2.799239766	0.15
12.69	7	-1.942921812	0.27
9.34	8	-1.086603858	0.48
6.68	9	-0.230285904	1.02
4.32	10	0.62603205	2.10
2.86	11	1.482350004	4.59
1.74	12	2.338667959	8.87
1.14	13	3.194985913	18.40
2.01	14	4.051303867	57.47
run;

/* fit the model to the data */
PROC NLMIXED DATA=TEMP01;
   PARAMETERS A=0 B=1;
   PRED=EXP(A+B*RANKING);
   LL=WEIGHT*ABS(PRED-TARGET);
   MODEL Y ~ GENERAL(-LL);
   ODS OUTPUT PARAMETERESTIMATES=TEMP_PARAM(KEEP=ESTIMATE);
RUN;

proc print data=Temp_Param; run;

/* visualize the fit */
data Pred;
set Temp01;
eta = -7.5314 + 0.8273 * Ranking;
Pred = exp(eta);
run;

proc sgplot data=Pred;
   scatter x=Ranking y=Target;
   series x=Ranking y=Pred;
   xaxis grid integer;
   yaxis grid;
run;

[lienbb2]

Thank you very much it worked miracles.

But when I checked the result, I found out that sum of weight(i)*target(i) didn't equal to sum of weight(i)*target_new(i), which I need for my problem. How can I add such a constraint in the code?

Moreover, I still wonder what is the difference between PROC HPNLMOD and NLMIXED that result the situation I encountered? Is there a specific method HPNLMOD use and another for NLMIXED.

Thank you again for your so helpful reply.

[Rick_SAS]

> Moreover, I still wonder what is the difference between PROC HPNLMOD and NLMIXED that result the situation I encountered? Is there a specific method HPNLMOD use and another for NLMIXED.

Different procedures have different default options and methods (see the doc), but you could use HPNLMOD if you prefer. Take my example and replace "NLMIXED" with "HPNLMOD":

PROC HPNLMOD DATA=TEMP01;
PARAMETERS A=0 B=1;
PRED=EXP(A+B*RANKING);
LL=WEIGHT*ABS(PRED-TARGET);
MODEL Y ~ GENERAL(-LL);
ODS OUTPUT PARAMETERESTIMATES=TEMP_PARAM(KEEP=ESTIMATE);
RUN;

proc print data=Temp_Param; run;

/* visualize the fit */
data Pred;
set Temp01;
eta = -9.9997 + 1.0036 * Ranking;
Pred = exp(eta);
run;

proc sgplot data=Pred;
   scatter x=Ranking y=Target;
   series x=Ranking y=Pred;
   xaxis grid integer;
   yaxis grid;
run;

I am not sure what target_new(i) means, but perhaps it means the predicted values of the model. There is no reason to expect that the sum(weight[i]*Y[i]) is equal to the sum(weight[i]*Pred[i]). You are minimizing sum(weight[i]*abs(Y[i]-Pred[i])), which does not require that the sum of weights be equal. 

[lienbb2]

Thank you for your great help ^^