erpFtest {ERP}

Functional Analysis-of-Variance (Anova) testing of Event-Related Potentials (ERP) data

Description

Factor-based generalized Likelihood-Ratio Test for functional ANOVA in ERP designs. The procedure is described in details in Causeur, Sheu, Perthame and Rufini (2018).

Usage

erpFtest(dta,design,design0=NULL,nbf=NULL,pvalue=c("Satterthwaite","MC","none"), 
nsamples=200,min.err=0.01,verbose=FALSE,
nbfmax=min(c(nsamples,nrow(design)))-ncol(design)-1,
wantplot=ifelse(is.null(nbf),TRUE,FALSE),svd.method=c("fast.svd","irlba"))

Arguments

dta

Data frame containing the ERP measurements: 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.

nbf

Number of factors in the residual covariance model. Default is NULL: the number of factors is determined by minimization of the variance inflation criterion as suggested in Friguet et al. (2009).

pvalue

If "Satterthwaite", then the Monte-Carlo p-value is calculated with a Satterthwaite approximation of the null distribution. The other possible value is "none", for no calculation of the p-value or "MC" for the Monte-Carlo p-value.

nsamples

Number of Monte-Carlo samples for the estimation of the null distribution. Default is nsamples=200, recommended when the Satterthwaite approximation is used.

min.err

Control parameter for convergence of the iterative algorithm. Default is 1e-02.

verbose

If TRUE, details are printed along the iterations of the algorithm. Default is FALSE.

nbfmax

Only required if nbf=NULL. The largest possible number of factors.

wantplot

If TRUE, a diagnostic plot is produced to help choosing the number of factors. Only active if nbf=NULL.

svd.method

the EM algorithm starts from an SVD estimation of the factor model parameters. The default option to implement this SVD is fast.svd. An alternative option is an approximate but faster SVD by function irlba.

Details

The method is described in Causeur et al. (2018). It can be viewed as a Hotelling's T-squared multivariate ANOVA test based on a factor decomposition of the time-dependence across pointwise F-tests. For 1-way functional ANOVA, it can be compared to function anova.onefactor in package fda.usc.

Value

Fgls

The generalized LRT statistics comparing the nonnull model with design matrix design and the null model with design matrix design0.

Fols

The LRT statistics ignoring time-dependence across pointwise F-tests.

pval

p-value of the generalized LRT statistics.

pval.Fols

p-value of the LRT statistics ignoring time-dependence across pointwise F-tests.

Author(s)

David Causeur, IRMAR, UMR 6625 CNRS, Agrocampus Ouest, Rennes, France. Flavia Rufini, Agrocampus Ouest, Rennes, France.

References

Causeur, D., Sheu, C.-F., Perthame, E. and Rufini, F. (2018). A functional generalized F-test for signal detection with applications to event-related potentials significance analysis. Submitted.

Examples

data(impulsivity)

# Comparison of 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)

Ftest = erpFtest(erpdta.highCPZ,design,design0,nbf=NULL,wantplot=TRUE,pvalue="none")
   # with pvalue="none", just to choose a number of factors
Ftest = erpFtest(erpdta.highCPZ,design,design0,nbf=6)
Ftest$pval          # p-value of the Generalized LRT statistic
Ftest$pval.Fols     # p-value of the LRT statistic when time-dependence is ignored

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
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)