R Programming/Maximum Likelihood

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Packages and functions :

• mle() in the "stats4" package
• The "maxLik" library
• fitdistr() in the "MASS" package for univariate problems
• nlm()
• optimize()
• optim()

If you need to program yourself your maximum likelihood estimator (MLE) you have to use one built-in optimizer such as nlm(), optim() or optimize(). optimize() is only available for one dimensional problems.

As an example we can write a simple maximum likelihood estimator for a Cauchy distribution using the nlm() optimizer. We first draw a vector x from a Cauchy distribution. Then we define the log likelihood function and then we optimize using the nlm() function.

Note that nlm() is minimizer and not a maximizer.

> n <- 100
> x <- rcauchy(n)
> mlog.1 <- function(mu, x) { 
+   sum(-dcauchy(x, location = mu, log = TRUE)) 
+   } 
> mu.start <- median(x)
> out <- nlm(mlog.1, mu.start, x = x) 
> out
$minimum
[1] 241.5354

$estimate
[1] -0.08364306

$gradient
[1] 6.423306e-06

$code
[1] 1

$iterations
[1] 2

Contents 1 Tests 1.1 Likelihood Ratio Test 2 Resources 3 References

[edit] Tests

[edit] Likelihood Ratio Test

• lrtest in the lmtest package^[1].

[edit] Resources

• Charles Geyer : Maximum Likelihood in R (pdf, 9 pages)
• Marco Steenbergen Maximum Likelihood Programming in R (pdf, 7 pages)
• Michael Ward : Maximum Likelihood

[edit] References

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Index

Next: Bayesian Methods