A note on bimodality in the log-likelihood function for penalized spline mixed models

A - Papers appearing in refereed journals

Welham, S. J. and Thompson, R. 2009. A note on bimodality in the log-likelihood function for penalized spline mixed models. Computational Statistics & Data Analysis. 53 (4), pp. 920-931. https://doi.org/10.1016/j.csda.2008.10.031

AuthorsWelham, S. J. and Thompson, R.

For a smoothing spline or general penalized spline model, the smoothing parameter can be estimated using residual maximum likelihood (REML) methods by expressing the spline in the form of a mixed model. The possibility of bimodality in the profile log-likelihood function for the smoothing parameter of these penalized spline mixed models is demonstrated. A canonical transformation into independent observations is used to provide efficient evaluation of the log-likelihood function and gives insight into the incompatibilities between the model and data that cause bimodality. This transformation can also be used to assess the influence of different frequency components in the data on the estimated smoothing parameter. It is demonstrated that, where bimodality occurs in the log-likelihood, Bayesian penalized spline models may show poor mixing in MCMC chains and be sensitive to the choice of prior distributions for variance components.

Year of Publication2009
JournalComputational Statistics & Data Analysis
Journal citation53 (4), pp. 920-931
Digital Object Identifier (DOI)https://doi.org/10.1016/j.csda.2008.10.031
Open accessPublished as non-open access
Funder project or codeCentre for Mathematical and Computational Biology (MCB)
Research in statistics relevant to biological processes
Output statusPublished
Publication dates
Online05 Nov 2008
Publication process dates
Accepted25 Oct 2008
Copyright licensePublisher copyright
PublisherElsevier Science Bv

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