st: Re: ZINB inflation equation marginal effects

[Maarten Buis <maartenlbuis@gmail.com>]

On Tue, Sep 25, 2012 at 2:35 PM, susannahsong wrote me privately:
> Coud I ask if you may help me with calculating marginal effects using ZINB
> command in Stata, please? I need to use ZINB regression, but I'm confused
> about what I should present and interpret in a paper. I only know the
> margins command to report the marginal effects of the outcome equation, but
> what if I'd like to report the marginal effects of the inflation equation?
> Could I run a logit model of the inflation equation first (the dependent
> variable = 1 if one incident happens and 0 otherwise) and then generate
> marginal effects using margins? Would this be wrong?

Such questions need to be sent to the Statalist not to individual
members. For reasons why this is the case see:
<http://www.stata.com/support/faqs/resources/statalist-faq/#private>.
So I have sent this reply to Statalist and I expect to see any future
questions there and not in my inbox.

For me the two main reasons are:

- Much of the benefit of Statalist is that an answer to a question
might well interest other people. Thinking that an answer might help
many is an incentive to everyone. Or say you start a thread and then
you take it private. Your response is now invisible to others who may
be interested in the thread.

- Time spent posting to Statalist is time unavailable for doing the
other things in life. So guessing that Stata-active people have more
time available for private support is likely to be wrong.

For you an important reason is that by sending such questions to
Statalist you can get a much wider range of views. On the topic of
marginal effects my views are not shared by everybody, so what I tell
you may be true (I obviously think it is...), but it may by no means
be the consensus in the field.

My view is that I don't like marginal effects, especially the practice
of reporting one (average) marginal effect per variable. Think of what
you are doing when reporting one marginal effect per parameter: You
are in effect reporting the results of a linear approximation of your
non-linear effect. In essence, you fitted a linear model on top of
your non-linear model. So, if you do that than you wanted to estimate
a simple linear model but weren't brave enough to admit it. By
estimating a linear model in such a roundabout way you get all the
disadvantages of a linear model without the advantage that tools and
graphs for checking for problems in a linear model are well developed.
This is especially problematic because apparently one chooses a
non-linear model because one believes that the linear model is
problematic. So I am going to do you a favor and not tell you how to
estimate the marginal effects you are looking for.

Instead I would interpret your model in terms of incidence rate ratios
and odds ratios. For some reason StataCorp decided to only report the
coefficients and not the odds ratios, so you need to use a trick:

*------------------ begin example ----------------------
webuse fish

// make sure that 0 in persons falls within
// the range of the data
replace persons = persons - 1

zinb count persons livebait, inflate(child camper) irr

// to also interpret the selection equation we
// need to exponentiate those coefficients as well
ereturn display, eform("exp(b)")
*------------------- end example -----------------------

So, a person alone not using live bait can expect to catch .17 fishes
if he is not a "structural zero fish catcher". Every person extra
means that this expected number of fishes increases by a factor 2.6,
i.e. the expected number of fishes increase by (2.6-1)*100%=160%. For
persons without children and no camper we expect that there are .06
"structural zero fish catchers" for every "non-structural zero fish
catcher". This odds increases by a factor 24 for every child included
in the group.

-- Maarten

---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

http://www.maartenbuis.nl
---------------------------------
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/