Re: [R] glm questions --- saturated model

[David Firth]

On Tuesday, Mar 16, 2004, at 14:51 Europe/London, BXC (Bendix 
Carstensen) wrote:

-----Original Message-----
From: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED] On Behalf Of David Firth
Sent: Tuesday, March 16, 2004 1:12 PM
To: Paul Johnson
Cc: [EMAIL PROTECTED]
Subject: Re: [R] glm questions
Dear Paul

Here are some attempts at your questions.  I hope it's of some help.

On Tuesday, Mar 16, 2004, at 06:00 Europe/London, Paul Johnson wrote:

Greetings, everybody. Can I ask some glm questions?

1. How do you find out -2*lnL(saturated model)?

In the output from glm, I find:

Null deviance:  which I think is  -2[lnL(null) - lnL(saturated)]
Residual deviance:   -2[lnL(fitted) - lnL(saturated)]
The Null model is the one that includes the constant only
(plus offset
if specified). Right?

I can use the Null and Residual deviance to calculate the
"usual model
Chi-squared" statistic
-2[lnL(null) - lnL(fitted)].
But, just for curiosity's sake, what't the saturated model's -2lnL ?
It's important to remember that lnL is defined only up to an additive
constant.  For example a Poisson model has lnL contributions -mu +
y*log(mu) + constant, and the constant is arbitrary.  The
differencing
in the deviance calculation eliminates it.  What constant would you
like to use??
I have always been und the impression that the constant chosen by glm 
is
that which makes the deviance of the saturated model 0, the saturated
model being the one with one parameter per observation in the dataset.
...
But a look at the deviance formula above ---
   -2[lnL(fitted) - lnL(saturated)]
--- shows us that *any* constant can be added to lnL, and the deviance 
for the saturated model will still be zero.

David

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