ERP (version 1.0.1)

erpfatest: Adaptive Factor-Adjustement for multiple testing of ERP data

Description

An adaptive factor-adjusted FDR- and FWER-controlling multiple testing procedures for ERP data. The procedure is described in detail in Sheu, Perthame, Lee, and Causeur (2014).

Usage

erpfatest(dta, design, design0 = NULL, method = "BH", nbf = NULL, nbfmax = 15, 
   alpha = 0.05, pi0 = 1, wantplot = FALSE, s0 = NULL, min.err = 0.001, 
   maxiter = 5, verbose = FALSE)

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 full 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 full model, obtained by removing columns from design. Default is NULL, corresponding to the model with no covariates.

method

FDR- or FWER- controlling multiple testing procedures as available in the function p.adjust. Default is "BH", for the Benjamini-Hochberg procedure (see Benjamini and Hochberg, 1995).

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).

nbfmax

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

alpha

The FDR or FWER control level. Default is 0.05

pi0

An estimate of the proportion of true null hypotheses, which can be plugged into an FDR controlling multiple testing procedure to improve its efficiency. Default is 1, corresponding to the classical FDR controlling procedures. If NUL

wantplot

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

s0

Prior knowledge of the time frames for which no signal is expected. For example, s0=c(1:50, 226:251) specifies that the first 50 time frames and time frames between 226 and 251 are known not to contain ERP signal. s0 can also be spec

min.err

Control parameter for convergence of the iterative algorithm. Default is 1e-03.

maxiter

Maximum number of iterations in algorithms. Default is 5.

verbose

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

Value

• pval
  p-values of the Adaptive Factor-Adjusted tests.
• correctedpval
  Corrected p-values, for the multiplicity of tests. Depends on the multiple testing method (see function p.adjust).
• significant
  Indices of the time points for which the test is positive.
• pi0
  Value for pi0: if the input argument pi0 is NULL, the output is the estimated proportion of true null hypotheses using the method by Storey and Tibshirani (2003).
• test
  Factor-Adjusted F-statistics.
• df1
  Residual degrees of freedom for the full model.
• df0
  Residual degrees of freedom for the null model.
• nbf
  Number of factors for the residual covariance model.
• signal
  Estimated signal: a pxT matrix, where p is the difference between the numbers of parameters in the full and null models and T the number of frames.
• r2
  R-squared values for each of the T linear models.

Details

The method is described in Sheu et al. (2014). It combines a decorrelation step based on a regression factor model as in Leek and Storey (2008), Friguet et al. (2009) or Sun et al. (2012) with an adaptive estimation of the ERP signal. The multiple testing corrections of the p-values are described in the help documentation of the function p.adjust of package stats.

References

Causeur, D., Chu, M.-C., Hsieh, S., Sheu, C.-F. 2012. A factor-adjusted multiple testing procedure for ERP data analysis. Behavior Research Methods, 44, 635-643. Friguet, C., Kloareg, M., Causeur, D. 2009. A factor model approach to multiple testing under dependence. Journal of the American Statistical Association, 104, 1406-1415. Leek, J.T., Storey, J.D. 2008. A general framework for multiple testing dependence. Proceedings of the National Academy of Sciences of the United States of America, 105, 18718-18723. Sheu, C.-F., Perthame, E., Lee Y.-S. and Causeur, D. 2014. Accounting for time dependence in large-scale multiple testing of event-related potential data. Submitted. Storey, J. D., Tibshirani, R. 2003. Statistical significance for genome-wide experiments. Proceedings of the National Academy of Sciences of the United States of America, 100, 9440-9445. Sun, Y., Zhang, N.R., Owen, A.B. 2012. Multiple hypothesis testing adjusted for latent variables, with an application to the AGEMAP gene expression data. The Annals of Applied Statistics, 6, no. 4, 1664-1688.

See Also

erpavetest, erptest, gbtest, p.adjust, pval.estimate.eta0

Examples

require(mnormt)
require(fdrtool)

data(erpcz)
data(simerp)

# Paired t-tests for the comparison of ERP curves between two groups

tests = erpfatest(erpcz[,1:251],design=model.matrix(~Subject+Instruction,data=erpcz),
   design0=model.matrix(~Subject,data=erpcz),nbf=3,s0=c(1:50,226:251),min.err=1e-01)

frames = seq(0,1001,4)
plot(frames,tests$signal,type="l",xlab="Time (ms)",ylab="Difference ERP curves")
points(frames[tests$significant],rep(0,length(tests$significant)),pch=16,col="blue")
title("Paired comparison at electrode CZ")

# Tests for significance of correlations

tests = erpfatest(simerp[,1:251],design=model.matrix(~y,data=simerp),
   nbf=5,min.err=1e-01,maxiter=10)
plot(frames,sign(tests$signal)*sqrt(tests$r2),type="l",
   xlab="Time (ms)",ylab="Correlation",ylim=c(-1,1))
points(frames[tests$significant],rep(-1,length(tests$significant)),
   pch=16,col="blue")
title("Simulation")