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.

Sliding into happiness: A new tool for measuring affective responses to words.

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The cave of shadows: Addressing the human factor with generalized additive mixed models

“…a strong interaction with Trial. The appendix reports two models, one with a single multivariate smooth for these two predictors, and one in which their joint effect is decomposed into separate, additive, main effects of Trial, Frequency, and their interaction (see also Matuschek et al, 2015). These three partial effects are presented in Figure 16.…”

Prevalence of spelling errors affects reading behavior across languages.

“…Instead, the GAMM enables a flexible smoothing of nonlinear relations in any number of dimensions. In a GAMM, multiple predictors may be combined into a single smooth term (often modeled as a tensor product), yielding either a nonlinear functional relationship (between one independent variable and a dependent variable), a wiggly surface (when two independent variables are combined) or a wiggly hypersurface (when three or more independent variables are combined) (e.g., Matuschek, Kliegl, & Holschneider, 2015). We opted for GAMM so as to avoid imposing a specific (linear) form on the relationship between critical predictors and outcomes.…”