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RE: st: Multinomial Logit vs. Regression with dummy


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Multinomial Logit vs. Regression with dummy
Date   Mon, 21 Jun 2004 15:00:53 +0100

I agree with the advice that multiple logit 
does not sound likely to be very helpful to the original 
questioner -- in fact my own advice was initially to 
forget modelling and look at some graphs -- 
but I am a little uneasy with the general assertions 
here. (The implication that a decision process should 
be always identifiable sounds like a local criterion 
from microeconomics.) 

In statistics much of what we do is often "curve 
fitting" at one level or another. In general 
I would always prefer to have a theoretical 
derivation or at least to have a form of model 
that had some kind of theoretical interpretation 
-- who wouldn't? -- but nature or society is 
not always so obliging. 

More generally, it is, naturally, important to 
think about what is implied by any modelling 
exercise, but that in turn shows that a given 
statistical model in different contexts can 
be applied with different purposes. 

Using just simpler examples from ordinary logit, 
how successfully one can predict sex from height, 
or whether a car is foreign from its mpg, or whether 
a plant grows somewhere given temperature and rainfall, 
is one way of measuring how closely variables 
are related. The lack of a direct causal link in most if not 
all of these cases doesn't make the practical question  
of predictability meaningless. 

A bigger issue, not yet raised in this thread, 
I believe, is that although population density sounds 
a well-formed variable -- just population / area --
in practice it is so sensitive to the mesh of areas 
laid down, often without any reference to demography,  
that it is not even clear that cities in the 
same country can be compared usefully. 

Nick 
n.j.cox@durham.ac.uk 

R.E. De Hoyos
 
> Before carrying on any estimation you have to ask your self 
> what is it that
> you want to estimate. Every model has a theoretical 
> background, regardless
> of yielding a desired outcome or not, you have to constraint 
> your analysis
> to this framework. Multinomial logit--as Clive mentioned 
> it--is used in
> another context. If you estimate -mlogit- your dependent variable is
> "cities", and the outcome of such an estimation makes no sense at all.
> 
> You results from the mlogit will read like this: "an increase in the
> population density changes the probability (or the log odds 
> ratio) of city
> being "i" relative to being "j", where "j" is the base 
> outcome". And this is
> not what you want; there is not a decision process taking place!
> 
> If the variable of interest is Population Density then this 
> has to be the
> right hand side, dependent variable.

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