# Re: [R] Likelihood between observed and predicted response

From: Ben Bolker <bolker_at_ufl.edu>
Date: Wed, 14 May 2008 14:49:00 +0000 (UTC)

Christophe LOOTS <Christophe.Loots <at> ifremer.fr> writes:

>
> 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

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