title: Smoothing spline ANOVA decomposition of arbitrary splines: an application to eye movements in reading.
abstract: The Smoothing Spline ANOVA (SS-ANOVA) requires a specialized construction of basis and penalty terms in order to incorporate prior knowledge about the data to be fitted. Typically, one resorts to the most general approach using tensor product splines. This implies severe constraints on the correlation structure, i.e. the assumption of isotropy of smoothness can not be incorporated in general. This may increase the variance of the spline fit, especially if only a relatively small set of observations are given. In this article, we propose an alternative method that allows to incorporate prior knowledge without the need to construct specialized bases and penalties, allowing the researcher to choose the spline basis and penalty according to the prior knowledge of the observations rather than choosing them according to the analysis to be done. The two approaches are compared with an artificial example and with analyses of fixation durations during reading.
authors: Focus Area for Dynamics of Complex Systems, University of Potsdam, Karl-Liebknecht-Str. 24, D-14476 Potsdam, Germany; Department of Psychology, University of Potsdam, Karl-Liebknecht-Str. 24, D-14476 Potsdam, Germany.
authors: Hannes
authors: H
authors: Matuschek
authors: Department of Psychology, University of Potsdam, Karl-Liebknecht-Str. 24, D-14476 Potsdam, Germany.
authors: Reinhold
authors: R
authors: Kliegl
authors: Focus Area for Dynamics of Complex Systems, University of Potsdam, Karl-Liebknecht-Str. 24, D-14476 Potsdam, Germany.
authors: Matthias
authors: M
authors: Holschneider
mesh_terms: D000704:Analysis of Variance; D005133:Eye Movements; D005403:Fixation, Ocular; D006801:Humans; D009716:Numerical Analysis, Computer-Assisted; D011932:Reading