# Spatial and/or Temporal Smoothing of EEG Data Smooths single- or multi-channel electroencephalography (EEG) with respect to space and/or time. Uses the `bigspline`, `bigtps`, and `bigssa` functions (from `bigsplines` package) for smoothing. ```r eegsmooth(voltage, space = NULL, time = NULL, nknots = NULL, rparm = NULL, lambdas = NULL, skip.iter = TRUE, se.fit = FALSE, rseed = 1234) ``` ## Arguments - `voltage`: Vector of recorded EEG voltage at each row in `space`. - `space`: Matrix of electrode coordinates (in three-dimensions) at which EEG was recorded. If `space=NULL`, data are temporally smoothed only. - `time`: Vector of time points at which EEG was recorded. If `time=NULL`, data are spatially smoothed only. - `nknots`: Number of knots to sample for smoothing. Positive integer. - `rparm`: Rounding parameter(s) to use for smoothing. See Notes and Examples. - `lambdas`: Smoothing parameter(s) to use for smoothing. - `skip.iter`: If `FALSE`, iterative spatial-temporal smoothing is skipped. Ignored if `space=NULL` or `time=NULL`. - `se.fit`: If `TRUE`, standard errors of smoothed values are calculated. - `rseed`: Random seed to use for knot selection. Set `rseed=NULL` to obtain different knots each time, or set `rseed` to any positive integer to use a different random seed. ## Returns For temporal smoothing only: an object of class "bigspline" (see `bigspline`). For spatial smoothing only: an object of class "bigtps" (see `bigtps`). For spatial-temporal smoothing: an object of class "bigssa" (see `bigssa`). ## References Helwig, N. E. (2013). **Fast and stable smoothing spline analysis of variance models for large samples with applications to electroencephalography data analysis**. Unpublished doctoral dissertation. University of Illinois at Urbana-Champaign. https://www.ideals.illinois.edu/items/44427 Helwig, N.E. (2015). **bigsplines: Smoothing Splines for Large Samples**. tools:::Rd_expr_doi("10.32614/CRAN.package.bigsplines") , R package version 1.1-1, https://CRAN.R-project.org/package=bigsplines Helwig, N. E. & Ma, P. (2015). Fast and stable multiple smoothing parameter selection in smoothing spline analysis of variance models with large samples. **Journal of Computational and Graphical Statistics, 24**(3), 715-732. tools:::Rd_expr_doi("10.1080/10618600.2014.926819") Helwig, N. E. & Ma, P. (2016). Smoothing spline ANOVA for super large samples: Scalable computation via rounding parameters. **Statistics and Its Interface, 9**(4), 433-444. tools:::Rd_expr_doi("10.4310/SII.2016.v9.n4.a3") ## Author(s) Nathaniel E. Helwig ## Note For temporal smoothing only (i.e., `space=NULL`), the input `rparm` should be a positive scalar less than 1. Larger values produce faster (but less accurate) approximations. Default is 0.01, which I recommend for temporal smoothing; `rparm=0.005` may be needed for particuarly rough signals, and `rparm=0.02` could work for smoother signals. For spatial smoothing only (i.e., `time=NULL`), the input `rparm` should be a positive scalar giving the rounding unit for the spatial coordinates. For example, `rparm=0.1` rounds each coordinate to the nearest 0.1 (same as `round(space,1)`). For spatial-temporal smoothing (i.e., both `space` and `time` are non-null), the input `rparm` should be a list of the form `rparm=list(space=0.1,time=0.01)`, where the 0.1 and 0.01 can be replaced by your desired rounding parameters. Setting `rparm=NA` will use the full data solution; this is more computationally expensive, and typically produces a solution very similar to using `rparm=0.01` (see references). ## Examples ```r ########## EXAMPLE 1: Temporal ########## # get "PZ" electrode of "c" subjects in "eegdata" data data(eegdata) idx <- which(eegdata$channel=="PZ" & eegdata$group=="c") eegdata <- eegdata[idx,] # temporal smoothing eegmod <- eegsmooth(eegdata$voltage,time=eegdata$time) # define data for prediction time <- seq(min(eegdata$time),max(eegdata$time),length.out=100) yhat <- predict(eegmod,newdata=time,se.fit=TRUE) # plot results using eegtime eegtime(time*1000/255,yhat$fit,voltageSE=yhat$se.fit,ylim=c(-4,4),main="Pz") ########## EXAMPLE 2: Spatial ########## # get time point 65 (approx 250 ms) of "c" subjects in "eegdata" data data(eegdata) idx <- which(eegdata$time==65L & eegdata$group=="c") eegdata <- eegdata[idx,] # remove ears, nose, and reference (Cz) idx <- c(which(eegdata$channel=="X"),which(eegdata$channel=="Y"), which(eegdata$channel=="nd"),which(eegdata$channel=="Cz")) eegdata <- eegdata[-idx,] # match to eeg coordinates data(eegcoord) cidx <- match(eegdata$channel,rownames(eegcoord)) # spatial smoothing eegmod <- eegsmooth(eegdata$voltage,space=eegcoord[cidx,1:3]) # use dense cap for prediction mycap <- levels(factor(eegdata$channel)) ix <- eegcapdense(mycap,type="2d",index=TRUE) data(eegdense) space <- eegdense[ix,1:3] yhat <- predict(eegmod,newdata=space) # plot results using eegspace #eegspace(space,yhat) eegspace(eegdense[ix,4:5],yhat) ########## EXAMPLE 3: Spatial-Temporal (not run) ########## # # get "c" subjects of "eegdata" data # data(eegdata) # idx <- which(eegdata$group=="c") # eegdata <- eegdata[idx,] # # remove ears, nose, and reference (Cz) # idx <- c(which(eegdata$channel=="X"),which(eegdata$channel=="Y"), # which(eegdata$channel=="nd"),which(eegdata$channel=="Cz")) # eegdata <- eegdata[-idx,] # # match to eeg coordinates # data(eegcoord) # cidx <- match(eegdata$channel,rownames(eegcoord)) # # spatial-temporal smoothing # eegmod <- eegsmooth(eegdata$voltage,space=eegcoord[cidx,1:3],time=eegdata$time) # # time main effect # newdata <- list(time=seq(min(eegdata$time),max(eegdata$time),length.out=100)) # yhat <- predict(eegmod,newdata=newdata,se.fit=TRUE,include="time") # eegtime(newdata$time,yhat$fit,voltageSE=yhat$se.fit,ylim=c(-2,4),main="Time Main Effect") # # space main effect # mycap <- levels(factor(eegdata$channel)) # ix <- eegcapdense(mycap,type="2d",index=TRUE) # data(eegdense) # newdata <- list(space=eegdense[ix,1:3]) # yhat <- predict(eegmod,newdata=newdata,include="space") # eegspace(newdata$space,yhat) # # interaction effect (spatial map at time point 65) # newdata <- list(space=eegdense[ix,1:3],time=rep(65,nrow(eegdense[ix,]))) # yhat <- predict(eegmod,newdata=newdata,include="space:time") # eegspace(newdata$space,yhat) # # full prediction (spatial map at time point 65) # newdata <- list(space=eegdense[ix,1:3],time=rep(65,nrow(eegdense[ix,]))) # yhat <- predict(eegmod,newdata=newdata) # eegspace(newdata$space,yhat) ```

eegsmooth function