Dear R users, I'im trying to find the parameters of a dynamic biomass model using maximum likelihood estimation. I used two approaches, one by hand, with optim() function and the other using mle2() function from package bbmle. My problem is that the results change a lot depending on the initial values... I can't see what I am doing wrong...
Thank you for any help! # 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> 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 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.