  # st: RE: Multinomial logit

 From "Daniel Mueller" To Subject st: RE: Multinomial logit Date Thu, 24 Jul 2003 08:50:20 +0200

```> From: Ronnie Babigumira
> Sent: Wednesday, July 23, 2003 11:22 PM
>
> Hi, (using stata8, win2K). I have a household data set and
> would like to explain the choice of coping strategies.
>
> 3 main strategies are used by households however, some
> households choose more than one strategy. After looking at
> the data, I have 6 "strategies". 3 are pure (if a household
> pursues either 1, 2 or 3 exclusively) and 3 are mixed
> strategies (combinations of the pure ones to give new
> strategies 4, 5 and 6). The data would look something like this
>
> hhid  strategy
> 1          2
> 2          3
> 3          1
> 4          5
> 5          4
> 6          1
> 7          6
>
> I have been thinking of using a multinomial logit. My
> question is, is the fact that strategy 2 is nested in 6
> (which is a combination of 2 and 3) and problem.

It is indeed a problem as MNL assumes the disturbances to be independently distributed. The calculated probabilities would
be unaffected if you add another category (the classic example is the redbus/blue bus paradoxon -- Maddala (1983):
Limited-dependent and qualitative variables in econometrics. Cambridge University Press). This phenomenon is called the
'independence of irrelevant alternatives' (IIA).

In your example strategy 2 and 6 would have a certain relationship. The relative probability of observing strategy 2 would
probably decrease if you add strategy 6 to the set of alternatives. So the assumption of IIA would be violated leading to
inefficient (however, according to Greene, not inconsistent) estimates. To test for IIA you could use e.g. -mlogtest-. A
nested logit is probably more appropriate in your case. Other alternatives to get around could be multilevel modelling
(-gllamm-).

HTH,
Daniel

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