# [Limdep Nlogit List] R2 Mc Fadden and other R2 in NLOGIT?

RAUX Charles Charles.Raux at laet.ish-lyon.cnrs.fr
Wed Oct 3 19:50:14 AEST 2018

```Hello,
I am running nlogit (MNL nlogit, scaled smnlogit, latent class lclogit) models which give different R2 outputs and I am wondering about the signification of these. I went through the documentation and did not find any suitable answer.
We know that
McFadden's pseudo R2 = 1 - logL/logL0
where L0 stands for all slopes are zero, i.e. model with a constant only.

When estimating an mnl:

|-> nlogit	; choices=air, car, bus, train, none
; lhs=choicem
; model: U(air, car, bus, train) = <asca, ascc, 0, asct>
+ dd * duration + pc * price
/ U(none) = anone
; show model\$
...

I get

Discrete choice (multinomial logit) model
Dependent variable               Choice
Log likelihood function     -1734.80120
Estimation based on N =   1758, K =   6
Inf.Cr.AIC  =   3481.6 AIC/N =    1.980
---------------------------------------
Log likelihood R-sqrd R2Adj
Constants only  -2159.8972  .1968 .1961
Note: R-sqrd = 1 - logL/Logl(constants)
...

There is no output explicitly named "Mc Fadden pseudo R2".
Is "Constants only" the same as "McFadden Pseudo R-squared"?

When I run smnlogit

|-> smnlogit; choices=air, car, bus, train, none
; lhs=choicem
; model: U(air, car, bus, train) = <asca, ascc, 0, asct>
+ <da, dc, db, dt> * duration + pc * price
/ U(none) = anone
; pds=6; pts=100; halton
; showmodel\$

I get

Scaled Multinomial Logit Model
Dependent variable              CHOICEM
Log likelihood function     -1667.35565
Restricted log likelihood   -2829.39185
Chi squared [ 10](P= .000)   2324.07240
Significance level               .00000
McFadden Pseudo R-squared      .4107018
Estimation based on N =   1758, K =  10
Inf.Cr.AIC  =   3354.7 AIC/N =    1.908
---------------------------------------
Log likelihood R-sqrd R2Adj
No coefficients -2829.3919  .4107 .4099
Constants only  -2159.8972  .2280 .2269
At start values -1720.2080  .0307 .0293
Note: R-sqrd = 1 - logL/Logl(constants)
...

I see the "McFadden Pseudo R-squared" which has the same value as "No coefficients R2" (.4107) but not the same as "Constants only R2".
Could anybody clarify about these R2?
Thanks
Charles Raux

```