TY  - GEN
A1  - Hohenstein, Sven
A1  - Matuschek, Hannes
A1  - Kliegl, Reinhold
T1  - Linked linear mixed models
BT  - a joint analysis of fixation locations and fixation durations in natural reading
T2  - Postprints der Universität Potsdam Humanwissenschaftliche Reihe
N2  - 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.
T3  - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - 552 
KW  - linear mixed model
KW  - model linkage
KW  - eye movements
KW  - reading
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-428281
SN  - 1866-8364
IS  - 552
ER  - 
TY  - JOUR
A1  - Sorensen, Tanner
A1  - Hohenstein, Sven
A1  - Vasishth, Shravan
T1  - Bayesian linear mixed models using Stan: A tutorial for psychologists, linguists, and cognitive scientists
JF  - Tutorials in Quantitative Methods for Psychology
N2  - With the arrival of the R packages nlme and lme4, linear mixed models (LMMs) have come to be widely used in experimentally-driven areas like psychology, linguistics, and cognitive science. This tutorial provides a practical introduction to fitting LMMs in a Bayesian framework using the probabilistic programming language Stan. We choose Stan (rather than WinBUGS or JAGS) because it provides an elegant and scalable framework for fitting models in most of the standard applications of LMMs. We ease the reader into fitting increasingly complex LMMs, using a two-condition repeated measures self-paced reading study.
KW  - Bayesian data analysis
KW  - linear mixed models
Y1  - 2016
U6  - https://doi.org/10.20982/tqmp.12.3.p175
SN  - 2292-1354
VL  - 12
SP  - 175
EP  - 200
PB  - University of Montreal, Department of Psychology
CY  - Montreal
ER  -