McFadden R2

[Jamil Hamadneh]

Dears,
I want to find the McFadden R2 for Mixed logit model, any help?
One more question, why do I have McFadden R2 much lower than McFadden when I use R software (multinomial logit model)?
Thanks

[Andrew Musau]

You are mixing two things. Mixed effects logit (melogit command in Stata) is random-effects logit whereas mlogit is multinomial logit. If your interest is in the latter, use the right estimator which reports McFadden's Pseudo R2.

[Jamil Hamadneh]

Thanks Andrew Musau for your reply. Could you please give me more details about what you mean.

[Andrew Musau]

Unless I misunderstand your question, are you asking how to obtain McFadden's Pseudo R2 after estimating a multinomial logit model? If so, my suggestion is to use mlogit not melogit.

[ME] melogit -- Multilevel mixed-effects logistic regression
(View complete PDF manual entry)


Syntax

melogit depvar fe_equation [|| re_equation] [|| re_equation ...] [, options]

where the syntax of fe_equation is

[indepvars] [if] [in] [weight] [, fe_options]

and the syntax of re_equation is one of the following:

for random coefficients and intercepts

levelvar: [varlist] [, re_options]

for random effects among the values of a factor variable in a crossed-effects model

[R] mlogit -- Multinomial (polytomous) logistic regression
(View complete PDF manual entry)


Syntax

mlogit depvar [indepvars] [if] [in] [weight] [, options]

options Description
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Main
noconstant suppress constant term
baseoutcome(#) value of depvar that will be the base outcome
constraints(constraints) apply specified linear constraints

SE/Robust
vce(vcetype) vcetype may be oim, robust, cluster clustvar, bootstrap, or jackknife

Reporting
level(#) set confidence level; default is level(95)
rrr report relative-risk ratios
nocnsreport do not display constraints
display_options control columns and column formats, row spacing, line width, display of omitted variables and base and empty cells, and factor-variable labeling

Maximization
maximize_options control the maximization process; seldom used

collinear keep collinear variables
coeflegend display legend instead of statistics
----------------------------------------------------------------------------------------------------------

See

help mlogit
help melogit

[Jamil Hamadneh]

Thanks for your clarification. why should I use the base outcome in Stata (i.e. both constant and coefficients are set to zero of the base outcome). I want to find the parameters of all alternatives. The results should be alternative specific and one of the outcome has zero intercept (only the intercept), am I right?
More question, how can I obtain the McFadden's Pseudo R2 for Mixed Logit model? I obtained it in R, but how can I find it in Stata?

[Andrew Musau]

why should I use the base outcome in Stata (i.e. both constant and coefficients are set to zero of the base outcome). I want to find the parameters of all alternatives. The results should be alternative specific and one of the outcome has zero intercept (only the intercept), am I right?

Maybe you are thinking about the marginal effects which do not depend on the base category. See

help mlogit_postestimation

More question, how can I obtain the McFadden's Pseudo R2 for Mixed Logit model? I obtained it in R, but how can I find it in Stata?

The concept of R2 is difficult for mixed effects models. If they are implementations in R, then they are not universally accepted and are just suggestions from one or two people. See #6 of the following thread where I provide a link that discusses the matter https://www.statalist.org/forums/for...unning-xtmixed. I see that I also need to make a correction.

[Jamil Hamadneh]

Thank you very much. You mean I can use the margins instead, very interesting!.

Should I include the unchosen alternatives in the analysis, like in the panel-data when I run multinomial logit model?
and what should I do if I have very low Mcfadden R2 like 0.02 and 0.06?

[Andrew Musau]

Thank you very much. You mean I can use the margins instead, very interesting!.

Here is an example where the base category is rep78=3, but I can subsequently use margins to compute the average marginal effect of each regressor on the probability of each of the outcomes (including the base).

sysuse auto, clear
mlogit rep78 mpg displ
margins, dydx(*) predict(outcome(1)) predict(outcome(2)) ///
predict(outcome(3)) predict(outcome(4)) predict(outcome(5))

Res.:

. mlogit rep78 mpg displ

Iteration 0:   log likelihood = -93.692061  
Iteration 1:   log likelihood = -84.527865  
Iteration 2:   log likelihood = -82.573765  
Iteration 3:   log likelihood = -82.282101  
Iteration 4:   log likelihood = -82.278743  
Iteration 5:   log likelihood =  -82.27874  

Multinomial logistic regression                 Number of obs     =         69
                                                LR chi2(8)        =      22.83
                                                Prob > chi2       =     0.0036
Log likelihood =  -82.27874                     Pseudo R2         =     0.1218

------------------------------------------------------------------------------
       rep78 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
1            |
         mpg |  -.0021573   .2104309    -0.01   0.992    -.4145942    .4102797
displacement |  -.0052312   .0126927    -0.41   0.680    -.0301085    .0196461
       _cons |  -1.566574   6.429681    -0.24   0.808    -14.16852    11.03537
-------------+----------------------------------------------------------------
2            |
         mpg |   .0150954   .1235325     0.12   0.903    -.2270239    .2572147
displacement |   .0020254   .0063719     0.32   0.751    -.0104634    .0145142
       _cons |   -2.09099   3.664348    -0.57   0.568    -9.272981    5.091001
-------------+----------------------------------------------------------------
3            |  (base outcome)
-------------+----------------------------------------------------------------
4            |
         mpg |   .0070871   .0883698     0.08   0.936    -.1661146    .1802888
displacement |  -.0066993   .0053435    -1.25   0.210    -.0171723    .0037737
       _cons |    .704788   2.704785     0.26   0.794    -4.596493    6.006069
-------------+----------------------------------------------------------------
5            |
         mpg |   .0808328   .0983973     0.82   0.411    -.1120224    .2736879
displacement |  -.0231922   .0119692    -1.94   0.053    -.0466514    .0002671
       _cons |   .6527964   3.545047     0.18   0.854    -6.295367     7.60096
------------------------------------------------------------------------------

.
. margins, dydx(*) predict(outcome(1)) predict(outcome(2)) predict(outcome(3)) predict(outcome(4)) predict(outcome(5))

Average marginal effects                        Number of obs     =         69
Model VCE    : OIM

dy/dx w.r.t. : mpg displacement
1._predict   : Pr(rep78==1), predict(outcome(1))
2._predict   : Pr(rep78==2), predict(outcome(2))
3._predict   : Pr(rep78==3), predict(outcome(3))
4._predict   : Pr(rep78==4), predict(outcome(4))
5._predict   : Pr(rep78==5), predict(outcome(5))

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
mpg          |
    _predict |
          1  |  -.0005117   .0056718    -0.09   0.928    -.0116282    .0106049
          2  |   .0005468   .0115176     0.05   0.962    -.0220273    .0231209
          3  |   -.004905   .0163699    -0.30   0.764    -.0369894    .0271794
          4  |  -.0026643   .0141136    -0.19   0.850    -.0303265    .0249978
          5  |   .0075342   .0079805     0.94   0.345    -.0081074    .0231758
-------------+----------------------------------------------------------------
displacement |
    _predict |
          1  |  -1.28e-06   .0003301    -0.00   0.997    -.0006483    .0006457
          2  |   .0006224   .0006012     1.04   0.301     -.000556    .0018007
          3  |   .0016077   .0009552     1.68   0.092    -.0002645    .0034798
          4  |  -.0002394    .000956    -0.25   0.802    -.0021131    .0016343
          5  |  -.0019893   .0010984    -1.81   0.070    -.0041421    .0001635
------------------------------------------------------------------------------

Should I include the unchosen alternatives in the analysis, like in the panel-data when I run multinomial logit model?
and what should I do if I have very low Mcfadden R2 like 0.02 and 0.06?

If an alternative is not chosen, then it means that it drops out of your model. Don't bother about the Pseudo R2, low values are very common.

[Jamil Hamadneh]

Thank you very much. if I have insignificant variables in any alternative, should I keep them in the model or remove them because the model will give low accuracy in predication (p>>0.05)?

[Andrew Musau]

That is nothing that I would recommend. You choose your variables based on theory (or past studies) and live with the results. Some people use significance, but I am not one of them.

[Jamil Hamadneh]

Thank you very much for your answers