[Limdep Nlogit List] Nlogit - Intercept in Hierarchical Logit Models

[William Greene]

The "intercept" is what is reported as the "Random Parameter in Utility
Function.
beta(i) = beta + delta'z(i) + sigma*u(i).


On Mon, May 11, 2020 at 3:34 AM Junhao Liu via Limdep <
limdep at mailman.sydney.edu.au> wrote:

> Dear all,
>
> I am estimating an RPLOGIT model with heterogeneity in the means of the
> random parameters. In this two-level model, the mean of the utility weights
> (beta) is modelled as an intercept term plus the effects from some choice
> invariant characteristics. My question is: does Nlogit report the estimate
> of this intercept term?
>
> Below is an example using the classic Nlogit "mnc" data, where the utility
> weight for GC is a hierarchical parameter affected by HINC. But I cannot
> find the intercept term in the "heterogeneity in mean" model in the output,
> only the estimate of GC:HIN. Any advice is appreciated!
>
> |-> rplogit;lhs=mode;
>     ; Choices = air,train,bus,car
>     ; Rhs = gc,ttme,invt
>     ; Rh2 = one
>     ; RPL= hinc
>     ; Fcn = gc(n),ttme[n],invt[n]
>     $
> Iterative procedure has converged
> Normal exit:   6 iterations. Status=0, F=    .1949974D+03
>
>
> -----------------------------------------------------------------------------
> (The MNL output omitted)
>
> -----------------------------------------------------------------------------
>
> Line search at iteration 21 does not improve the function
> Exiting optimization
>
>
> -----------------------------------------------------------------------------
> Random Parameters Multinom. Logit Model
> Dependent variable                 MODE
> Log likelihood function      -175.66089
> Restricted log likelihood    -291.12182
> Chi squared [ 10](P= .000)    230.92185
> Significance level               .00000
> McFadden Pseudo R-squared      .3966069
> Estimation based on N =    210, K =  10
> Inf.Cr.AIC  =    371.3 AIC/N =    1.768
> ---------------------------------------
>             Log likelihood R-sqrd R2Adj
> No coefficients  -291.1218  .3966 .3869
> Constants only   -283.7588  .3809 .3710
> At start values  -194.9974  .0992 .0846
> Note: R-sqrd = 1 - logL/Logl(constants)
> ---------------------------------------
> Response data are given as ind. choices
> Replications for simulated probs. = 100
> Pseudo random draws (Mersenne twister).
> BHHH estimator used for asymp. variance
> Number of obs.=   210, skipped    0 obs
>
> --------+--------------------------------------------------------------------
>         |                  Standard            Prob.      95% Confidence
>     MODE|  Coefficient       Error       z    |z|>Z*         Interval
>
> --------+--------------------------------------------------------------------
>         |Random parameters in utility functions..........................
>       GC|    -.08302         .10337     -.80  .4219     -.28562    .11958
>     TTME|    -.68311*        .41072    -1.66  .0963    -1.48812    .12189
>     INVT|    -.03704         .02401    -1.54  .1229     -.08410    .01001
>         |Nonrandom parameters in utility functions.......................
>    A_AIR|    23.8605       15.47836     1.54  .1232     -6.4765   54.1976
> A_TRAIN|    33.3785       21.39271     1.56  .1187     -8.5504   75.3075
>    A_BUS|    30.7295       19.73732     1.56  .1195     -7.9549   69.4140
>         |Heterogeneity in mean, Parameter:Variable.......................
>   GC:HIN|    -.00036         .00178     -.20  .8421     -.00385    .00314
> TTME:HIN|        0.0    .....(Fixed Parameter).....
> INVT:HIN|        0.0    .....(Fixed Parameter).....
>         |Distns. of RPs. Std.Devs or limits of triangular................
>     NsGC|     .06457         .07420      .87  .3841     -.08085    .21000
>   NsTTME|     .44440         .31382     1.42  .1567     -.17068   1.05947
>   NsINVT|     .03000         .01941     1.55  .1223     -.00805    .06804
>
> --------+--------------------------------------------------------------------
> ***, **, * ==>  Significance at 1%, 5%, 10% level.
> Fixed parameter ... is constrained to equal the value or
> had a nonpositive st.error because of an earlier problem.
> Model was estimated on May 11, 2020 at 05:22:28 PM
>
> -----------------------------------------------------------------------------
>
> Parameter Matrix for Heterogeneity in Means.
> --------+--------------
> Delta_RP|             1
> --------+--------------
>        1|  -.355329E-03
>        2|       .000000
>        3|       .000000
>
>
> Junhao LIU | Postdoctoral Research Associate
> Discipline of Finance | The University of Sydney Business School
>
> THE UNIVERSITY OF SYDNEY
> Rm 512, H69 - Codrington Building | The University of Sydney | NSW | 2006
> E junhao.liu at sydney.edu.au<mailto:junhao.liu at sydney.edu.au> | W
> https://protect-au.mimecast.com/s/n1UeCp81lrt5xB7rFPi78T?domain=junhaoliu.com<https://protect-au.mimecast.com/s/3P5eCq71mwf97oVAFXZj5n?domain=junhaoliu.com>
>
>
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>

-- 
William Greene
Department of Economics, emeritus
Stern School of Business, New York University
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