Penalized Spline Smoothing and Generalized Linear Mixed Models - Some Theory and Applications
by Prof. GÃ¶ran Kauermann
Abstract: Penalized spline fitting as smoothing technique has become more and more popular over the last years. Labelled by Eilers & Marx (1996, Statistical Science) with the phrase P-spline smoothing, the recent book by Ruppert, Wand & Carroll (2003, Semiparametric Regression, Cambridge University Press) has shown the real practical benefits of this approach. In particular, it is the link between smoothing and Linear Mixed Models which makes the procedure so attractive, both, in terms of theory and practice. In fact, P-spline estimates are equivalent to posterior Bayes estimates in a Linear Mixed Model where the spline basis coefficients are treated as normally distributed. This connection can be exploited for smoothing parameter selection.
The presentation shows some theoretical results in this matter. A particular focus is on smoothing parameter selection in the presence of correlated residuals. It is well known that this is a delicate issue (see Opsomer, Wang & Yang, 2001, Statistical Science) and standard smoothing parameter selection routines tend to overfit the data. We show, however, that the link to Mixed Models circumvents this problem and data driven smoothing parameter selection works fine.
Further results will be provided based on non normal models in a generalized regression model style. This in turn builds a connection to duration time models.
For More Information: Owen Jones tel. 8344-6412 email: email@example.com