[R] distributions and glm

[Rubén Roa-Ureta]

drbn wrote:
> Hello,
> I have seen that some papers do this:
>
> 1.) Group data by year (e.g. 35 years) 
>
> 2.) Estimate the mean of the key variable through the distribution that fits
> better (some years is a normal distribution , others is a more skewed, gamma
> distribution, etc.)
>
> 3.) With these estimated means of each year do a GLM.
>
> I'd like to know if it is possible (to use these means in a GLM) or is a
> wrong idea.
>
> Thanks in advance
>
> David
>   
David,
You can model functions of data, such as means, but you must be careful 
to carry over most of the uncertainty in the original data into the 
model. If you don't, for example if you let the model know only the 
values of the means, then you are actually assuming that these means 
were observed with absolute certainty instead of being estimated from 
the data. To carry over the uncertainty in the original data to your 
modeling you can use a Bayesian approach or you can use a marginal 
likelihood approach. A marginal likelihood is a true likelihood function 
not of the data, but of functions of the data, such as of maximum 
likelihood estimates. If your means per year were estimated using 
maximum likelihood (for example with fitdistr in package MASS) and you 
sample size is not too small then you can use a normal marginal 
likelihood model for the means. Note however that each mean may come 
from a different distribution so the full likelihood model for your data 
would be a mixture of normal distributions. You may not be able to use  
the pre-built glm function so you may face the challenge to write your 
own code.
HTH
Rubén