R version 2.13.0 Under development (unstable) (2011-02-26 r54603)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> pkgname <- "stats4"
> source(file.path(R.home("share"), "R", "examples-header.R"))
> options(warn = 1)
> library('stats4')
> 
> assign(".oldSearch", search(), pos = 'CheckExEnv')
> cleanEx()
> nameEx("mle")
> ### * mle
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: mle
> ### Title: Maximum Likelihood Estimation
> ### Aliases: mle
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Avoid printing to unwarranted accuracy
> od <- options(digits = 5)
> x <- 0:10
> y <- c(26, 17, 13, 12, 20, 5, 9, 8, 5, 4, 8)
> ## This needs a constrained parameter space: most methods will accept NA
> ll <- function(ymax = 15, xhalf = 6)
+     if(ymax > 0 && xhalf > 0) -sum(stats::dpois(y, lambda=ymax/(1+x/xhalf), log=TRUE)) else NA
> (fit <- mle(ll, nobs=length(y)))

Call:
mle(minuslogl = ll, nobs = length(y))

Coefficients:
   ymax   xhalf 
24.9931  3.0571 
> mle(ll, fixed=list(xhalf=6))

Call:
mle(minuslogl = ll, fixed = list(xhalf = 6))

Coefficients:
  ymax  xhalf 
19.288  6.000 
> ## alternative using bounds on optimization
> ll2 <- function(ymax=15, xhalf=6)
+     -sum(stats::dpois(y, lambda=ymax/(1+x/xhalf), log=TRUE))
> mle(ll2, method = "L-BFGS-B", lower = rep(0, 2))

Call:
mle(minuslogl = ll2, method = "L-BFGS-B", lower = rep(0, 2))

Coefficients:
   ymax   xhalf 
24.9994  3.0558 
> 
> AIC(fit)
[1] 61.208
> BIC(fit)
[1] 62.004
> 
> summary(fit)
Maximum likelihood estimation

Call:
mle(minuslogl = ll, nobs = length(y))

Coefficients:
      Estimate Std. Error
ymax   24.9931     4.2244
xhalf   3.0571     1.0348

-2 log L: 57.208 
> logLik(fit)
'log Lik.' -28.604 (df=2)
> vcov(fit)
         ymax   xhalf
ymax  17.8459 -3.7206
xhalf -3.7206  1.0708
> plot(profile(fit), absVal = FALSE)
> confint(fit)
Profiling...
        2.5 %  97.5 %
ymax  17.8845 34.6194
xhalf  1.6616  6.4792
> 
> ## use bounded optimization
> ## the lower bounds are really > 0, but we use >=0 to stress-test profiling
> (fit1 <- mle(ll, method = "L-BFGS-B", lower = c(0, 0)))

Call:
mle(minuslogl = ll, method = "L-BFGS-B", lower = c(0, 0))

Coefficients:
   ymax   xhalf 
24.9994  3.0558 
> plot(profile(fit1), absVal=FALSE)
> 
> ## a better parametrization:
> ll2 <- function(lymax = log(15), lxhalf = log(6))
+     -sum(stats::dpois(y, lambda=exp(lymax)/(1+x/exp(lxhalf)), log=TRUE))
> (fit2 <- mle(ll2))

Call:
mle(minuslogl = ll2)

Coefficients:
 lymax lxhalf 
3.2189 1.1170 
> plot(profile(fit2), absVal = FALSE)
> exp(confint(fit2))
Profiling...
         2.5 %  97.5 %
lymax  17.8815 34.6186
lxhalf  1.6615  6.4794
> 
> options(od)
> 
> 
> 
> cleanEx()
> nameEx("update-methods")
> ### * update-methods
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: update-methods
> ### Title: Methods for Function 'update' in Package 'stats4'
> ### Aliases: update-methods update,ANY-method update,mle-method
> ### Keywords: methods
> 
> ### ** Examples
> 
> x <- 0:10
> y <- c(26, 17, 13, 12, 20, 5, 9, 8, 5, 4, 8)
> ll <- function(ymax=15, xhalf=6)
+     -sum(stats::dpois(y, lambda=ymax/(1+x/xhalf), log=TRUE))
> fit <- mle(ll)
Warning in dpois(x, lambda, log) : NaNs produced
> ## note the recorded call contains ..1, a problem with S4 dispatch
> update(fit, fixed=list(xhalf=3))

Call:
mle(minuslogl = ll, fixed = ..1)

Coefficients:
    ymax    xhalf 
25.19609  3.00000 
> 
> 
> 
> ### * <FOOTER>
> ###
> cat("Time elapsed: ", proc.time() - get("ptime", pos = 'CheckExEnv'),"\n")
Time elapsed:  1.945 0.014 1.966 0 0 
> grDevices::dev.off()
null device 
          1 
> ###
> ### Local variables: ***
> ### mode: outline-minor ***
> ### outline-regexp: "\\(> \\)?### [*]+" ***
> ### End: ***
> quit('no')