topic Re: get a value after minimizing sum of squares in Mathematical Optimization, Discrete-Event Simulation, and OR

get a value after minimizing sum of squares

Decay2020 — Thu, 16 Sep 2021 12:03:04 GMT

data have1;

input bucket$ probability ;
cards;
first 0.0025
second 0.37
third 0.53
fourth 0.89
;
run;

data have2;

input bucket$ z;
cards;
first -2.81
second -0.60
third -0.15
fourth 0.69

;
run;

Hi Everyone,

I have 2 data sets as above. I want to calculate a value(v) as

v = cdf('normal', z+c)

where z = z-value from table have2

c = constant which we will start with 1 and continuously changing it to get the minimum sum of squares difference of V and probability( from table have1).

We are interested in getting the value of C (initially equals 1) such that (V - probability)^2 is minimised.

Re: get a value after minimizing sum of squares

Ksharp — Thu, 16 Sep 2021 13:32:07 GMT

If you have SAS/OR ,could try the following code . or calling @RobPratt

Or if you have SAS/IML ,could try many optimize function like CALL NLPNRA () ,CALL NLPLM() .

@Rick_SAS wrote may blogs about it.

data have1;
input bucket$  probability ;
cards;
first  0.0025
second  0.37
third  0.53
fourth  0.89
;
run;

 

data have2;
input bucket$  z;
cards;
first -2.81
second -0.60
third -0.15
fourth 0.69

;
run;

proc optmodel;
set <str> B;
num p{B} ;
num z{B};
read data have1 into B=[bucket] p=probability;
read data have2 into B=[bucket] z=z;

var c ;

min min=sum{i in B} (cdf('normal', z[i]+c)-p[i])**2;
solve ;

print c.sol;
quit;

Re: get a value after minimizing sum of squares

Decay2020 — Thu, 16 Sep 2021 13:49:25 GMT

Hi, Thank you for your quick response. I don't have the mentioned components. Can we use SAS/STAT in this. Or is there any other other way without using SAS/OR and SAS/IML. Thanks.

Re: get a value after minimizing sum of squares

RobPratt — Thu, 16 Sep 2021 16:04:32 GMT

Looks correct to me. I have only two suggestions.

1. Change the second READ DATA statement as follows:

read data have2 into [bucket] z;

The index set B has already been populated from the previous READ DATA statement, and z=z is redundant.

2. Use the INIT option to initialize c, as requested by the user:

   var c init 1;

Re: get a value after minimizing sum of squares

Decay2020 — Fri, 17 Sep 2021 04:15:51 GMT

Hi RobPratt,
Can we do this without using SAS/OR and SAS/IML? I don't have the required components as of now.
Can we use SAS/STAT in any way for this?

Re: get a value after minimizing sum of squares

Ksharp — Fri, 17 Sep 2021 11:40:47 GMT

OK. Here is. The same result with SAS/OR .

data have1;
input bucket$  probability ;
cards;
first  0.0025
second  0.37
third  0.53
fourth  0.89
;
run;
proc sort data=have1;by bucket;run;

data have2;
input bucket$  z;
cards;
first -2.81
second -0.60
third -0.15
fourth 0.69

;
run;
proc sort data=have2;by bucket;run;

data want;
 merge have1 have2;
 by bucket;
run;

proc nlin data=want;
parms c 1;
mean=cdf('normal', z+c);

model probability=mean;
run;