From junhao.liu at sydney.edu.au Mon May 11 17:34:04 2020 From: junhao.liu at sydney.edu.au (Junhao Liu) Date: Mon, 11 May 2020 07:34:04 +0000 Subject: [Limdep Nlogit List] Nlogit - Intercept in Hierarchical Logit Models Message-ID: 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 | W https://protect-au.mimecast.com/s/EC1ICBNqjlCvP5lPTzCfBG?domain=junhaoliu.com From wgreene at stern.nyu.edu Tue May 12 00:45:23 2020 From: wgreene at stern.nyu.edu (William Greene) Date: Mon, 11 May 2020 10:45:23 -0400 Subject: [Limdep Nlogit List] Nlogit - Intercept in Hierarchical Logit Models In-Reply-To: References: Message-ID: 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 | W > https://protect-au.mimecast.com/s/n1UeCp81lrt5xB7rFPi78T?domain=junhaoliu.com > > > _______________________________________________ > Limdep site list > Limdep at mailman.sydney.edu.au > http://limdep.itls.usyd.edu.au > > -- William Greene Department of Economics, emeritus Stern School of Business, New York University 44 West 4 St. New York, NY, 10012 URL: https://protect-au.mimecast.com/s/6BAfCr81nytxDGWKT4PP-J?domain=people.stern.nyu.edu Email: wgreene at stern.nyu.edu Ph. +1.646.596.3296 Editor in Chief: Journal of Productivity Analysis Editor in Chief: Foundations and Trends in Econometrics Associate Editor: Economics Letters Associate Editor: Journal of Business and Economic Statistics