@phdthesis{Matuschek2015,
  author    = {Matuschek, Hannes},
  title     = {Applications of reproducing Kernel Hilbert spaces and their approximations},
  school      = {Universit{\"a}t Potsdam},
  pages     = {83},
  year      = {2015},
  language  = {en}
}
@article{MatuschekKlieglVasishthetal.2017,
  author    = {Matuschek, Hannes and Kliegl, Reinhold and Vasishth, Shravan and Baayen, Harald R. and Bates, Douglas},
  title     = {Balancing Type I error and power in linear mixed models},
  series = {Journal of memory and language},
  volume    = {94},
  journal   = {Journal of memory and language},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0749-596X},
  doi       = {10.1016/j.jml.2017.01.001},
  pages     = {305 -- 315},
  year      = {2017},
  abstract  = {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, Levy, Scheepers \& Tily, 2013), presumably to keep Type I error down to the nominal a 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. (C) 2017 The Authors. Published by Elsevier Inc.},
  language  = {en}
}
@article{ThomasMatuschekGrima2013,
  author    = {Thomas, Philipp and Matuschek, Hannes and Grima, Ramon},
  title     = {How reliable is the linear noise approximation of gene regulatory networks?},
  series = {BMC genomics},
  volume    = {14},
  journal   = {BMC genomics},
  number    = {4},
  publisher = {BioMed Central},
  address   = {London},
  issn      = {1471-2164},
  doi       = {10.1186/1471-2164-14-S4-S5},
  pages     = {15},
  year      = {2013},
  abstract  = {Background: The linear noise approximation (LNA) is commonly used to predict how noise is regulated and exploited at the cellular level. These predictions are exact for reaction networks composed exclusively of first order reactions or for networks involving bimolecular reactions and large numbers of molecules. It is however well known that gene regulation involves bimolecular interactions with molecule numbers as small as a single copy of a particular gene. It is therefore questionable how reliable are the LNA predictions for these systems. Results: We implement in the software package intrinsic Noise Analyzer (iNA), a system size expansion based method which calculates the mean concentrations and the variances of the fluctuations to an order of accuracy higher than the LNA. We then use iNA to explore the parametric dependence of the Fano factors and of the coefficients of variation of the mRNA and protein fluctuations in models of genetic networks involving nonlinear protein degradation, post-transcriptional, post-translational and negative feedback regulation. We find that the LNA can significantly underestimate the amplitude and period of noise-induced oscillations in genetic oscillators. We also identify cases where the LNA predicts that noise levels can be optimized by tuning a bimolecular rate constant whereas our method shows that no such regulation is possible. All our results are confirmed by stochastic simulations. Conclusion: The software iNA allows the investigation of parameter regimes where the LNA fares well and where it does not. We have shown that the parametric dependence of the coefficients of variation and Fano factors for common gene regulatory networks is better described by including terms of higher order than LNA in the system size expansion. This analysis is considerably faster than stochastic simulations due to the extensive ensemble averaging needed to obtain statistically meaningful results. Hence iNA is well suited for performing computationally efficient and quantitative studies of intrinsic noise in gene regulatory networks.},
  language  = {en}
}
@article{ThomasMatuschekGrima2012,
  author    = {Thomas, Philipp and Matuschek, Hannes and Grima, Ramon},
  title     = {Intrinsic noise analyzer A software package for the exploration of stochastic biochemical kinetics using the system size expansion},
  series = {PLoS one},
  volume    = {7},
  journal   = {PLoS one},
  number    = {6},
  publisher = {PLoS},
  address   = {San Fransisco},
  issn      = {1932-6203},
  doi       = {10.1371/journal.pone.0038518},
  pages     = {20},
  year      = {2012},
  abstract  = {The accepted stochastic descriptions of biochemical dynamics under well-mixed conditions are given by the Chemical Master Equation and the Stochastic Simulation Algorithm, which are equivalent. The latter is a Monte-Carlo method, which, despite enjoying broad availability in a large number of existing software packages, is computationally expensive due to the huge amounts of ensemble averaging required for obtaining accurate statistical information. The former is a set of coupled differential-difference equations for the probability of the system being in any one of the possible mesoscopic states; these equations are typically computationally intractable because of the inherently large state space. Here we introduce the software package intrinsic Noise Analyzer (iNA), which allows for systematic analysis of stochastic biochemical kinetics by means of van Kampen's system size expansion of the Chemical Master Equation. iNA is platform independent and supports the popular SBML format natively. The present implementation is the first to adopt a complementary approach that combines state-of-the-art analysis tools using the computer algebra system Ginac with traditional methods of stochastic simulation. iNA integrates two approximation methods based on the system size expansion, the Linear Noise Approximation and effective mesoscopic rate equations, which to-date have not been available to non-expert users, into an easy-to-use graphical user interface. In particular, the present methods allow for quick approximate analysis of time-dependent mean concentrations, variances, covariances and correlations coefficients, which typically outperforms stochastic simulations. These analytical tools are complemented by automated multi-core stochastic simulations with direct statistical evaluation and visualization. We showcase iNA's performance by using it to explore the stochastic properties of cooperative and non-cooperative enzyme kinetics and a gene network associated with circadian rhythms. The software iNA is freely available as executable binaries for Linux, MacOSX and Microsoft Windows, as well as the full source code under an open source license.},
  language  = {en}
}
@misc{HohensteinMatuschekKliegl2017,
  author    = {Hohenstein, Sven and Matuschek, Hannes and Kliegl, Reinhold},
  title     = {Linked linear mixed models: A joint analysis of fixation locations and fixation durations in natural reading},
  series = {Psychonomic bulletin \& review : a journal of the Psychonomic Society},
  volume    = {24},
  journal   = {Psychonomic bulletin \& review : a journal of the Psychonomic Society},
  publisher = {Springer},
  address   = {New York},
  issn      = {1069-9384},
  doi       = {10.3758/s13423-016-1138-y},
  pages     = {637 -- 651},
  year      = {2017},
  abstract  = {The complexity of eye-movement control during reading allows measurement of many dependent variables, the most prominent ones being fixation durations and their locations in words. In current practice, either variable may serve as dependent variable or covariate for the other in linear mixed models (LMMs) featuring also psycholinguistic covariates of word recognition and sentence comprehension. Rather than analyzing fixation location and duration with separate LMMs, we propose linking the two according to their sequential dependency. Specifically, we include predicted fixation location (estimated in the first LMM from psycholinguistic covariates) and its associated residual fixation location as covariates in the second, fixation-duration LMM. This linked LMM affords a distinction between direct and indirect effects (mediated through fixation location) of psycholinguistic covariates on fixation durations. Results confirm the robustness of distributed processing in the perceptual span. They also offer a resolution of the paradox of the inverted optimal viewing position (IOVP) effect (i.e., longer fixation durations in the center than at the beginning and end of words) although the opposite (i.e., an OVP effect) is predicted from default assumptions of psycholinguistic processing efficiency: The IOVP effect in fixation durations is due to the residual fixation-location covariate, presumably driven primarily by saccadic error, and the OVP effect (at least the left part of it) is uncovered with the predicted fixation-location covariate, capturing the indirect effects of psycholinguistic covariates. We expect that linked LMMs will be useful for the analysis of other dynamically related multiple outcomes, a conundrum of most psychonomic research.},
  language  = {en}
}
@inproceedings{KlieglMatuschekHolschneider2012,
  author    = {Kliegl, Reinhold and Matuschek, Hannes and Holschneider, Matthias},
  title     = {Multivariate analyses of fixation durations in reading with linear mixed and additive mixed models},
  series = {International journal of psychology},
  volume    = {47},
  booktitle = {International journal of psychology},
  number    = {33},
  publisher = {Wiley},
  address   = {Hove},
  issn      = {0020-7594},
  pages     = {139 -- 139},
  year      = {2012},
  language  = {en}
}
@article{MatuschekKliegl2017,
  author    = {Matuschek, Hannes and Kliegl, Reinhold},
  title     = {On the ambiguity of interaction and nonlinear main effects in a regime of dependent covariates},
  series = {Behavior research methods : a journal of the Psychonomic Society},
  volume    = {50},
  journal   = {Behavior research methods : a journal of the Psychonomic Society},
  number    = {5},
  publisher = {Springer},
  address   = {New York},
  issn      = {1554-351X},
  doi       = {10.3758/s13428-017-0956-9},
  pages     = {1882 -- 1894},
  year      = {2017},
  abstract  = {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.},
  language  = {en}
}
@article{MatuschekKlieglHolschneider2015,
  author    = {Matuschek, Hannes and Kliegl, Reinhold and Holschneider, Matthias},
  title     = {Smoothing Spline ANOVA Decomposition of Arbitrary Splines: An Application to Eye Movements in Reading},
  series = {PLoS one},
  volume    = {10},
  journal   = {PLoS one},
  number    = {3},
  publisher = {PLoS},
  address   = {San Fransisco},
  issn      = {1932-6203},
  doi       = {10.1371/journal.pone.0119165},
  pages     = {15},
  year      = {2015},
  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.},
  language  = {en}
}