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Autoregressive Generalized Linear Mixed Effect Models with Crossed Random Effects: An Application to Intensive Binary Time Series Eye-Tracking Data

Published online by Cambridge University Press:  01 January 2025

Sun-Joo Cho ,
Sarah Brown-Schmidt  and
Woo-yeol Lee
Sun-Joo Cho*
Affiliation:
Vanderbilt University
Sarah Brown-Schmidt
Affiliation:
Vanderbilt University
Woo-yeol Lee
Affiliation:
Vanderbilt University
*
Correspondence should be made to Sun-Joo Cho, Vanderbilt University, Nashville, TN, USA. Email: sj.cho@vanderbilt.edu; URL: http://www.vanderbilt.edu/psychological_sciences/bio/sun-joo-cho
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Abstract

As a method to ascertain person and item effects in psycholinguistics, a generalized linear mixed effect model (GLMM) with crossed random effects has met limitations in handing serial dependence across persons and items. This paper presents an autoregressive GLMM with crossed random effects that accounts for variability in lag effects across persons and items. The model is shown to be applicable to intensive binary time series eye-tracking data when researchers are interested in detecting experimental condition effects while controlling for previous responses. In addition, a simulation study shows that ignoring lag effects can lead to biased estimates and underestimated standard errors for the experimental condition effects.

Keywords

eye-tracking datageneralized linear mixed effect modelintensive binary time series datarandom item effect

Information

Type
Original Paper
Information
Psychometrika , Volume 83 , Issue 3 , September 2018 , pp. 751 - 771
Copyright
Copyright © The Psychometric Society 2018

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References

Aitkin, M., &Alfó, M. (1998). Regression models for binary longitudinal responses. Statistics and Computing, 8,289–307.CrossRefGoogle Scholar
Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716–723.CrossRefGoogle Scholar
Baayen, R. H. ()2008). Analyzing linguistic data: A practical introduction to statistics using R.New York, NYCambridge University PressCrossRefGoogle Scholar
Baayen, R. H.,Davidson, D. J., &Bates, D. M. (2008). Mixed-effects modeling with crossed random effects for subjects and items. Journal of Memory and Language, 59,390–412.CrossRefGoogle Scholar
Barr, D. J. (2008). Analyzing ‘visual world’ eyetracking data using multilevel logistic regression. Journal of Memory and Language, 59,457–474.CrossRefGoogle Scholar
Bates, D.,Mächler, M., Bolker, B., &Walker, S. (2015). Fitting linear mixed-effects models using lme4. Journal of Statistical Software, 67,1–48.CrossRefGoogle Scholar
Bauer, D. J., &Cai, L. (2009). Consequences of unmodeled nonlinear effects in multilevel models. Journal of Educational and Behavioral Statistics, 34,97–114.CrossRefGoogle Scholar
Bisconti, T.,Bergeman, C. S., &Boker, S. M. (2004). Emotional well-being in recently bereaved windows: A dynamical system approach. Journal of Gerontology, Series, B: Psychological Sciences and Social Sciences, 59,158–167.CrossRefGoogle Scholar
Box, G. EP., &Jenkins, G. M. ()1976). Time series analysis: Forecasting and control.RevisedSan Francisco, CAHolden-DayGoogle Scholar
Bringmann, L. F.,Hamaker, E. L.,Vigo, D. E.,Aubert, A.,Borsboom, D., &Tuerlinckx, F. (2017). Changing dynamics: Time-varying autoregressive models using generalized additive modeling. Psychological Methods, 22,409–425.10.1037/met000008527668421CrossRefGoogle ScholarPubMed
Broadbent, D. E.,Cooper, P. F.,FitzGerald, P., &Parkes, K. R. (1982). The Cognitive Failures Questionnaire (CFQ) and its correlates. British Journal of Clinical Psychology, 21,1–16.CrossRefGoogle ScholarPubMed
Browne, M. W., &Nesselroade, J. R. (2005). Representing psychological processes with dynamic factor models: Some promising uses and extensions of ARMA time series model.Maydeu-Olivares, A.McArdle, J. J. Psychometrics: A festschrift to Roderick. P. McDonald, 415–452. Mahwah, NJLawrence Erlbaum Associates, Inc.Google Scholar
Brown-Schmidt, S., &Fraundorf, S. H. (2015). Interpretation of informational questions modulated by joint knowledge and intonational contours. Journal of Memory and Language, 84,49–74.CrossRefGoogle Scholar
Chatfield, C. ()2004). The analysis of time series: An introduction.6LondonChapman and Hall/CRCGoogle Scholar
Cho, S-J., &Rabe-Hesketh, S. (2011). Alternating imputation posterior estimation of models with crossed random effects. Computational Statistics and Data Analysis, 55,12–25.CrossRefGoogle Scholar
Cho, S.-J., Partchev, I., &De Boeck, P. (2012). Parameter estimation of multiple item profiles models. British Journal of Mathematical and Statistical Psychology, 65,438–466.CrossRefGoogle Scholar
Cho, S.-J., & De Boeck, P.. (in press). A note on N\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$N$$\end{document} in Bayesian information criterion (BIC) for item response models. Applied Psychological Measurement.Google Scholar
Cox, M. D. (1970). A mathematical model of the Indian Ocean. Deep Sea Research and Oceanographic Abstracts, 17,47–75.CrossRefGoogle Scholar
De Boeck, P. (2008). Random item IRT models. Psychometrika, 73,533–559.CrossRefGoogle Scholar
de Haan-Rietdijk, S.,Kuppens, P.,Bergeman, C. S.,Sheeber, L. B.Allen, N. B., &Hamaker, E. L. (2017). On the use of mixed Markov models for intensive longitudinal data. Multivariate Behavioral Research, 52,747–767.10.1080/00273171.2017.137036428956618CrossRefGoogle ScholarPubMed
Gelman, A., & Su, Y.-S. (2016). Arm: Data analysis using regression and multilevel/hierarchical models. R package version 1.9-3. Retrieved March 10, 2017, from https://CRAN.R-project.org/package=arm.Google Scholar
Greven, S., &Kneib, T. (2010). On the behaviour of marginal and conditional AIC in linear mixed models. Biometrika, 97,773–789.CrossRefGoogle Scholar
Hallett, P. E. (1986). Eye movement.Buff, K.,Kaufman, L., &Thomas, J. P. Handbook of perception and human performance, New York, NYWileyGoogle Scholar
Hanna, J. E., &Brennan, S. E. (2007). Speakers eye gaze disambiguates referring expressions early during face-to-face conversation. Journal of Memory and Language, 57,596–615.CrossRefGoogle Scholar
Hamaker, E. L., van Hattum, P.,Kuiper, R. M., &Hoijtink, H. (2011). Model selection based on information criteria in multilevel modeling.Hox, J., &Roberts, J. K. Handbook of advanced multilevel analysis, New York, NYTaylor & Francis 231–255.Google Scholar
Hamaker, E. L., &Grasman, R. P. (2014). To center or not to center? Investigating inertia with a multilevel autoregressive model. Frontiers in Psychology, 5,149225688215Google ScholarPubMed
Heagerty, P. J., &Zeger, S. L. (1998). Lorelogram: A regression approach to exploring dependence in longitudinal categorical responses. Journal of the American Statistical Association, 93,150–162.CrossRefGoogle Scholar
Heckman, J. J. (1981). The incidental parameters problem and the problem of initial condition in estimating a discrete time-discrete data stochastic process.Manski, C. F., &McFadden, D. L. Structural analysis of discrete data and econometric applications, Cambridge, MAMIT Press 179–195.Google Scholar
Heller, D.,Grodner, D., &Tanenhaus, M. K. (2008). The role of perspective in identifying domains of reference. Cognition, 108,831–836.CrossRefGoogle ScholarPubMed
Hsiao, C. ()2003). Analysis of Panel Data.2New YorkCambridge University PressCrossRefGoogle Scholar
Hung, Y.,Zarnitsyna, V.,Zhang, Y.,Zhu, C., &Wu, C. FJ. (2008). Binary time series modeling with application to adhesion frequency experiments. Journal of the American Statistical Association, 483,1248–1259.CrossRefGoogle Scholar
Irwin, D. E. (2004). Fixation location and fixation duration as indices of cognitive processing.Henderson, J., &Ferreira, F. The interface of language, vision, and action: Eye movements and the visual world.New York, NYPsychology Press 105–134.Google Scholar
Jaeger, T. F. (2008). Categorical data analysis: Away from ANOVAs (transformation or not) and towards logit mixed models. Journal of Memory and Language, 59,434–446.CrossRefGoogle ScholarPubMed
Joe, H. (2008). Accuracy of Laplace approximation for discrete response mixed models. Computational Statistics and Data Analysis, 52,5066–5074.CrossRefGoogle Scholar
Jongerling, J., Laurenceau, J. P., &Hamaker, E. L. (2015). A multilevel AR(1) model: Allowing for inter-individual differences in trait-scores, inertia, and innovation variance. Multivariate Behavioral Research, 50,334–349.CrossRefGoogle ScholarPubMed
Kaiser, E., &Trueswell, J. C. (2008). Interpreting pronouns and demonstratives in Finnish: Evidence for a form-specific approach to reference resolution. Language and Cognitive Processes, 23,709–748.CrossRefGoogle Scholar
Kaufmann, H. (1987). Regression models for nonstationary categorical time series: Asymptotic estimation theory. Annals of Statistics, 15,79–98.CrossRefGoogle Scholar
Liu, S. (2017). Person-specific versus multilevel autoregressive models: Accuracy in parameter estimates at the population and individual levels. British Journal of Mathematical and Statistical Psychology,. https://doi.org/10.1111/bmsp.12096.CrossRefGoogle ScholarPubMed
Maas, C. JM., &Hox, J. J. (2004). Robustness issues in multilevel regression analysis. Statistica Neerlandica, 58,127–137.CrossRefGoogle Scholar
McMurray, B.,Samelson, V. M.,Lee, S. H., &Tomblin, J. B. (2010). Individual differences in online spoken word recognition: Implications for SLI. Cognitive Psychology, 60,1–39.CrossRefGoogle ScholarPubMed
Mirman, D.,Dixon, J. A., aMagnuson, J. S. (2008). Statistical and computational models of the visual world paradigm: Growth curves and individual differences. Journal of Memory and Language, 59,475–494.CrossRefGoogle ScholarPubMed
Molenaar, P. (1985). A dynamic factor model for the analysis of multivariate time series. Psychometricka, 50,181–202.CrossRefGoogle Scholar
Molenaar, P., &Ram, N. (2009). Advances in dynamic factor analysis of psychological processes.Valsiner, J.,Molenaar, P.,Lyra, M., &Chaudhary, N. Dynamic process methodology in the social and developmental sciences, 255–268.New York, NYSpringerCrossRefGoogle Scholar
Molenberghs, G., &Verbeke, G. (2007). Likelihood ratio, score, and Wald tests in a constrained parameter space. The American Statistician, 61,22–27.CrossRefGoogle Scholar
Quené, H., &van den Bergh, H. (2008). Examples of mixed-effects modeling with crossed random effects and with binomial data. Journal of Memory and Language, 59,413–425.CrossRefGoogle Scholar
R Core Team. (2016). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Retrieved November 1, 2016, from https://www.R-project.org/.Google Scholar
Raaijmakers, J. GW.,Schrijnemakers, J. MC., &Gremmen, F. (1999). How to deal with the language-as-fixed-effect fallacy: Common misconceptions and alternative solutions. Journal of Memory and Language, 41,416–426.CrossRefGoogle Scholar
Rovine, M. J., &Walls, T. A. (2006). Multilevel autoregressive modeling of interindividual differences in the stability of a process.Walls, T. A., &Schafer, J. L. Models for intensive longitudinal data, 124–147.New York, NYOxford University PressCrossRefGoogle Scholar
Ryskin, R.,Benjamin, A.,Tullis, J., &Brown-Schmidt, S. (2015). Perspective-taking in comprehension, production, and memory: An individual differences approach. Journal of Experimental Psychology: General, 144,898–915.CrossRefGoogle ScholarPubMed
Ryskin, R. A.,Qi, Z.,Duff, M. C., &Brown-Schmidt, S. (2017). Verb biases are shaped through lifelong learning. Journal of Experimental Psychology: Learning, Memory, and Cognition, 43,5781–794.27762578Google ScholarPubMed
Salverda, A.,Kleinschmidt, D., &Tanenhaus, M. (2014). Immediate effects of anticipatory coarticulation in spoken-word recognition. Journal of Memory and Language, 71,145–163.CrossRefGoogle ScholarPubMed
Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6,461–464.CrossRefGoogle Scholar
Sedivy, J. C.,Tanenhaus, M. K.,Chambers, C. G., &Carlson, G. N. (1999). Achieving incremental semantic interpretation through contextual representation. Cognition, 71,109–147.CrossRefGoogle ScholarPubMed
Self, S. G., &Liang, K-Y. (1987). Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. Journal of the American Statistical Association, 82,605–610.CrossRefGoogle Scholar
Skrondal, A., & Rabe-Hesketh, S. (2014). Handling initial conditions and endogenous covariates in dynamic/transition models for binary data with unobserved heterogeneity. Journal of the Royal Statistical Society: Series C (Applied Statistics), 63,211–237.Google Scholar
Song, H.,&Zhang, Z. (2014). Analyzing multiple multivariate time series data using multilevel dynamic factor models. Multivariate Behavioral Research, 49,67–77.CrossRefGoogle ScholarPubMed
Tanenhaus, M. K.,Spivey-Knowlton, M. J.,Eberhard, K. M., &Sedivy, J. C. (1995). Integration of visual and linguistic information in spoken language comprehension. Science, 268,1632–1634.CrossRefGoogle ScholarPubMed
Unema, P. J. A.,Pannasch, S.,Joos, M., &Velichkovsky, B. M. (2005). Time course of information processing during scene perception: The relationship between saccade amplitude and fixation duration. Visual Cognition, 12,473–494.CrossRefGoogle Scholar
van Buuren, S. (1997). Fitting ARMA time series by structural equation models. Psychometrika, 62,215–236.CrossRefGoogle Scholar
van Rijn, P.,Dolan, C. V., &Molenaar, P. C. M. (2010). State space methods for item response modeling of multisubject time series.Molenaar, P. C. M.Newell, K. M. Individual pathways of change: Statistical models for analyzing learning and development, 125–151.Washington, DCAmerican Psychological AssociationCrossRefGoogle Scholar
Wang, X.,Berger, J. O., &Burdick, D. S. (2013). Bayesian analysis of dynamic item response models in educational testing. The Annals of Applied Statistics, 7,126–153.CrossRefGoogle Scholar
Yoon, S. O., &Brown-Schmidt, S. (2014). Adjusting conceptual pacts in three-party conversation. Journal of Experimental Psychology: Learning, Memory, and Cognition, 40,919–937.24707779Google ScholarPubMed