Hi everyone, I have a problem with maximum-likelihood-estimation in the following situation:
Assume a functional relation y = f(x) (the specific form of f should be irrelevant). For my observations I assume (for simplicity) white noise, such that hat(y_i) = f(x_i) + epsilon_i, with the epsilon_i iid N(0, sigma^2). Y_i should then be N(f(x_i), sigma^2)-distributed and due to the iid assumption the density of Y = (Y_1, ..., Y_n) is simply the product of the individual densities, taking the log gives the the sum of the log of individual densities. I tried coding this in R with a simple example: f(x) = a*x + b (simple linear regression). This way I wanted to compare the results from my ml-estimation (specifying the log-likelihood manually and estimating with mle()) with the results from using lm(y~x). In my example however it doesn't work: x <- 1:10 y <- 3*x - 1 + rnorm(length(x), mean=0, sd=0.5) library("stats4") nLL <- function(a, b, sigma) { -sum(dnorm(y, mean=a*x+b, sd=sigma, log=TRUE)) } fit <- mle(nLL1, start=list(a=0, b=0, sigma=1), nobs=length(y)) summary(lm(y~x)) summary(fit) These should be the same but the aren't. I must have made some mistake specifying the (negative) log-likehood (but I just don't see it). I also actually don't care much (at the moment) for estimating sigma but I don't know of a way to specify (and estimate) the (negative) log-likelihood without estimating sigma. Thanks a lot and kind regards Ronald Koelpin ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.