Robust Functional Mixed Models for Spatially Correlated Fun - PowerPoint Presentation

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Robust Functional Mixed Models for Spatially Correlated Functional Regression-- with Application to Event-Related Potentials for Nicotine-Addicted Individuals

Hongxiao ZhuVirginia TechJune 15, 2015 ICSA/Graybill 2015Collaborated with Francesco Versace, Paul Cinciripini, Jeffrey S. Morris

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ERP data in a smoking cessation study.Review existing methods.Proposed approach.ERP analysis results.OutlineSlide3

The Event-related potentials (ERPs) data ERPs : electrophysiological signals recorded from human’s scalp surface.

Obtained by averaging over electroencephalogram (EEG) measurements. Visual stimuli is often presented during experiment. 3EEG trajectoriesERP signal

EEG experiments

Visual StimulusSlide4

The ERP data for Nicotine-Addicted Individuals180 smokers

4 stimuli: Cigarettes, Neutral, Pleasant, Unpleasant. 129 electrodes (channels). Total number of ERP signals: 180X4X129 = 92880 — crossed design. Each ERP curve: 225 time points range from -100 to 800 ms. Goal: detect systematic differences among different visual stimuli. 4

Geodesic Sensor NetSlide5

Characteristics of the ERP data set ERP curves are functional data. Effects of stimuli vary across cortical regions.

Spatial correlation between electrodes. 5Slide6

Commonly used methods on ERP data analysis Typically focus on features: amplitude of the peak, mean voltages in a time window, are often extracted.

6ERP components: waveforms with + or - deflections.Slide7

Main idea: the functional mixed model (FMM) framework7

Fixed effectRandom effectTo be estimatedSlide8

Gaussian functional mixed models (Gfmm) Guo (2002), Morris & Carroll(2006).

8Priors:

Model Fitting

Discrete Wavelet Transform:

Assume Gaussian Process:

separable structureSlide9

Robust functional mixed models (Rfmm) Zhu, Brown and Morris (2011, JASA)

9Column (j,k)

Key idea: scale mixture of normal

Priors:

Equivalent

Bayesian Lasso

Allow functions with outliers and outlying regions.

Fast scalable computation using Gibbs.

i.i.d.

i.i.d.

i.i.d.Slide10

Generalization 1 – correlated channel-specific fixed effects. 10

stimulus 1

stimulus 2

stimulus 3

stimulus 4

Assume correlated shrinkage prior for

(Griffin & Brown, 2012)Slide11

Generalization 2 – Model the correlation in E(t) in Gfmm11Slide12

Generalization 3 – Model the correlation in E(t) in Rfmm12Slide13

Posterior Inference – 2D smoothing across scalp 13Slide14

Posterior Inference14

Meyer et al. (2015). Slide15

Automated workflow15Slide16

ERP data analysis -- regions flagged using BFDR (delta = 0.7)16Slide17

ERP data analysis – summary plots using BFDR (delta=0.7)17Slide18

ERP data analysis – conclusion18

Our analysis reveals significant neurological effects induced by different types of visual stimuli. There are extensive differences between neutral images and emotion-evoking images of cigarette, pleasant, and unpleasant types during the time period 248-700ms in various cortical regions. Within this period, the cigarette profile was more similar to the pleasant stimulus than unpleasant stimulus during the 248-512ms time period, and was similar to both pleasant and unpleasant stimuli from 516-700ms. Compared with the initial results of Versace et al. (2011), our FMMc models provide more refined information about the timing and locations in which the stimuli effects differ, and are able to produce these results in a semi-automated fashion without having to preselect temporal or cortical regions to consider.Slide19

Reference Griffin, J. E., and Brown, P. J. (2012), “Structuring shrinkage: some correlated priors for regression,” Biometrika

, 99(2), 481–487. Meyer, M. J., Coull, B. A., Versace, F., Cinciripini, P., and Morris, J. S. (2015), “Bayesian function-on-function regression for multilevel functional data,” Biometrics. Morris, J. S. and Carroll R. J. (2006). Wavelet-based functional mixed models. J R Stat Soc, Ser B. 68,179–199. Ruppert, D., Wand, M. P., and Carroll, R. J. (2003), Semiparametric Regression, Cambridge Series in Statistical and Probabilistic Mathematics, UK: Cambridge University Press. Versace, F., Minnix, J. A., Robinson, J. D., Lam, C. Y., Brown, V. L., and Cinciripini, P. M. (2011), Brain reactivity to emotional, neutral and cigarette-related stimuli in smokers, Addiction Biology, 16, 296–307.  Zhu, H., Brown, P. J. and Morris, J. S. (2011) Robust, adaptive functional regression in functional mixed model framework, 

J Am Stat

Assoc

106 (495) 1167-1179.

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Contact:

Hongxiao Zhu

hongxiao@vt.edu

1-540-231-0400

Department of Statistics, Virginia Tech

406-A Hutcheson Hall

Blacksburg, VA 24061-0439 United StatesSlide20

AppendixSlide21

Use SimBaS to flag regions on which |C(s,t)|>021Slide22

Use BFDR to flag regions on which |C(s,t)|>delta22Slide23

Model Selection using Posterior Predictive Likelihood23Slide24

ERP data analysis – model selection using posterior predictive likelihood24

140 subjects in the training set.Applied 6 models to each regions.Calculate the LPPL for each model on each region.Select the model with the highest LPPL.Slide25

ERP data analysis -- summary of time intervals with pronounced flagging patterns25

Various degree of similarities Between Cigarette and Emotional Stimuli.Cigarette differ with emotional Stimuli.

No evident similarities are found.Slide26

ERP data analysis – computational time26