I made no attempt to examine your details for problems, but in general, My problem > is that the results change a lot depending on the initial values... I can't > see what I am doing wrong... > > This is a symptom of an overparameterized model: The parameter estimates > are unstable even though the predictions may not change much. In other > words, your model may be too complex for your data.
Whether that is true here, you or others will have to determine. Try simplifying your model as a start. -- Bert > > > # Data > x <- 1995:2010 > B <- c(3500, 3200, 3000, 2800, 2600, 3000, 3200, 3800, 4200, 4300, 4400, > 4400, 4500, 4600, 5000, 4300) > Ct <- c(912, 767, 642, 482, 353, 331, 332, 309, 366, 402, 392, 478, 408, > 434, 407, 637) > a <- c(0.539, 0.603, -0.948, 0.166, 1.895, 0.786, 0.901, 0.844, 0.337, > 0.429, 0.304, 0.230, 1.001, 0.750, 0.507, 1.502) > Ag <- 0.55 > > # Function with quantity to minimize > modl <- function(par) { > ro <- par[1] > ko <- par[2] > n <- length(B) > Be <- rep(NA, n) > Be[1] <- ko * Ag > for ( k in 2:n) > Be[k] <- Be[k-1] + ro * a[k-1] * Be[k-1] * (1 - Be[k-1]/ko) - Ct[k-1] > err <- (log(B) - log(Be))^2 > ee <- sqrt( sum(err)/(n-2) ) > LL <- (1/(sqrt(2*pi)*ee)) * exp( -(err/(2*ee^2) ) ) > -crossprod(LL) > } > > # Using function optim() > par.optim <- optim(par = list(ro=0.4, ko=8000), modl, method = "BFGS") > ro <- par.optim$par[1] > ko <- par.optim$par[2] > > # estimated values of "B" > n <- length(B) > Be <- rep(NA, n) > Be[1] <- ko * Ag > for ( k in 2:n) > Be[k] <- Be[k-1] + ro * a[k-1] * Be[k-1] * (1 - Be[k-1]/ko) - Ct[k-1] > > # Plot, estimation of "B" seems reasonable.... > plot(x, B, ylim=c(1000, 7000)) > lines(x, Be, col="blue", lwd=2) > > > # ... but it is very sensible to initial values... > par.optim2 <- optim(par = list(ro=0.4, ko=10000), modl, method = "BFGS") > ro2 <- par.optim2$par[1] > ko2 <- par.optim2$par[2] > > Be2 <- rep(NA, n) > Be2[1] <- ko2 * Ag > for ( k in 2:n) > Be2[k] <- Be2[k-1] + ro2 * a[k-1] * Be2[k-1] * (1 - Be2[k-1]/ko2) - > Ct[k-1] > > lines(x, Be2, col="blue", lwd=2, lty=3) > > > > # Uing mle2 function > library(bbmle) > LL <- function(ro, ko, mu, sigma) { > n <- length(B) > Be <- rep(NA, n) > Be[1] <- ko * Ag > for ( k in 2:n) > Be[k] <- Be[k-1] + ro * a[k-1] * Be[k-1] * (1 - Be[k-1]/ko) - Ct[k-1] > err <- log(B) - log(Be) > R <- (dnorm(err, mu, sigma, log=TRUE)) > -sum(R) > } > > Bc.mle <- mle2(LL, start = list(ro=0.4, ko=8000, mu=0, sigma=1)) > summary(Bc.mle) > > ro3 <- coef(Bc.mle)[1] > ko3 <- coef(Bc.mle)[2] > > Be3 <- rep(NA, n) > Be3[1] <- ko3 * Ag > for ( k in 2:n) > Be3[k] <- Be3[k-1] + ro3 * a[k-1] * Be3[k-1] * (1 - Be3[k-1]/ko3) - > Ct[k-1] > > lines(x, Be3, col="red", lwd=2) > > > -- > > Héctor Villalobos <hector.villalobo...@gmail.com <javascript:;>> > > Depto. de Pesquerías y Biología Marina > > Centro Interdisciplinario de Ciencias Marinas-Instituto Politécnico > Nacional > > CICIMAR-I.P.N. > > A.P. 592. Colonia Centro > > La Paz, Baja California Sur, MÉXICO. 23000 > > Tels.: (+52 612) 122 53 44; 123 46 58; 123 47 34 ext.: 81602 > > Fax: (+52 612) 122 53 22 > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@r-project.org <javascript:;> 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. -- Bert Gunter "Data is not information. Information is not knowledge. And knowledge is certainly not wisdom." -- Clifford Stoll [[alternative HTML version deleted]] ______________________________________________ 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.