Change of sign on alternative-specific constant in nested logit

[Ellen Sterk]

Dear all,

I am analyzing a discrete choice experiment with Stata 17. My alternatives are types of concrete, where there are three types of recycled concrete (A, B, C) and a status-quo option (conventional concrete). The main alternative-specific variables are the costs and the share of recycled aggregates contained. I use cmxtmixlogit, but since it is an unlabelled experiment, I use nlogit when I want to include respondents' individual characteristics. I constrain the dissimilarity parameter of of the status-quo nest to 1 since this nest is degenerate (has only one option). I also include an alternative-specific constant (ASC) that is coded 0 for the status-quo option and 1 for all three recycled concrete options.

Now the sign of the ASC in the basic model is positive (suggesting that respondents generally are more likely to choose recycled concrete over conventional concrete). However, when I add three individual characteristics (how much they value sustainability, whether they feel responsible for considering sustainability, and whether they are familiar with recycled concrete), the ASC changes its sign to negative.
I am unsure how to interpret this and would really appreciate any help!

Some information on the individual characteristics:
- Sust is a continuous variable, scaled from 0 to 100 - the higher, the more people value sustainability.
- Resp is a dummy variable, coded 0 for people who do not and 1 for people who do feel responsible for considering sustainability.
- Fam is a dummy variable, coded 0 for people who are not and 1 for people who are familiar with recycled concrete.

Here is my code and the results.
First the basic model without individual characteristics:

constraint 1 [/nests]conventional_tau = 1
nlogit choice costs rec_agg asc || nests: , base(conventional) ||alternative:, noconstant case(id4) constraints(1)

RUM-consistent nested logit regression         Number of obs      =     24,896
Case variable: id4                             Number of cases    =       6224

Alternative variable: alternative              Alts per case: min =          4
                                                              avg =        4.0
                                                              max =          4

                                                  Wald chi2(5)    =    2329.17
Log likelihood = -6069.0435                       Prob > chi2     =     0.0000

 ( 1)  [/nests]conventional_tau = 1
--------------------------------------------------------------------------------
        choice | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
---------------+----------------------------------------------------------------
alternative    |
       costs |   -.034275   .0030905   -11.09   0.000    -.0403323   -.0282178
       rec_agg |   .0091333   .0008623    10.59   0.000     .0074433    .0108234
          asc |   .3149329   .1778457     1.77   0.077    -.0336383    .6635042
--------------------------------------------------------------------------------
dissimilarity parameters
--------------------------------------------------------------------------------
/nests         |
      rbeton_tau |   .8846722   .0801112                      .7276571    1.041687
   conventional_tau |          1  (constrained)
--------------------------------------------------------------------------------
LR test for IIA (tau=1): chi2(1) = 2.02                   Prob > chi2 = 0.1557

And the model with individual characteristics:

constraint 1 [/nests]conventional_tau = 1
nlogit choice costs rec_agg asc || nests: Sust Fam Resp, base(conventional) ||alternative:, noconstant case(id4) constraints(1)

RUM-consistent nested logit regression         Number of obs      =     22,896
Case variable: id4                             Number of cases    =       5724

Alternative variable: alternative              Alts per case: min =          4
                                                              avg =        4.0
                                                              max =          4

                                                  Wald chi2(8)    =    1938.01
Log likelihood = -5416.7478                       Prob > chi2     =     0.0000

 ( 1)  [/nests]conventional_tau = 1
--------------------------------------------------------------------------------
        choice | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
---------------+----------------------------------------------------------------
alternative    |
      costs |  -.0398292   .0034295   -11.61   0.000    -.0465509   -.0331075
      rec_agg |    .010634   .0009678    10.99   0.000     .0087371    .0125309
        asc |  -1.513539    .232661    -6.51   0.000    -1.969546   -1.057532
--------------------------------------------------------------------------------
nests equations
--------------------------------------------------------------------------------
rbeton         |
     Sust |   .0158093   .0018108     8.73   0.000     .0122602    .0193585
     Fam |    .353931   .1033461     3.42   0.001     .1513763    .5564856
    Resp |   .5156833   .1084387     4.76   0.000     .3031472    .7282193
---------------+----------------------------------------------------------------
conventional        |
       Sust |          0  (base)
       Fam |          0  (base)
      Resp |          0  (base)
--------------------------------------------------------------------------------
dissimilarity parameters
--------------------------------------------------------------------------------
/nests         |
     rbeton_tau |   1.012496   .0878331                      .8403463    1.184646
   conventional_tau |          1  (constrained)
--------------------------------------------------------------------------------
LR test for IIA (tau=1): chi2(1) = 0.02                   Prob > chi2 = 0.8871

I will add that the ASC is consistently positive (and highly significant) in the cmxtmixlogit models.

Thank you in advance!