[R] Strange behavior with poisosn and glm

[Rolf Turner]

On 2/03/2010, at 9:02 PM, Noah Silverman wrote:

> Hi,
> 
> I'm just learning about poison links for the glm function.
> 
> One of the data sets I'm playing with has several of the variables as 
> factors (i.e. month, group, etc.)
> 
> When I call the glm function with a formula that has a factor variable, 
> R automatically converts the variable to a series of variables with 
> unique names and binary values.
> 
> For example, with this pseudo data:
> 
> y        v1        month
> 2        1            january
> 3        1.4        februrary
> 1.5    6.3        february
> 1.2    4.5        january
> 5.5    4.0        march
> 
> I use this call:
> 
> m <- glm(y ~ v1 + month, family="poisson")
> 
> R gives me back a model with variables of
> Intercept
> v1
> monthJanuary
> monthFebruary
> monthMarch

	No it didn't!!!  You are kidding the troops/being economical with the truth.

	If you had used the data that you show, it would've ``given you a model with
	variables'':

	Intercept
	v1
	monthfebruray
	monthjanuary
	monthmarch

	No caps in the month name and note the miss-spelling of ``february''.

	You actually have ***four*** levels for the month factor:

		january februrary february march

	If you had spelt ``februrary'' correctly you would have got variables

	Intercept
	v1
	monthjanuary
	monthmarch

	The first level, february would have been omitted, under the default contrasts
	(contr.treatment).  You need k-1 dummy variables to specify a factor with k levels.

> I'm concerned that this might be doing some strange things to my model.

	No, you are doing strange things.

	Notice also that the Poisson distribution is a distribution of ***counts***.
	Non-negative integers.  Whole numbers.  Values like 1.5 and 1.2 make no immediate
	sense in terms of the Poisson distribution.  The Poisson likelihood can be evaluated
	with non-integer responses, but the glm() function will quite rightly worry about
	non-integer values and give you a warning.  (Which you didn't mention.)

	If you really have non-integer valued responses you shouldn't be using the Poisson
	family; the quasi family *might* be appropriate --- if you know what you're doing.

> Can anyone offer some enlightenment?

	I hope you feel enlightened.

		cheers,

			Rolf Turner
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