[R] Strange error with log-normal models

[peter dalgaard]

On Apr 16, 2013, at 22:20 , Noah Silverman wrote:

> @Duncan, You make a very good point.  Somehow I overlooked that 0 is not positive.  I guess that rules out the log normal model.
> 
> My challenge here is  finding the right model for this data.  Originally it was a nice count of students.  Relatively easy to model with a zero inflated Poisson model.  The resulting residuals seemed reasonable.
> 
> However, I was then instructed to change the count of students to a "rate" which was calculated as students / population (Each school has its own population.)) This is now no longer a count variable, but a proportion between 0 and 1.  
> 
> This "rate" (students/population) is no longer Poisson, but is certainly not normal either.  So, I'm a bit lost as to the appropriate distribution to represent it.
> 
> Any thoughts?
> 

Off the cuff: Could it be more natural to model as a ZIP with log(pop) as an offset on the log-lambda scale? 

> 
> --
> Noah Silverman, M.S.
> UCLA Department of Statistics
> 8117 Math Sciences Building
> Los Angeles, CA 90095
> 
> On Apr 16, 2013, at 12:44 PM, Thomas Lumley <tlumley at uw.edu> wrote:
> 
>> On Wed, Apr 17, 2013 at 5:19 AM, Noah Silverman <noahsilverman at ucla.edu> wrote:
>> Hi,
>> 
>> I have some data, that when plotted looks very close to a log-normal distribution.  My goal is to build a regression model to test how this variable responds to several independent variables.
>> 
>> [snip]
>> 
>> When I try to build a simple model, I also get an error:
>> 
>> l <- glm(y~ x, family=gaussian(link="log"))
>> 
>> Error in eval(expr, envir, enclos) :  cannot find valid starting values: please specify some
>> 
>> 
>> Duncan has described the problems with the lognormal.  I will just point out that this 'simple model' is not lognormal.  It is a model with normal errors and log link, ie.
>> 
>> y ~ N(mu, sigma^2)
>> log(mu) = x \beta
>> 
>> 
>>    -thomas
>> 
>> -- 
>> Thomas Lumley
>> Professor of Biostatistics
>> University of Auckland
> 
> 
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-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com