Penalized likelihood inference for mixed-effects models

Mixed-effects models are an extension to standard regression models, designed to allow for the dependence between observations which may be induced by latent effects not explained by the observed covariates. These models are used extensively across ecology, social science and medical applications, and often maximum likelihood methods are used to conduct inference about the model parameters. While this approach is well-justified by asymptotic arguments, in some practical settings the amount of information available about some of the parameters is not sufficiently large for this approach to work well. For example, in some settings, the maximum likelihood estimate might not be finite, or the actual coverage of confidence intervals might be far from the nominal level.

This PhD project will identify types of models for which standard maximum likelihood inference performs badly, and develop methods to improve the quality of inference for these models. In standard regression models, inference conducted by using a penalized version of the likelihood has been successful in avoiding some of these problems and improving the statistical properties of the inference, and this project will develop penalties to replicate this success for mixed-effect models. The link with prior distributions for Bayesian inference in these models could also be investigated. In addition to the theoretical and methodological elements, a key part of this project will be to write code in R to implement new methods, to allow them to be used in practice across a wide range of disciplines.

ENQUIRIES: For more information, contact Dr Helen Ogden ([Email Address Removed]).