
R Under development (unstable) (2022-03-19 r81942) -- "Unsuffered Consequences"
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> pkgname <- "stats4"
> source(file.path(R.home("share"), "R", "examples-header.R"))
> options(warn = 1)
> library('stats4')
> 
> base::assign(".oldSearch", base::search(), pos = 'CheckExEnv')
> base::assign(".old_wd", base::getwd(), 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)
> 
> ## Simulated EC50 experiment with count data
> x <- 0:10
> y <- c(26, 17, 13, 12, 20, 5, 9, 8, 5, 4, 8)
> 
> ## Easy one-dimensional MLE:
> nLL <- function(lambda) -sum(stats::dpois(y, lambda, log = TRUE))
> fit0 <- mle(nLL, start = list(lambda = 5), nobs = NROW(y))
> 
> ## sanity check --- notice that "nobs" must be input
> ## (not guaranteed to be meaningful for any likelihood)
> stopifnot(nobs(fit0) == length(y))
> 
> 
> # For 1D, this is preferable:
> fit1 <- mle(nLL, start = list(lambda = 5), nobs = NROW(y),
+             method = "Brent", lower = 1, upper = 20)
> 
> ## 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, lower = rep(0, 2))

Call:
mle(minuslogl = ll2, 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
> (fit2 <- mle(ll2, lower = c(0, 0)))

Call:
mle(minuslogl = ll2, lower = c(0, 0))

Coefficients:
   ymax   xhalf 
24.9994  3.0558 
> plot(profile(fit2), absVal = FALSE)
> 
> ## A better parametrization:
> ll3 <- function(lymax = log(15), lxhalf = log(6))
+     -sum(stats::dpois(y, lambda = exp(lymax)/(1+x/exp(lxhalf)), log = TRUE))
> (fit3 <- mle(ll3))

Call:
mle(minuslogl = ll3)

Coefficients:
 lymax lxhalf 
3.2189 1.1170 
> plot(profile(fit3), absVal = FALSE)
> exp(confint(fit3))
Profiling...
         2.5 %  97.5 %
lymax  17.8815 34.6186
lxhalf  1.6615  6.4794
> 
> # Regression tests for bounded cases (this was broken in R 3.x)
> fit4 <- mle(ll, lower = c(0, 4)) # has max on boundary
> confint(fit4)
Profiling...
       2.5 %  97.5 %
ymax  17.446 26.5081
xhalf     NA  6.9109
> 
> ## direct check that fixed= and constraints work together
> mle(ll, lower = c(0, 4), fixed=list(ymax=23)) # has max on boundary

Call:
mle(minuslogl = ll, fixed = list(ymax = 23), lower = c(0, 4))

Coefficients:
 ymax xhalf 
   23     4 
> 
> ## Linear regression using MLE
> x <- 1:10 
> y <- c(0.48, 2.24, 2.22, 5.15, 4.64, 5.53, 7, 8.8, 7.67, 9.23)
> 
> LM_mll <- function(formula, data = environment(formula))
+ {
+      y <- model.response(model.frame(formula, data))
+      X <- model.matrix(formula, data)
+      b0 <- numeric(NCOL(X))
+      names(b0) <- colnames(X)
+      function(b=b0, sigma=1)
+          -sum(dnorm(y, X %*% b, sigma, log=TRUE))
+ }
> 
> mll <- LM_mll(y ~ x)
> 
> summary(lm(y~x)) # for comparison -- notice variance bias in MLE

Call:
lm(formula = y ~ x)

Residuals:
   Min     1Q Median     3Q    Max 
-0.937 -0.500 -0.211  0.278  1.273 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   0.0927     0.5376    0.17     0.87    
x             0.9461     0.0866   10.92  4.4e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.787 on 8 degrees of freedom
Multiple R-squared:  0.937,	Adjusted R-squared:  0.929 
F-statistic:  119 on 1 and 8 DF,  p-value: 4.39e-06

> summary(mle(mll, lower=c(-Inf,-Inf, 0.01)))
Maximum likelihood estimation

Call:
mle(minuslogl = mll, lower = c(-Inf, -Inf, 0.01))

Coefficients:
              Estimate Std. Error
b.(Intercept) 0.092667   0.480869
b.x           0.946061   0.077499
sigma         0.703919   0.157400

-2 log L: 21.357 
> summary(mle(mll, lower=list(sigma = 0.01))) # alternative specification
Maximum likelihood estimation

Call:
mle(minuslogl = mll, lower = list(sigma = 0.01))

Coefficients:
              Estimate Std. Error
b.(Intercept) 0.092667   0.480869
b.x           0.946061   0.077499
sigma         0.703919   0.157400

-2 log L: 21.357 
> 
> confint(mle(mll, lower=list(sigma = 0.01)))
Profiling...
                 2.5 % 97.5 %
b.(Intercept) -0.94831 1.1336
b.x            0.77829 1.1138
sigma          0.48017 1.1755
> plot(profile(mle(mll, lower=list(sigma = 0.01))))
> 
> Binom_mll <- function(x, n)
+ {
+     force(x); force(n) ## beware lazy evaluation
+     function(p=.5) -dbinom(x, n, p, log=TRUE)
+ }
> 
> ## Likelihood functions for different x.
> ## This code goes wrong, if force(x) is not used in Binom_mll:
> 
> curve(Binom_mll(0, 10)(p), xname="p", ylim=c(0, 10))
> mll_list <- list(10)
> for (x in 1:10)
+     mll_list[[x]] <- Binom_mll(x, 10)
> for (mll in mll_list)
+     curve(mll(p), xname="p", add=TRUE)
> 
> mll <- Binom_mll(4,10)
> mle(mll, lower = 1e-16, upper = 1-1e-16) # limits must be inside (0,1)

Call:
mle(minuslogl = mll, lower = 1e-16, upper = 1 - 1e-16)

Coefficients:
  p 
0.4 
> 
> ## Boundary case: This works, but fails if limits are set closer to 0 and 1  
> mll <- Binom_mll(0, 10)
> mle(mll, lower=.005, upper=.995)

Call:
mle(minuslogl = mll, lower = 0.005, upper = 0.995)

Coefficients:
    p 
0.005 
> 
> ## Not run: 
> ##D ## We can use limits closer to the boundaries if we use the
> ##D ## drop-in replacement optimr() from the optimx package.
> ##D 
> ##D mle(mll, lower = 1e-16, upper = 1-1e-16, optim=optimx::optimr)
> ## End(Not run)
> 
> 
> 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 stats::dpois(y, lambda = ymax/(1 + x/xhalf), log = TRUE) :
  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>
> ###
> cleanEx()
> options(digits = 7L)
> base::cat("Time elapsed: ", proc.time() - base::get("ptime", pos = 'CheckExEnv'),"\n")
Time elapsed:  2.16 0.024 2.2 0 0 
> grDevices::dev.off()
null device 
          1 
> ###
> ### Local variables: ***
> ### mode: outline-minor ***
> ### outline-regexp: "\\(> \\)?### [*]+" ***
> ### End: ***
> quit('no')