I have a problem to calculate the AIC. Indeed, I estimate the parameters of my 3 models: "mod_linear", which is a linear model and "mod_exp" and "mod_logis" which are two non linear models.
I used the function AIC():
AIC(mod_linear,mod_exp,mod_logis)
df AIC
mod_linear 4 3.015378
mod_exp 5 -11.010469
mod_logis 5 54.015746
But I tried to calculate the AIC with the formule AIC=2k+nlog(RSS/n) where K is the number of parameters, n the number of the sample and RSS the residual sum of squares.
k=4
n=21
#Calcul of nls for the linear model:
mod_linear=nls(data$P~P_linear(P0,K0,a),data=data,
start=c(P0=4.2,K0=4.5,a=0.)
2*k+n*log(sum(residuals(mod_linear)^2)/n)
-56.58004
As you can see, is not the same result and It's the same thing for the two other models. Someone could help me?
Regards
You should always take care that you use consistent definitions of AIC.
AIC uses the usual definition of 2k-2*ln(L). The log-likelihood is calculated, e.g., by stats:::logLik.lm as 0.5 * (- N * (log(2 * pi) + 1 - log(N) + log(sum(res^2)))).
An example:
fit <- lm(Sepal.Length ~ Sepal.Width, data = iris)
AIC(fit)
#[1] 371.9917
logL <- 0.5 * (- length(residuals(fit)) * (log(2 * pi) + 1 - log(length(residuals(fit))) + log(sum(residuals(fit)^2))))
2 * (fit$rank + 1) - 2 * logL
#[1] 371.9917
However, help("AIC") warns:
The log-likelihood and hence the AIC/BIC is only defined up to an additive constant. Different constants have conventionally been used for different purposes ... Particular care is needed when comparing fits of different classes [...].
See stats:::logLik.nls for how the log-likelihood is calculated for nls fits.