@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?


--
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@uw.edu> wrote:

> On Wed, Apr 17, 2013 at 5:19 AM, Noah Silverman <noahsilverman@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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