[R] Error using glm with poisson family and identity link

[Spencer Graves]

Hi, Peter: 

      Thanks for the comment and reply. 

      I generally avoid constrained optimizers for three reasons: 

      1.  My experience with them has included many cases where the 
optimizer would stop with an error when testing parameter values that 
violate the constraints.  If I transform the parameter space to remove 
the constraints, that never happens.  The constrained optimizers in R 
2.0.1 may not exhibit this behavior, but I have not checked. 

      2.  In a few cases, I've plotted the log(likelihood) vs. parameter 
values using various transformations.  When I've done that, I typically 
found that the most nearly parabolic performance used unconstrained 
parameterizations.  This makes asymptotic normality more useful and 
increases the accuracy of simple, approximate sequential Bayesian 
procedures. 

      3.  When I think carefully about a particular application, I often 
find a rationale for claiming that a certain unconstrained 
parameterization provides a better description of the application.  For 
example, interest income on investments is essentially additive on the 
log scale.  Similarly, the concept of "materiality" in Accounting is 
closer to being constant in log space:  One might look for an error of a 
few Euros in the accounts of a very small business, but in auditing some 
major government accounts, errors on the order of a few Euros might not 
be investigated.  Also, measurement errors with microvolts are much 
smaller than with megavolts;  expressing the measurements in decibels 
(i.e., on the log scale) makes the measurement errors more nearly 
comparable. 

      Thanks again for your comments. 
      Best Wishes,
      Spencer Graves        

Peter Dalgaard wrote:

>Spencer Graves <spencer.graves at pdf.com> writes:
>
>  
>
>>Hi, Peter:     What do you do in such situations?     Sundar Dorai-Raj
>>and I have extended "glm" concepts to models driven by a sum of k
>>independent Poissons, with the a linear model for log(defectRate[i])
>>for each source (i = 1:k).  To handle convergence problems, etc., I
>>think we need to use informative Bayes, but we're not there yet.  In
>>any context where things are done more than once [which covers most
>>human activities], informative Bayes seems sensible.     A related
>>question comes with data representing the differences between Poisson
>>counts, e.g., with d[i] = X[i]-X[i-1] = the number of new defects
>>added between steps i-1 and i in a manufacturing process.  Most of the
>>time, d[i] is nonnegative.  However, in some cases, it can be
>>negative, either because of metrology errors in X[i] or because of
>>defect removal between steps i-1 and i.     Comments?
>>    
>>
>
>I haven't got all that much experience with it, but obviously, the
>various algorithms for constrained optimization (box- or otherwise) at
>least allow you to find a proper maximum likelihood estimator.
>
>
>  
>

-- 
Spencer Graves, PhD, Senior Development Engineer
O:  (408)938-4420;  mobile:  (408)655-4567