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

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  • Sun-Joo Cho

    (Vanderbilt University)

  • Sarah Brown-Schmidt

    (Vanderbilt University)

  • Woo-yeol Lee

    (Vanderbilt University)

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.

Suggested Citation

  • Sun-Joo Cho & Sarah Brown-Schmidt & Woo-yeol Lee, 2018. "Autoregressive Generalized Linear Mixed Effect Models with Crossed Random Effects: An Application to Intensive Binary Time Series Eye-Tracking Data," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 751-771, September.
    • Handle: RePEc:spr:psycho:v:83:y:2018:i:3:d:10.1007_s11336-018-9604-2
    DOI: 10.1007/s11336-018-9604-2
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    References listed on IDEAS

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    1. Anders Skrondal & Sophia Rabe-Hesketh, 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, Royal Statistical Society, vol. 63(2), pages 211-237, February.
    2. Bates, Douglas & Mächler, Martin & Bolker, Ben & Walker, Steve, 2015. "Fitting Linear Mixed-Effects Models Using lme4," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 67(i01).
    3. Cho, S.-J. & Rabe-Hesketh, S., 2011. "Alternating imputation posterior estimation of models with crossed random effects," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 12-25, January.
    4. Cora J. M. Maas & Joop J. Hox, 2004. "Robustness issues in multilevel regression analysis," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(2), pages 127-137, May.
    5. Toni L. Bisconti & C. S. Bergeman & Steven M. Boker, 2004. "Emotional Well-Being in Recently Bereaved Widows: A Dynamical Systems Approach," The Journals of Gerontology: Series B, The Gerontological Society of America, vol. 59(4), pages 158-167.
    6. Molenberghs, Geert & Verbeke, Geert, 2007. "Likelihood Ratio, Score, and Wald Tests in a Constrained Parameter Space," The American Statistician, American Statistical Association, vol. 61, pages 22-27, February.
    7. Hung, Ying & Zarnitsyna, Veronika & Zhang, Yan & Zhu, Cheng & Wu, C. F. Jeff, 2008. "Binary Time Series Modeling With Application to Adhesion Frequency Experiments," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1248-1259.
    8. Joe, Harry, 2008. "Accuracy of Laplace approximation for discrete response mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5066-5074, August.
    9. Peter Molenaar, 1985. "A dynamic factor model for the analysis of multivariate time series," Psychometrika, Springer;The Psychometric Society, vol. 50(2), pages 181-202, June.
    10. Ludwig Fahrmeir & Heinz Kaufmann, 1987. "Regression Models For Non‐Stationary Categorical Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(2), pages 147-160, March.
    11. Paul Boeck, 2008. "Random Item IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 533-559, December.
    12. Sonja Greven & Thomas Kneib, 2010. "On the behaviour of marginal and conditional AIC in linear mixed models," Biometrika, Biometrika Trust, vol. 97(4), pages 773-789.
    13. Daniel J. Bauer & Li Cai, 2009. "Consequences of Unmodeled Nonlinear Effects in Multilevel Models," Journal of Educational and Behavioral Statistics, , vol. 34(1), pages 97-114, March.
    14. Stef Buuren, 1997. "Fitting arma time series by structural equation models," Psychometrika, Springer;The Psychometric Society, vol. 62(2), pages 215-236, June.
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    Cited by:

    1. Sun-Joo Cho & Sarah Brown-Schmidt & Paul De Boeck & Jianhong Shen, 2020. "Modeling Intensive Polytomous Time-Series Eye-Tracking Data: A Dynamic Tree-Based Item Response Model," Psychometrika, Springer;The Psychometric Society, vol. 85(1), pages 154-184, March.
    2. Michel Wedel & Rik Pieters & Ralf Lans, 2023. "Modeling Eye Movements During Decision Making: A Review," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 697-729, June.

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