arXiv subjects

Reinhold Kliegl

Publications and source records attributed to Reinhold Kliegl.

7 recordsLinked to original sources

arXiv2019

How to capitalize on a priori contrasts in linear (mixed) models: A tutorial

Factorial experiments in research on memory, language, and in other areas are often analyzed using analysis of variance (ANOVA). However, for effects with more than one numerator degrees of freedom, e.g., for experimental factors with more than two levels, the ANOVA omnibus F-test is not informative about the source of a main effect or interaction. Because researchers typically have specific hypotheses about which condition means differ from each other, a priori contrasts (i.e., comparisons planned before the sample means are known) between specific conditions or combinations of conditions are the appropriate way to represent such hypotheses in the statistical model. Many researchers have pointed out that contrasts should be "tested instead of, rather than as a supplement to, the ordinary `omnibus' F test" (Hays, 1973, p. 601). In this tutorial, we explain the mathematics underlying different kinds of contrasts (i.e., treatment, sum, repeated, polynomial, custom, nested, interaction contrasts), discuss their properties, and demonstrate how they are applied in the R System for Statistical Computing (R Core Team, 2018). In this context, we explain the generalized inverse which is needed to compute the coefficients for contrasts that test hypotheses that are not covered by the default set of contrasts. A detailed understanding of contrast coding is crucial for successful and correct specification in linear models (including linear mixed models). Contrasts defined a priori yield far more useful confirmatory tests of experimental hypotheses than standard omnibus F-test. Reproducible code is available from https://osf.io/7ukf6/.

stat.ME↗

arXiv2018

Parsimonious Mixed Models

The analysis of experimental data with mixed-effects models requires decisions about the specification of the appropriate random-effects structure. Recently, Barr, Levy, Scheepers, and Tily, 2013 recommended fitting `maximal' models with all possible random effect components included. Estimation of maximal models, however, may not converge. We show that failure to converge typically is not due to a suboptimal estimation algorithm, but is a consequence of attempting to fit a model that is too complex to be properly supported by the data, irrespective of whether estimation is based on maximum likelihood or on Bayesian hierarchical modeling with uninformative or weakly informative priors. Importantly, even under convergence, overparameterization may lead to uninterpretable models. We provide diagnostic tools for detecting overparameterization and guiding model simplification.

stat.ME↗

arXiv2017

On the Ambiguity of Interaction and Nonlinear Main Effects in a Regime of Dependent Covariates

The analysis of large experimental datasets frequently reveals significant interactions that are difficult to interpret within the theoretical framework guiding the research. Some of these interactions actually arise from the presence of unspecified nonlinear main effects and statistically dependent covariates in the statistical model. Importantly, such nonlinear main effects may be compatible (or, at least, not incompatible) with the current theoretical framework. In the present literature this issue has only been studied in terms of correlated (linearly dependent) covariates. Here we generalize to nonlinear main effects (i.e., main effects of arbitrary shape) and dependent covariates. We propose a novel nonparametric method to test for ambiguous interactions where present parametric methods fail. We illustrate the method with a set of simulations and with reanalyses (a) of effects of parental education on their children's educational expectations and (b) of effects of word properties on fixation locations during reading of natural sentences, specifically of effects of length and morphological complexity of the word to be fixated next. The resolution of such ambiguities facilitates theoretical progress.

stat.AP↗

arXiv2017

Balancing Type I Error and Power in Linear Mixed Models

Linear mixed-effects models have increasingly replaced mixed-model analyses of variance for statistical inference in factorial psycholinguistic experiments. Although LMMs have many advantages over ANOVA, like ANOVAs, setting them up for data analysis also requires some care. One simple option, when numerically possible, is to fit the full variance-covariance structure of random effects (the maximal model; Barr et al. 2013), presumably to keep Type I error down to the nominal alpha in the presence of random effects. Although it is true that fitting a model with only random intercepts may lead to higher Type I error, fitting a maximal model also has a cost: it can lead to a significant loss of power. We demonstrate this with simulations and suggest that for typical psychological and psycholinguistic data, higher power is achieved without inflating Type I error rate if a model selection criterion is used to select a random effect structure that is supported by the data.

stat.AP↗

arXiv2016

The cave of Shadows. Addressing the human factor with generalized additive mixed models

Generalized additive mixed models are introduced as an extension of the generalized linear mixed model which makes it possible to deal with temporal autocorrelational structure in experimental data. This autocorrelational structure is likely to be a consequence of learning, fatigue, or the ebb and flow of attention within an experiment (the `human factor'). Unlike molecules or plots of barley, subjects in psycholinguistic experiments are intelligent beings that depend for their survival on constant adaptation to their environment, including the environment of an experiment. Three data sets illustrate that the human factor may interact with predictors of interest, both factorial and metric. We also show that, especially within the framework of the generalized additive model, in the nonlinear world, fitting maximally complex models that take every possible contingency into account is ill-advised as a modeling strategy. Alternative modeling strategies are discussed for both confirmatory and exploratory data analysis.

stat.AP↗

arXiv2016

A Semiparametric Model for Bayesian Reader Identification

We study the problem of identifying individuals based on their characteristic gaze patterns during reading of arbitrary text. The motivation for this problem is an unobtrusive biometric setting in which a user is observed during access to a document, but no specific challenge protocol requiring the user's time and attention is carried out. Existing models of individual differences in gaze control during reading are either based on simple aggregate features of eye movements, or rely on parametric density models to describe, for instance, saccade amplitudes or word fixation durations. We develop flexible semiparametric models of eye movements during reading in which densities are inferred under a Gaussian process prior centered at a parametric distribution family that is expected to approximate the true distribution well. An empirical study on reading data from 251 individuals shows significant improvements over the state of the art.

cs.LG↗

arXiv2004

Scaling of Horizontal and Vertical Fixational Eye Movements

Eye movements during fixation of a stationary target prevent the adaptation of the photoreceptors to continuous illumination and inhibit fading of the image. These random, involuntary, small, movements are restricted at long time scales so as to keep the target at the center of the field of view. Here we use the Detrended Fluctuation Analysis (DFA) in order to study the properties of fixational eye movements at different time scales. Results show different scaling behavior between horizontal and vertical movements. When the small ballistics movements, i.e. micro-saccades, are removed, the scaling exponents in both directions become similar. Our findings suggest that micro-saccades enhance the persistence at short time scales mostly in the horizontal component and much less in the vertical component. This difference may be due to the need of continuously moving the eyes in the horizontal plane, in order to match the stereoscopic image for different viewing distance.

cond-mat.stat-mech↗