In electro/psychophysiological experiments, linear mixed-effect modeling is an effective statistical technique for data repeatedly observed from the same experimental participants or stimulus items. This review describes the application of mixed-effect modeling to functional responses, in particular those observed in event-related EEG or MEG experiments, using a discrete wavelet transform. The technique is illustrated with a design with several covariates, and procedures for generating posterior samples and computing a Bayesian false discovery rate are described.
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References
G. D. Dawson, A summation technique for detecting small signals in a large irregular background,” J. Physiol., 115, 2 (1951).
T. C. Handy, Event-Related Potentials: A Methods Handbook, MIT Press, Cambridge (2004).
L. Sornmo and P. Laguna, Bioelectric Signal Processing in Cardiac and Neurological Applications, Elsevier, Academic Press, Amsterdam (2005).
J. C. Pinheiro and D. M. Bates, Mixed-Effects Models in S and S-Plus, Springer, Berlin (2000).
H. Baayen, D. J. Davidson, and D. Bates, “Mixed-effects modeling with crossed random effects for subjects and items,” J. Memory Language, 59, 390–412 (2008).
J. S. Morris and R. J. Carroll, “Wavelet-based functional mixed models,” J. Roy. Stat. Soc. Ser. B, 68, 179–199 (2006).
S. G. Mallat, “A theory for multiresolution signal decomposition: The wavelet representation,” IEEE Trans. Pattern Anal. Machine Intell., 11, 674–693 (1989).
D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis, Cambridge Univ. Press, Cambridge (2000).
B. Vidakovic, Statistical Modeling by Wavelets, Wiley, New York (1999).
A. Bruns, “Fourier-, Hilbert- and wavelet-based signal analysis: Are they really different approaches?” J. Neurosci. Methods, 137, 321–332 (2004).
M. K. van Vugt, P. B. Sederberg, and M. J. Kahana, “Comparison of spectral analysis methods for characterizing brain oscillations,” J. Neurosci. Methods, 162, 49–63 (2007).
V. J. Samar, K. P. Swartz, M. R. Raghuveer, “Multiresolution analysis of event-related potentials by wavelet decomposition,” Brain Cognition, 27, 398–438 (1995).
O. Bertrand, J. Bohorquez, and J. Pernier, “Time-frequency digital filtering based on an invertible wavelet transform: An application to evoked potentials,” IEEE Trans. Biomed. Eng., 41, 77–88 (1994).
E. A. Bartnik, K. J. Blinowska, P. J. Durka, “Single evoked potential reconstruction by means of wavelet transform,” Biol. Cybern., 67, 175–181 (1992).
N. V. Thakor, G. Xin-Rong, S. Yi-Chun, and D. F. Hanley, “Multiresolution wavelet analysis of evoked potentials,” IEEE Trans. Biomed. Eng., 40, 1085–1094 (1993).
T. Demiralp, J. Yordanova, V. Kolev, et al., “Time-frequency analysis of single-sweep event-related potentials by means of fast wavelet transform,” Brain Language, 66, 129–145 (1999).
S. J. Kiebel and K. J. Friston, “Statistical parametric mapping for event-related potentials (II): A hierarchical temporal model,” Neuroimage, 22, 503–520 (2004).
J. Raz, B. I. Turetsky, and L. W. Dickerson, “Inference for a random wavelet packet model of single-channel event-related potentials,” J. Am. Statist. Assoc., 96, 409–420 (2001).
X. F. Wang, Q. Yang, Z. Fan, et al., “Assessing time- dependent association between scalp EEG and muscle activation: A functional random-effects model approach,” J. Neurosci. Methods, 177, 232–240 (2009).
D. L. Donoho and I. M. Johnstone, “Minimax estimation via wavelet shrinkage,” Annu. Statistics, 26, 879–921 (1998).
R. Quian Quiroga and H. Garcia, “Single-trial event-related potentials with wavelet denoising,” Clin. Neurophysiol., 114, 376–390 (2003).
Z. Wang, A. Maier, D. A. Leopold, et al., “Single-trial evoked potential estimation using wavelets,” Comput. Biol. Med., 37, 463–473 (2007).
A. Effern, K. Lehnertz, T. Grunwald, et al., “Time adaptive denoising of single trial event-related potentials in the wavelet domain,” Psychophysiology, 37, 859–865 (2000).
A. Effern, K. Lehnertz, G. Fernandez, et al., “Single trial analysis of event-related potentials: Non-linear denoising with wavelets,” Clin. Neurophysiol., 111, 2255–2263 (2000).
A. Effern, K. Lehnertz, T. Schreiber, et al., “Nonlinear denoising of transient signal with application to event related potentials,” Physica D, 140, 257–266 (2000c).
B. M. Sayers, H. A. Beagley, and W. R. Henshall, “The mechanism of auditory evoked EEG responses,” Nature, 247, 481–483 (1974).
E. Basar, EEG-Brain Dynamics: Relation between EEG and Brain Evoked Potentials, Elsevier, New York (1980).
O. Hauk and F. Pulvermüller, “Effects of word length and frequency on the human event-related potential,” Clin. Neurophysiol., 115, 1090–1103 (2004).
O. Hauk, M. H. Davis, M. Ford, et al., “The time course of visual word recognition as revealed by linear regression analysis of ERP data,” Neuroimage, 30, 1383–1400 (2006).
S. G. Costafreda, G. J. Barker, and M. J. Brammer, “Bayesian wavelet-based analysis of functional magnetic resonance time series,” Magn. Res. Imaging, Nov. 5 (2008).
M. J. Fadili and E. T. Bullmore, “A comparative evaluation of wavelet-based methods for hypothesis testing of brain activation maps,” Neuroimage, 23, 1112–1128 (2004).
L. Sendur, J. Suckling, B. Whitcher, and E. Bullmore, “Resampling methods for improved wavelet-based multiple hypothesis testing of parametric maps in functional MRI,” Neuroimage, 37, 1186–1194 (2007).
G. A. Miller, W. Lutzenberger, and R. Ulrich, “A jackknife-based method for measuring LRP onset latency differences,” Psychophysiology, 35, 99–115 (1998).
D. Guthrie and J. S. Buchwald, “Significance testing of difference potentials,” Psychophysiology, 28, 240–244 (1991).
R. C. Blair and W. Karniski, “An alternative method for significance testing of waveform difference potentials,” Psychophysiology, 30, 518–524 (1993).
A. Achim, “Signal detection in averaged evoked potentials: Monte Carlo comparison of the sensitivity of different methods,” Electroencephalogr. Clin. Neurophysiol., 96, 574–584 (1995).
E. Maris and R. Oostenveld, “Nonparametric statistical testing of EEG- and MEG-data,” J. Neurosci. Methods, 164, 177–190 (2007).
N. Laird and J. H. Ware, “Random-effects models for longitudinal data,” Biometrics, 38, 963–974 (1982).
W. S. Guo, “Functional mixed effect models,” Biometrics, 58, 121–128 (2002).
A. Antoniadis and T. Sapatinas, “Estimation and inference in functional mixed-effects models,” Comput. Stat. Data Anal., 51, 4793–4813 (2007).
F. Abramovich, A. Antoniadis, T. Sapatinas, and B. Vidakovic, “Optimal testing in a fixed effects functional analysis of variance model,” Int. J. Wavelets, Multiresolution Inform. Proc., 2, 323–349 (2004).
C. Bugli and P. Lambert, “Functional ANOVA with random functional effects: an application to event-related potentials modeling for electroencephalograms analysis,” Stat. Med., 25, 3718–3739 (2006).
A. P. Dawid, “Some matrix-variate distribution theory: Notational considerations and a Bayesian application,” Biometrika, 68, 265–274 (1981).
J. S. Morris, P. J. Brown, R. C. Herrick, et al., “Bayesian analysis of mass spectrometry proteomic data using wavelet based functional mixed models,” Biometrics, 64, 479–489 (2008).
D. J. Davidson and P. Indefrey, “An inverse relation between event-related and time-frequency violation responses in sentence processing,” Brain Res., 1158, 81–92 (2007).
M. Kutas and S. A. Hillyard, “Reading senseless sentences: Brain potentials reflect semantic incongruity,” Science, 207, 203–205 (1980).
R. H. Baayen, R. Piepenbrock, and L. Gulikers, The CELEX Lexical Functional mixed effects 27 Database (Release 2) [CD-ROM], Philadelphia, PA: Linguistic Data Consortium, University of Pennsylvania [Distributor]. (1995).
G. W. Wornell, Signal Processing with Fractals: A Wavelet-Based Approach, Upper Saddle River, NJ, Prentice-Hall. (1996).
E. Bullmore, C. Long, J. Suckling, J., et al., “Colored noise and computational inference in neurophysiological (fMRI) time series analysis: Resampling methods in time and wavelet domains,” Human Brain Mapping, 12, 61–78 (2001).
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Neirofiziologiya/Neurophysiology, Vol. 41, No. 1, pp. 79–87, January–February, 2009.
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Davidson, D.J. Functional Mixed-Effect Models for Electrophysiological Responses. Neurophysiology 41, 71–79 (2009). https://doi.org/10.1007/s11062-009-9079-y
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DOI: https://doi.org/10.1007/s11062-009-9079-y