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

[Junhao Liu]

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/EC1ICBNqjlCvP5lPTzCfBG?domain=junhaoliu.com<https://protect-au.mimecast.com/s/mGlSCD1vlpTXjlOjT5Xg_j?domain=junhaoliu.com>