Rのnls のAIC計算の暗黙の前提。
nlsのAICは等分散の正規分布を前提にしているので
分布が異なるときは中止
### nlsモデルのAICは正規分布の標準偏差一定を仮定。 y<-x^2+rnorm(length(x)) ans<-nls(y~a*x^2+b,start=c(a=1,b=1)) sigma2<-(mean((y-predict(ans))^2)) -length(y)/2*log(2*pi*sigma2)-length(y)/2 #-15.4633 logLik(ans) #-15.4633 -2*logLik(ans)+2*3 #36.92661 (df=3) AIC(ans) #[1] 36.92661 y<-x^2+(rexp(length(x))-1) ans<-nls(y~a*x^2+b,start=c(a=1,b=1)) sigma2<-(mean((y-predict(ans))^2)) -length(y)/2*log(2*pi*sigma2)-length(y)/2 # -17.74635 logLik(ans) #-17.74635 -2*logLik(ans)+2*3 # 41.4927 (df=3) AIC(ans) #41.4927 y<-x^2+(rnorm(length(x),sd=0.05*x^2)) ans<-nls(y~a*x^2+b,start=c(a=1,b=1)) sigma2<-(mean((y-predict(ans))^2)) -length(y)/2*log(2*pi*sigma2)-length(y)/2 -29.48691 logLik(ans) 'log Lik.' -29.48691 (df=3) -2*logLik(ans)+2*3 'log Lik.' 64.97381 (df=3) AIC(ans) 64.97381