[Limdep Nlogit List] Specification and interpretation of a nested model

[Dorothy Kobel]

Dear All,

I need help specifying and interpreting a model. I would like to fit a
nested model with 3 alternatives and 4 variables (SAN with 3 dummy
variables, LOC with 3 dummy variables, a continous variable DIR and cost).
The branches are OWN (own sanitation, represented by SAN3 among the
variables) and SHARED (shared sanitation, represented by SAN1 & SAN2). The
3rd alternative is the "no choice" alternative with cost set to 0. The
command I am using is:


NLOGIT

;lhs=choice3, nij3, alt

;choices= 1, 2, 3

;TREE= OWN(1), SHARED(3, 2)

;START=LOGIT

;IVSET:(OWN)=[1.0]

;MAXIT=100

;Model:

U(1)=PSAN3*SAN3+PLOC2*LOC2 +pLOC3*LOC3+ pDIR* DIR +pCost*cost/



U(2)=PSAN1*SAN1+PLOC2*LOC2 +pLOC3*LOC3+ pDIR* DIR + pCost*cost/



U(3)=pCost*cost$





The output I get is:

--> NLOGIT

    ;lhs=choice3, nij3, alt

    ;choices= 1, 2, 3

    ;TREE= OWN(1), SHARED(3, 2)

    ;START=LOGIT

    ;IVSET:(OWN)=[1.0]

    ;MAXIT=100

    ;Model:

    U(1)=PSAN3*SAN3+PLOC2*LOC2 +pLOC3*LOC3+ pDIR* DIR +pCost*cost/

    U(2)=PSAN1*SAN1+PLOC2*LOC2 +pLOC3*LOC3+ pDIR* DIR + pCost*cost/

    U(3)=pCost*cost$

Normal exit from iterations. Exit status=0.



              +---------------------------------------------+

              | Discrete choice (multinomial logit) model   |

              | Maximum Likelihood Estimates                |

              | Dependent variable               Choice     |

              | Weighting variable                  ONE     |

              | Number of observations             2400     |

              | Iterations completed                  4     |

              | Log likelihood function       -2538.335     |

              | Log-L for Choice   model =   -2538.3350     |

              | R2=1-LogL/LogL*  Log-L fncn  R-sqrd  RsqAdj |

              | No coefficients  -2792.6900  .09108  .08994 |

              | Constants only.  Must be computed directly. |

              |                  Use NLOGIT ;...; RHS=ONE $ |

              | Response data are given as ind. choice.     |

              | Number of obs.=  2400, skipped   0 bad obs. |

              +---------------------------------------------+

+---------+--------------+----------------+--------+---------+----------+

|Variable | Coefficient  | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|

+---------+--------------+----------------+--------+---------+----------+

 PSAN3     .6563932539      .11672947        5.623   .0000

 PLOC2    -.1269154727      .68921481E-01   -1.841   .0656

 PLOC3    -.3368833151      .85888539E-01   -3.922   .0001

 PDIR     -.4258302812E-02  .15917696E-02   -2.675   .0075

 PCOST    -.5545088459E-04  .91029324E-05   -6.092   .0000

 PSAN1     .1691248792E-01  .11997568         .141   .8879





Normal exit from iterations. Exit status=0.

              +---------------------------------------------+

              | FIML: Nested Multinomial Logit Model        |

              | Maximum Likelihood Estimates                |

              | Dependent variable              CHOICE3     |

              | Weighting variable                  ONE     |

              | Number of observations             7200     |

              | Iterations completed                  5     |

              | Log likelihood function       -2527.780     |

              | Restricted log likelihood     -2792.690     |

              | Chi-squared                    529.8202     |

              | Degrees of freedom                    7     |

              | Significance level             .0000000     |

              | R2=1-LogL/LogL*  Log-L fncn  R-sqrd  RsqAdj |

              | No coefficients  -2792.6900  .09486  .09354 |

              | Constants only.  Must be computed directly. |

              |                  Use NLOGIT ;...; RHS=ONE $ |

              | At start values  -2538.3350  .00416  .00270 |

              | Response data are given as ind. choice.     |

              +---------------------------------------------+



              +---------------------------------------------+

              | FIML: Nested Multinomial Logit Model        |

              | The model has 2 levels.                     |

              | Nested Logit form:IV parms = tauj|i,l,si|l  |

              | and fl. No normalizations imposed a priori. |

              | p(alt=k|b=j,l=i,t=l)=exp[bX_k|jil]/Sum      |

              | p(b=j|l=i,t=l)=exp[aY_j|il+tauj|ilIVj|il)]/ |

              | Sum. p(l=i|t=l)=exp[cZ_i|l+si|lIVi|l)]/Sum  |

              | p(t=l)=exp[exp[qW_l+flIVl]/Sum...           |

              | Number of obs.=  2400, skipped   0 bad obs. |

              +---------------------------------------------+

+---------+--------------+----------------+--------+---------+----------+

|Variable | Coefficient  | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|

+---------+--------------+----------------+--------+---------+----------+

          Attributes in the Utility Functions (beta)

 PSAN3     .3079128940      .13999943        2.199   .0279

 PLOC2    -.1890219262      .78542342E-01   -2.407   .0161

 PLOC3    -.3300097026      .92439341E-01   -3.570   .0004

 PDIR     -.9939668963E-02  .21661927E-02   -4.589   .0000

 PCOST    -.4783618501E-04  .10075943E-04   -4.748   .0000

 PSAN1     .3467545334      .14887998        2.329   .0199

          IV parameters, tau(j|i,l),sigma(i|l),phi(l)

 OWN       1.000000000    ........(Fixed Parameter)........

 SHARED    .1348288172      .21328356         .632   .5273




   1. Have I specified this correctly? Should I include the dummy variable
   for the 2nd sanitaion option in the utility function U(2) since it is a
   shared option?
   2. How should I interprete this output? It looks like most of the
   variables are significant and yet I get a low R sq. How could I improve
   the R sq?
   3. How do I interprete the magnitude of the IV parameter for SHARED? Do I
   want it closer to 1.0?

Kind regards,
Dorothy Kobel
PhD Candidate
University of Cape Town