gbtest {ERP}

The Guthrie-Buchwald procedure for significance analysis of ERP data

Description

Monte-Carlo implementation of the Guthrie-Buchwald procedure (see Guthrie and Buchwald, 1991) which accounts for the auto-correlation among test statistics to control erroneous detections of short intervals.

Usage

gbtest(dta, design, design0 = NULL, graphthresh = 0.05, nsamples = 1000)

Arguments

dta

Data frame containing the ERP curves: each column corresponds to a time frame and each row to a curve.

design

Design matrix of the nonnull model for the relationship between the ERP and the experimental variables. Typically the output of the function model.matrix

design0

Design matrix of the null model. Typically a submodel of the nonnull model, obtained by removing columns from design. Default is NULL, corresponding to the model with no covariates.

graphthresh

Graphical threshold (see Guthrie and Buchwald, 1991). Default is 0.05. As the FDR control level, the smaller is the graphical threshold, the more conservative is the procedure.

nsamples

Number of samples in the Monte-Carlo method to estimate the residual covariance. Default is 1000.

Details

The Guthrie-Buchwald method starts from a preliminary estimation of r, the lag-1 autocorrelation, among test statistics. Then, the null distribution of the lengths of the intervals I_alpha = t : pvalue_t <= alpha , where alpha is the so-called graphical threshold parameter of the method, is obtained using simulations of p-values p_t associated to auto-regressive t-test process of order 1 with mean 0 and auto-correlation r. Such an interval I_alpha is declared significant if its length exceeds the (1-alpha)-quantile of the null distribution. Note that the former method is designed to control erroneous detections of short significant intervals but not to control any type-I error rate.

Value

nbsignifintervals

Number of significant intervals.

intervals

List of length nbsignifintervals which components give the indices of each significant intervals.

significant

Indices of the time points for which the test is positive.

signal

Estimated signal: a pxT matrix, where p is the difference between the numbers of parameters in the nonnull and null models and T the number of frames.

rho

Estimated lag-1 auto-correlation.

r2

R-squared values for each of the T linear models.

Author(s)

David Causeur - [e-mail] and Mei-Chen Chu (National Cheng-Kung University, Tainan, Taiwan)

References

Guthrie, D. and Buchwald, J.S. (1991). Significance testing of difference potentials. Psychophysiology, 28, 240-244.

Sheu, C.-F., Perthame, E., Lee Y.-S. and Causeur, D. (2016). Accounting for time dependence in large-scale multiple testing of event-related potentials data. Annals of Applied Statistics. 10(1), 219-245.

See Also

erpavetest, erpfatest, erptest

Examples

data(impulsivity)

# Paired t-tests for the comparison of the ERP curves in the two conditions, 
# within experimental group High, at channel CPZ

erpdta.highCPZ = impulsivity[(impulsivity$Group=="High")&(impulsivity$Channel=="CPZ"),5:505] 
   # ERP curves for subjects in group 'High'
covariates.highCPZ = impulsivity[(impulsivity$Group=="High")&(impulsivity$Channel=="CPZ"),1:4]
covariates.highCPZ = droplevels(covariates.highCPZ)
   # Experimental covariates for subjects in group 'High'

design = model.matrix(~C(Subject,sum)+Condition,data=covariates.highCPZ)
   # Design matrix to compare ERP curves in the two conditions
design0 = model.matrix(~C(Subject,sum),data=covariates.highCPZ)
   # Design matrix for the null model (no condition effect)

tests = gbtest(erpdta.highCPZ,design,design0)

time_pt = seq(0,1000,2)     # sequence of time points (1 time point every 2ms in [0,1000])
nbs = 20                    # Number of B-splines for the plot of the effect curve
effect=which(colnames(design)=="ConditionSuccess")
erpplot(erpdta.highCPZ,design=design,frames=time_pt,effect=effect,xlab="Time (ms)",
        ylab=expression(Effect~curve~(mu~V)),bty="l",ylim=c(-3,3),nbs=nbs,
        cex.axis=1.25,cex.lab=1.25,interval="simultaneous")
   # with interval="simultaneous", both the pointwise and the simultaneous confidence bands
   # are plotted
points(time_pt[tests$significant],rep(0,length(tests$significant)),pch=16,col="blue")
   # Identifies significant time points by blue dots
title("Success-Failure effect curve with 95 percent C.I.",cex.main=1.25)
mtext(paste("12 subjects - Group 'High' - ",nbs," B-splines",sep=""),cex=1.25)