6.3 The Conditional Logit Model
Stata is also able to fit the more general McFadden conditional logit model discussed in the notes, a random-utility model where the expected utility of a choice may depend on characteristics of the alternatives, characteristics of the people making the choices, and variables which are specific to a combination of person and alternative, for example distance to a cinema. The special case where all predictors are individual characteristics is the multinomial logit model of the previous section.
Stata 10 introduced the asclogit command, short for
alternative specific conditional logit,
which greatly simplified fitting this model.
The model can also be fit, albeit with a bit more work, using
Stata's clogit command, which is designed for
matched case-control or fixed-effects logit models, and was
the only choice in earlier versions.
We provide a brief illustration using the contraceptive choice data. Here we don't have any alternative-specific variables but you'll see how they could be added. The first step is to expand the dataset so we have one record for each combination of individual and alternative. In our example the 3 women aged 15-19 who are sterilized become 3 records, one for sterilization, one for other methods and one for no method, which a dummy variable indicating that the first one of these was chosen. This structure is what makes posible adding alternative-specific predictors. We start by saving the dataset, creating an id, expanding it, coding the alternatives available and the one chosen
. preserve . gen id = _n . expand 3 (42 observations created) . sort id . by id: gen chosen = cuse == _n . by id: replace cuse = _n (42 real changes made)
To fit the model we specify the dummy variable indicating the choice
as outcome, followed by the predictors that vary by alternative,
of which we have none. The predictors that vary only by individual,
in our case age and age squared, are specified using the
casevars() option.
The structure of the data is defined using two options,
case() specifies a variable identifying each individual
and
alternatives() specifies a variable identifying the
alternatives.
The reference or base alternative is specified using the
basealternative() option.
Our last step is to restore the original data.
. asclogit chosen [fw=cases], case(id) casevars(age agesq) ///
> alternatives(cuse) basealternative(3)
Iteration 0: log likelihood = -2962.4334
Iteration 1: log likelihood = -2886.4722
Iteration 2: log likelihood = -2883.148
Iteration 3: log likelihood = -2883.1364
Iteration 4: log likelihood = -2883.1364
Alternative-specific conditional logit Number of obs = 9495
Case variable: id Number of cases = 3165
Alternative variable: cuse Alts per case: min = 3
avg = 3.0
max = 3
Wald chi2(4) = 351.79
Log likelihood = -2883.1364 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
chosen | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
sterilizat~n |
age | .7097186 .0455074 15.60 0.000 .6205258 .7989114
agesq | -.0097327 .0006588 -14.77 0.000 -.011024 -.0084415
_cons | -12.61816 .7574065 -16.66 0.000 -14.10265 -11.13367
-------------+----------------------------------------------------------------
other_method |
age | .2640719 .0470719 5.61 0.000 .1718127 .3563311
agesq | -.004758 .0007596 -6.26 0.000 -.0062469 -.0032692
_cons | -4.549798 .6938498 -6.56 0.000 -5.909718 -3.189877
-------------+----------------------------------------------------------------
no_method | (base alternative)
------------------------------------------------------------------------------
. restore
As you can see, the results are identical to those obtained using
the mlogit command.
Continue with Sequential Logit Models