topic Re: Proc Logistic returning different parameters in Statistical Procedures

Proc Logistic returning different parameters

pink_poodle — Tue, 15 Oct 2019 17:12:20 GMT

I provided the data from the following function to Proc Logistic:

P = 1 / [ 1 + e^(- 0.005 * x) ]

Sigmoid probability distribution has the following form:

P(event) = 1 / [ 1 + e^( - (a + bx) ], where x is the predictor variable.

Therefore, a = 0 and b = 0.005.

Then, I simulated binary response values as follows:

if P >= 0.6 then y = 1; else y = 0.

I used Proc Logistic to model y( event = '1') = x.

The Logistic procedure confidently returned the following parameters:

a = -182.5 and b = 2.2401.

Why are they different from what I provided?

Re: Proc Logistic returning different parameters

Reeza — Tue, 15 Oct 2019 17:21:17 GMT

Show your work please.

Re: Proc Logistic returning different parameters

pink_poodle — Tue, 15 Oct 2019 17:34:45 GMT

Thank you, here is the code:

data have;
set have (keep=x);
P = 1/(1+2.71828182846**(-0.005*x)); 
if P >= 0.6 then y = 1;
else y = 0;
drop P;
run;

proc logistic data=have alpha=0.05
	plots(only)=(effect oddsratio);
	model y(event='1')=x/clodds=pl;
run;

Re: Proc Logistic returning different parameters

Reeza — Tue, 15 Oct 2019 17:43:27 GMT

Have? X? Doesn't run for me.

Re: Proc Logistic returning different parameters

Reeza — Tue, 15 Oct 2019 18:01:50 GMT

One difference is you'll need to specify the NOINT option to fit a model without intercept.

EDIT (added):

What are you trying to do overall here that you need. If it's to fit an exponential model, there are other methods to do that, PROC UNIVARIATE for example. I'm guessing how the 0/1 is being assigned doesn't align with logistic regression somehow but can't remember enough of the math to say why.

Re: Proc Logistic returning different parameters

pink_poodle — Tue, 15 Oct 2019 18:03:07 GMT

After using NOINT, b = 0.002. This is pretty good, considering that I had to taint the probability distribution a little to avoid the perfect prediction, which prevented the model from converging.

Re: Proc Logistic returning different parameters

FreelanceReinh — Tue, 15 Oct 2019 21:17:19 GMT

Hi @pink_poodle,

@Reeza is right in that "how the 0/1 is being assigned doesn't align with logistic regression." You missed the (crucial) randomness in the assignment:

y=rand('bern',P);

Actually, you don't need to create a variable P (you drop it anyway), nor type the digits of e or the formula of the logistic function. Simply define

y=rand('bern',logistic(0.005*x));

Then, you may decide not to use the NOINT option and let PROC LOGISTIC find out -- input data permitting -- that the intercept (parameter a) must be (close to) zero. The results are likely similar with the NOINT option because, of course, a is zero (but you know b=0.005 in advance as well, so this shouldn't be the only reason for using NOINT).

Edit: Use CALL STREAMINIT in the DATA step using the RAND function in order to create reproducible results.

Re: Proc Logistic returning different parameters

pink_poodle — Wed, 16 Oct 2019 14:27:15 GMT

@FreelanceReinh, @Reeza,

Using your method, y = rand('bern',logistic(0.005*x)),

without NOINT option: intercept = 0.00160, slope = 0.00492;

with NOINT option: slope = 0.00494.

Thank you!