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
[email protected]
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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