[R] optimization problem

[Bert Gunter]

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.Villalobos.O at 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
>
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>
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>
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>
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-- 
Bert Gunter

"Data is not information. Information is not knowledge. And knowledge is
certainly not wisdom."
   -- Clifford Stoll

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