Statistics Seminar: Ian Marschner - Macquarie University -- Constrained GLMs using combinatorial EM algorithms with biostatistical applications

Motivated by applications in biostatistics, I will discuss computational methods 
for various constrained generalized linear models (GLMs) in which the linear 
predictor cannot range over the entire real line. Common examples include the 
binomial model with log or identity link, and the Poisson model with identity 
link. These models are important in biostatistics for obtaining adjusted 
relative risks, risk differences and rate differences. I will begin by 
illustrating the surprisingly unstable iterative behavior exhibited by 
conventional GLM software (primarily using R). This instability stems from the 
fact that Fisher scoring may have a repelling fixed point for such 
non-canonical models, which can induce periodicity and chaos in the iterative 
sequence. I will then discuss a class of algorithms called combinatorial EM 
(CEM) algorithms, which are an extension of the standard EM algorithm. CEM 
algorithms provide a stable alternative to standard GLM algorithms and are 
particularly suited to semi-parametric extensions through generalized additive 
models. I will primarily use the log link binomial model as a case study, 
including some practical data analysis examples, but I will also mention how CEM 
algorithms apply to other models.