[R] optimization problem

[Berend Hasselman]

Your model is producing -Inf entries in the vector Be (in function modl and LL) at some stage during the optimization process.
You should first do something about that before anything else.

Berend


> On 17 Oct 2015, at 03:01, Bert Gunter <bgunter.4567 at gmail.com> wrote:
> 
> 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
>> 
>> 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 at 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 at 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.