topic Re: exponential function error in SAS Programming

exponential function error

joon1 — Thu, 04 Feb 2021 02:48:05 GMT

Dear Madam/Sir,

I construct "r1" variable using financial data and calculate "pbp" with exponential function.

r1=-1.32-0.407 *size + 6.03*TLTA - 1.43*WCTA + 0.0757*CLCA - 2.37*NITA - 1.83*FUTL + 0.285*INTWO - 1.72*OENEG - 0.521*CHIN;
pbp=1/(1+exp(-r1));

However, I have the following error message and many "pbp" value generates missing values.

NOTE: Invalid argument to function EXP(1077.0290778) at line 226 column 10.
NOTE: Invalid argument to function EXP(730.03261995) at line 226 column 10.
NOTE: Invalid argument to function EXP(2948.7729907) at line 226 column 10.
NOTE: Invalid argument to function EXP(1961.5518226) at line 226 column 10.
NOTE: Invalid argument to function EXP(755.8640734) at line 226 column 10.
NOTE: Invalid argument to function EXP(1152.1594476) at line 226 column 10.
NOTE: Invalid argument to function EXP(950.27392335) at line 226 column 10.
NOTE: Invalid argument to function EXP(2908.9920974) at line 226 column 10.
NOTE: Invalid argument to function EXP(947.47746471) at line 226 column 10.

It will be highly appreciative if you can advise me how to resolve this issue.

Thanks

Joon1

Re: exponential function error

ChrisNZ — Thu, 04 Feb 2021 03:18:34 GMT

EXP(755.8640734) is 1.851809 × 10^328

That's a number larger than 10^308 that IEEE 754 computers can store.

What do you want to do with a 328-digit number?

Re: exponential function error

mkeintz — Thu, 04 Feb 2021 03:17:05 GMT

Take a look at documentation for the CONSTANT function (not the EXP function) at Constant Function

In there it says this about the constant "LOGBIG":

You can exponentiate any floating-point number less than or equal to CONSTANT('LOGBIG') by using the exponential function, EXP, without causing any overflows.

So let's see what this value is on my windows machine:

data _null_;
 lb=constant('logbig');
 put lb=;
run;

which generates:

lb=709.78271289

Your arguments are too big to be exponentiated on a windows machine using double-precision floating point arithmetic, because they would exponentiate to a value larger than constant('big') [ =1.797693E308 on my machine].

Re: exponential function error

SASKiwi — Thu, 04 Feb 2021 03:20:18 GMT

Trying to calculate a power of e, which is about 2.718, with a large number like 1,000 will result in such an impossibly large number that SAS cannot handle. Even e to the power of 100 will result in a number with 43 zeroes on the end of it! You need to consider limiting the range of values being supplied to the EXP function to something reasonable. PBP will be very close to 0 for large values coming from EXP.

Re: exponential function error

FreelanceReinh — Thu, 04 Feb 2021 09:36:19 GMT

Hello @joon1,

It looks like you're working with a logistic regression model and you want to apply the logistic function (i.e., the inverse of the logit function) to r1. You don't need to type in the formula for the logistic function because SAS has already implemented it in the LOGISTIC function.

Example:

data test;
do r1=-5, -10, -50, -100, -500, -1000;
  pbp=logistic(r1);
  output;
end;
run;

proc print data=test;
format pbp best21.;
run;

Result:

Obs       r1                      pbp

 1        -5         0.00669285092428
 2       -10          0.0000453978687
 3       -50      1.9287498479639E-22
 4      -100      3.7200759760208E-44
 5      -500     7.1245764067411E-218
 6     -1000                        0

The result pbp=0 for r1=-1000 is, of course, rounded down from 5.076E-435, but the unavoidable rounding errors of the other results are much greater than this and you don't get missing values or pesky notes in the log.

Re: exponential function error

joon1 — Sun, 07 Feb 2021 21:48:44 GMT

Thank you so much for your help, mkeintz.

Re: exponential function error

joon1 — Sun, 07 Feb 2021 21:49:22 GMT

Thank you so much for your help, SASkiwi.

Re: exponential function error

joon1 — Sun, 07 Feb 2021 21:51:15 GMT

Thank you so much for your help, FreelanceReinhard.