Agenda

Speaker: Ioannis Kosmidis, University of Warwick

The talk will also be available via Zoom https://unive.zoom.us/j/85153268624 
Meeting ID: 851 5326 8624
Passcode: SanMarco2

Abstract:
Maximum likelihood estimation in logistic regression with mixed effects is known to often result in estimates on the boundary of the parameter space. Such estimates, which include infinite values for fixed effects and singular or infinite variance components, can cause havoc to numerical estimation procedures and inference. We introduce an appropriately scaled additive penalty to the log-likelihood function, or an approximation thereof, which penalizes the fixed effects by the Jeffreys' invariant prior for the model with no random effects and the variance components by a composition of negative Huber loss functions. The resulting maximum penalized likelihood estimates are shown to lie in the interior of the parameter space. Appropriate scaling of the penalty guarantees that the penalization is soft enough to preserve the optimal asymptotic properties expected by the maximum likelihood estimator, namely consistency, asymptotic normality, and Cramér-Rao efficiency. Our choice of penalties and scaling factor preserves equivariance of the fixed effects estimates under linear transformation of the model parameters, such as contrasts. Maximum softly-penalized likelihood is compared to competing approaches on real-data examples, and through comprehensive simulation studies that illustrate its superior finite sample performance.

Joint work with: Philipp Sterzinger, University of Warwick

Relevant paper: https://doi.org/10.1007/s11222-023-10217-3

Bio Sketch:
Ioannis Kosmidis is Professor of Statistics in the Department of Statistics at the University of Warwick and Turing Fellow of The Alan Turing Institute, the UK’s national institute for data science and artificial intelligence. Ioannis' research interests include penalized and pseudo likelihood theory and methods, statistical computing and algorithms for regression models, methods for clustering, interdisciplinary data-analytic applications and software development.