RE: st: Count models and fractional variables

["Santos Silva, J.M.C." <jmcss@essex.ac.uk>]

Dear Fabiana,
 
Sorry for not seeing you post earlier. Let me see if I can clarify this.
 
First, your friend should not use the Tobit as it is meant for
truncated data and there is no truncation in this dataset.
 
Second, the ZI models can be estimated even if the dependent
variable is continuous. So, there is no need to round the data
and of course you get different results if you do.
 
The fact that you can estimate zero inflated models with
continuous data does not mean that it is a good idea to do it!
In particular, the results of zero inflated models are not invariant
to the scale of the dependent variable, and that explains why
different results are obtained if it is multiplied by 10000.
 
The reason for this is that by rescaling the variable you change
the amount of overdispersion (the mean is multiplied by k
and the variance by k^2). Therefore, studying the number of
patents per year of by quarter will give different results!
 
The advice is now obvious: go back to modeling the counts
using an appropriate count data model (is zero inflation really
needed?). In general, my advice is that one should model the
variable we care about and not some transformation of it; as this
example illustrates, messing with the dependent variable may
have very undesirable consequences.
 
All the best,
 
Joao

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