[Gretl-users] Re: grouped data logit
Below you have, for the dependent variable in gretl: "series y =
N/n_house" (which I guess means Ni/ni, with a switch of notation).
That's the wrong way round, it should be ni/Ni, giving values between
0 and 1.
There's reasonably explicit documentation of what gretl's "logistic"
command does, in the Command reference. Evidently, the software used
by Gujarati and Porter does something substantially different. I'm not
sure we can help in understanding what that is.
Allin Cottrell
On Sun, Mar 15, 2026 at 7:32 AM Ramki S <ramakrishnasalagrama(a)gmail.com> wrote:
>
> Thanks for your reply. The following is the output by gujarati and porter. I am
finding it difficult to understand the weight (w) here and interpreting the coefficients.
Any help?
>
> ˆ ∗
> Li = −1.59474√wi + 0.07862Xi∗
> se = (0.11046) (0.00539)
> t = (−14.43619) (14.56675) R2 = 0.9642
>
> X Ni ni pi_hat 1 - pi_hat
pi_hat / (1 - pi_hat) Li = ln(pi_hat / (1 - pi_hat)) wi = Ni pi_hat (1
- pi_hat) sqrt(wi) = sqrt(Ni pi_hat (1 - pi_hat)) Li* = Li sqrt(wi)
Xi* = Xi sqrt(wi)
>
> 6 40 8 0.20 0.80 0.25
-1.3863 6.40 2.5298 -3.5077 15.1788
> 8 50 21 0.42 0.58 0.72
-1.1526 9.12 3.0199 -3.4801 24.1592
> 10 60 18 0.30 0.70 0.43
-0.8472 12.60 3.5496 -3.0072 35.4960
> 13 80 33 0.35 0.65 0.54
-0.6190 18.20 4.2661 -2.6404 55.4593
> 15 100 45 0.45 0.55 0.82
-0.2007 24.75 4.9749 -0.9985 74.6235
> 20 70 51 0.51 0.49 1.04
0.0500 17.49 4.1816 0.1673 83.6506
> 25 65 36 0.60 0.40 1.50
0.4055 15.60 3.9497 1.6012 98.7425
> 30 50 33 0.66 0.34 1.94
0.6633 11.20 3.3496 2.2218 100.4880
> 35 40 30 0.75 0.25 3.0
1.0986 7.50 2.7386 3.0070 95.8505
> 40 25 20 0.80 0.20 4.0
1.3863 4.00 2.0000 2.7726 80.0000
>
> ________
> Gretl output as suggested by you:
> gretl version 2026a
> Current session: 2026-03-15 16:49
>
> ? series y = N/n_house
> Generated series y (ID 4)
> ? logistic y const X_inc
>
> Model 1: Logistic, using observations 1-10
> Dependent variable: y
> yhat =~ E(100 / (1 + exp(-X*b)))
>
> coefficient std. error t-ratio p-value
> --------------------------------------------------------
> const −2.95413 0.107181 −27.56 3.24e-09 ***
> X_inc −0.0399131 0.00463646 −8.609 2.57e-05 ***
>
> Statistics based on the transformed data:
>
> Sum squared resid 0.217306 S.E. of regression 0.164813
> R-squared 0.902566 Adjusted R-squared 0.890387
> F(1, 8) 74.10703 P-value(F) 0.000026
> Log-likelihood 4.955783 Akaike criterion −5.911567
> Schwarz criterion −5.306396 Hannan-Quinn −6.575437
>
> Statistics based on the original data:
>
> Mean dependent var 2.528896 S.D. dependent var 1.283018
> Sum squared resid 9.461319 S.E. of regression 1.087504