maxLik: A package for maximum likelihood estimation

Arne Henningsen and Ott Toomet have a new paper in Computational Statistics. The paper isn't directly related to multi-state modelling, but rather is on their package, maxLik, for general maximum likelihood estimation. Primarily their package is a wrapper for existing optimization packages in R such as optim and nlm. However, they do in addition provide an implementation of the BHHH (Berndt, Hall, Hall and Hausman) algorithm. This is a quasi-Newton algorithm in a similar vein to Fisher scoring, but rather than use the Expected Fisher information, it uses the mean of the outer product of the scores of each observation. Like the BFGS algorithm, a line search is performed to find the step length at each iteration.

For panel observed Markov multi-state models the Fisher scoring algorithm proposed by Kalbfleisch and Lawless (1985, JASA) and generalised by Gentleman et al (1994, Stat Med) is superior to BHHH. However, for data with a mixture of panel observed observations and exact times of absorption (e.g. death), the Fisher scoring algorithm cannot be applied. Here BHHH seems to perform significantly better than the BFGS algorithm supplying first derivatives.