Peter I see there is no mistake. The phrase about the 'number of parameters' confused me, it is a little ambiguous. Many thanks for taking the time to help me.
Geoff > On 5 Mar 2014, at 11:20, "Peter Dalgaard-2 [via R]" > <ml-node+s789695n4686243...@n4.nabble.com> wrote: > > > On 04 Mar 2014, at 21:21 , Geoff Loveman <[hidden email]> wrote: > > > > > > > In 'An Introduction to R', section 11.7 on nonlinear least squares fitting, > > the following example is given for obtaining the standard errors of the > > estimated parameters: > > > > "To obtain the approximate standard errors (SE) of the estimates we do: > > sqrt(diag(2*out$minimum/(length(y) - 2) * solve(out$hessian)))The 2 in the > > line above represents the number of parameters." > > > > I know the inverted Hessian is multiplied by the mean square error and that > > the denominator of the MSE is the degrees of freedom (number of samples - > > number of parameters) but why does the numerator of the MSE (which is the > > RSS) get multiplied by the number of parameters? I have read through > > explanations of the method for obtaining the SE but I don't see where the > > MSE gets multiplied by the number of parameters or why this is needed as > > shown in the example? > > > > > There are two 2's in that line, and I'd expect that only the last one has to > do with the number of parameters, and the other one has to do with whether > the Hessian is the second derivative of the sum of squares or of the negative > loglikelihood function (half the sum of squares). > > Quick check: In a linear model, we have > > ssd = || Y- X beta ||^2 > gradient = -2 (Y - X beta )'X > Hessian H = 2 X'X > > and as we know, V(beta) = sigma^2 (X'X)^-1 = 2 sigma^2 H^-1 > > -pd > > > Thanks for any help! > > > > Geoff Loveman > > Tech lead SMERAS > > QQ Maritime Life Support > > > > > > > > > > > > -- > > View this message in context: > > http://r.789695.n4.nabble.com/Is-this-a-mistake-in-An-Introduction-to-R-tp4686217.html > > Sent from the R help mailing list archive at Nabble.com. > > > > ______________________________________________ > > [hidden email] mailing list > > 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. > > -- > Peter Dalgaard, Professor > Center for Statistics, Copenhagen Business School > Solbjerg Plads 3, 2000 Frederiksberg, Denmark > Phone: (+45)38153501 > Email: [hidden email] Priv: [hidden email] > > ______________________________________________ > [hidden email] mailing list > 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. > > > If you reply to this email, your message will be added to the discussion > below: > http://r.789695.n4.nabble.com/Is-this-a-mistake-in-An-Introduction-to-R-tp4686217p4686243.html > To unsubscribe from Is this a mistake in 'An Introduction to R'?, click here. > NAML -- View this message in context: http://r.789695.n4.nabble.com/Is-this-a-mistake-in-An-Introduction-to-R-tp4686217p4686291.html Sent from the R help mailing list archive at Nabble.com. [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list 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.
