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

William Greene wgreene at stern.nyu.edu
Thu Oct 4 02:25:47 AEST 2018

```Charles:  In the case of the MNL, if it is possible to compute the log
likelihood for
the constants only model by using the sample proportions, nlogit will
return the
pseudo-Rsquared.  No, it doesn't list McFadden's name, but that is the
statistic,
as the legend implies.  Note, if the choice set is not the same for
everyone, or if
there are restrictions on the constant terms, then it is not possible to
compute the
statistic based only on the sample shares, and the step will be skipped.
But, in
this case, you can compute the constants only model with the right command,
then
obtain the statistic with a hand calculator.  For involved models, such as
the scaled
MNL, you have to be very careful, because the sample shares can't be used
to
obtain lnL for a scaled MNL with constants only.  So, you might not want to
trust
an internally generated value.  Again, use the model command to obtain the
value
for the model you want to be the base.
Regards
Bill Greene

On Wed, Oct 3, 2018 at 5:50 AM RAUX Charles <
Charles.Raux at laet.ish-lyon.cnrs.fr> wrote:

> 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
>
> _______________________________________________
> Limdep site list
> Limdep at mailman.sydney.edu.au
> http://limdep.itls.usyd.edu.au
>
>

--
William Greene
Department of Economics
Stern School of Business, New York University
44 West 4 St., 7-90
New York, NY, 10012
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Email: wgreene at stern.nyu.edu
Ph. +1.212.998.0876
Editor in Chief: Journal of Productivity Analysis
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```