topic Re: Logistic effect plot not corresponding to max likelihood table in Statistical Procedures

Logistic effect plot not corresponding to max likelihood table

pink_poodle — Tue, 22 Oct 2019 17:08:24 GMT

I am doing reference cell coding with a binary categorical predictor.

According to max likelihood table,

Intercept = 0.2335, and that is the predicted logit probability of the reference level.

However, the effect plot shows a dot at >0.50 for the predicted probability of that level.

Why is that? Please let me know possible explanations.

proc logistic data=have plots(only)=(effect oddsratio);
    class x(ref='<=60 min')/ param=ref;
    model y(event='1')= x / clodds=pl;
run;

Re: Logistic effect plot not corresponding to max likelihood table

Rick_SAS — Tue, 22 Oct 2019 18:38:51 GMT

Can you upload the image so we can see it?

Re: Logistic effect plot not corresponding to max likelihood table

pink_poodle — Tue, 22 Oct 2019 18:57:22 GMT

maximum likelihood tableeffect plot

Re: Logistic effect plot not corresponding to max likelihood table

Rick_SAS — Tue, 22 Oct 2019 19:04:19 GMT

You can get the exact predicted values by using

ods output effectplot=EFPLOT;

proc logistic....

run;

proc print data=EFPLOT; run;

The estimate for the Intercept (reference level) is 0.2335.

Then the predicted value for the reference category is

p = logistic( 0.2335 );

which is 0.5581. This looks like the height of the dot for the reference category, so it looks like all is well. If the height is different from 0.5581, let me know.

Re: Logistic effect plot not corresponding to max likelihood table

pink_poodle — Tue, 22 Oct 2019 19:50:59 GMT

The ods output value is 0.558105622519328. Thank you!

Re: Logistic effect plot not corresponding to max likelihood table

pink_poodle — Tue, 22 Oct 2019 20:14:03 GMT

Double-checked the logistic function:

logit(p) = ln(odds)

let logit(p) = a

odds = p / ( 1 - p )

p / (1 - p) = e^a

p = e^a - p*e^a

p*(1 + e^a) = e^a

p = e^a / (1 + e^a) = logistic(a)

Re: Logistic effect plot not corresponding to max likelihood table

Rick_SAS — Tue, 22 Oct 2019 20:26:47 GMT

Yes. Equivalently, p = 1 / (1 + exp(-a)), which is shorter to write.