R help - Sep 2008 - Likelihood between observed and predicted response

Thank you so much for your help.

The function "dbinom" seems to work very well.

However, I'm a bit lost with the "dnorm" function.

Apparently, I have to compute the mean "mu" and the standard deviation
"sd" but what does it mean exactly? I only have a vector of predicted 
response and a vector of observed response that I would like to compare!

What are "mu" and "sigma".

Thanks again.
Christophe


 > Hi,
 >
 > I've two fitted models, one binomial model with presence-absence data
 > that predicts probability of presence and one gaussian model (normal or
 > log-normal abundances).
 >
 > I would like to evaluate these models not on their capability of
 > adjustment but on their capability of prediction by calculating the
 > (log)likelihood between predicted and observed values for each type of
 > model.
 >
 > I found the following formula for Bernouilli model :
 >
 > -2 log lik = -2 sum (y*log phat + (1-y)*log(1-phat) ), with
"phat" is
 > the probaility (between 0 and 1) and "y" is the observed values
(0 or 1).
 >
 > 1) Is anybody can tell me if this formula is statistically true?

   This looks correct.

 > 2) Can someone tell me what is the formula of the likelihood between
 > observed and predicted values for a gaussian model ?
 >

    -2 L = sum( (x_i - mu_i)^2)/sigma^2 - 2*n*log(sigma) + C

assuming independence and equal variances:
but don't trust my algebra, see ?dnorm and take the log of the
likelihood shown there for yourself.
You're reinventing the wheel a bit here:

-2*sum(dbinom(y,prob=phat,size=1,log=TRUE))

and

-2*sum(dnorm(x,mean=mu,sd=sigma,log=TRUE))

will do what you want.

   Ben Bolker

-- 
Christophe LOOTS
PhD student - Hydrobiological modelling of fish habitats
Sea Fisheries Laboratory - IFREMER Boulogne sur Mer
150, Quai Gambetta. BP 699
62321 Boulogne sur Mer- FRANCE

T?l : +33(0)3 21 99 56 78
Fax : +33(0)3 21 99 56 01
E-mail : cloots at ifremer.fr
http://www.ifremer.fr/drvboulogne/labo/equipe.htm

Christophe LOOTS <Christophe.Loots <at> ifremer.fr> writes:
> 
> Thank you so much for your help.
> 
> The function "dbinom" seems to work very well.
> 
> However, I'm a bit lost with the "dnorm" function.
> 
> Apparently, I have to compute the mean "mu" and the standard
deviation
> "sd" but what does it mean exactly? I only have a vector of
predicted
> response and a vector of observed response that I would like to compare!
> 
> What are "mu" and "sigma".
> 

  mu is the mean (which you might as well set to the
predicted value).  sd is the standard deviation; in order
to calculate the likelihood in this case, you'll need an
*independent* estimate (from somewhere) of the standard
deviation.  Without thinking about it too carefully I think
you could probably get this from sqrt(sum((predicted-observed)^2)/(n-1))
....

> Thanks again.
> Christophe
>