# plotfit.fd: Plot a Functional Data Object With Data In fda: Functional Data Analysis

## Description

Plot either functional data observations 'x' with a fit 'fdobj' or residuals from the fit.

This function is useful for assessing how well a functional data object fits the actual discrete data.

The default is to make one plot per functional observation with fit if residual is FALSE and superimposed lines if residual==TRUE.

With multiple plots, the system waits to confirm a desire to move to the next page unless ask==FALSE.

## Usage

  1 2 3 4 5 6 7 8 9 10 11 plotfit.fd(y, argvals, fdobj, rng = NULL, index = NULL, nfine = 101, residual = FALSE, sortwrd = FALSE, titles=NULL, ylim=NULL, ask=TRUE, type=c("p", "l")[1+residual], xlab=NULL, ylab=NULL, sub=NULL, col=1:9, lty=1:9, lwd=1, cex.pch=1, axes=NULL, ...) plotfit.fdSmooth(y, argvals, fdSm, rng = NULL, index = NULL, nfine = 101, residual = FALSE, sortwrd = FALSE, titles=NULL, ylim=NULL, ask=TRUE, type=c("p", "l")[1+residual], xlab=NULL, ylab=NULL, sub=NULL, col=1:9, lty=1:9, lwd=1, cex.pch=1, axes=NULL, ...) 

## Arguments

 y a vector, matrix or array containing the discrete observations used to estimate the functional data object. argvals a vector containing the argument values corresponding to the first dimension of y. fdobj a functional data object estimated from the data. fdSm an object of class fdSmooth rng a vector of length 2 specifying the limits for the horizontal axis. This must be a subset of fdobj[['basis']][['rangeval']], which is the default. index a set of indices of functions if only a subset of the observations are to be plotted. Subsetting can also be achieved by subsetting y; see details, below. nfine the number of argument values used to define the plot of the functional data object. This may need to be increased if the functions have a great deal of fine detail. residual a logical variable: if TRUE, the residuals are plotted rather than the data and functional data object. sortwrd a logical variable: if TRUE, the observations (i.e., second dimension of y) are sorted for plotting by the size of the sum of squared residuals. titles a vector containing strings that are titles for each observation. ylim a numeric vector of length 2 giving the y axis limits; see 'par'. ask If TRUE and if 'y' has more levels than the max length of col, lty, lwd and cex.pch, the user must confirm page change before the next plot will be created. type type of plot desired, as described with plot. If residual == FALSE, 'type' controls the representation for 'x', which will typically be 'p' to plot points but not lines; 'fdobj' will always plot as a line. If residual == TRUE, the default type == "l"; an alternative is "b" for both. xlab x axis label. ylab Character vector of y axis labels. If(residual), ylab defaults to 'Residuals', else to varnames derived from names(fdnames[] or fdnames[] or dimnames(y)[]. sub subtitle under the x axis label. Defaults to the RMS residual from the smooth. col, lty, lwd, cex.pch Numeric or character vectors specifying the color (col), line type (lty), line width (lwd) and size of plotted character symbols (cex.pch) of the data representation on the plot. If ask==TRUE, the length of the longest of these determines the number of levels of the array 'x' in each plot before asking the user to acknowledge a desire to change to the next page. Each of these is replicated to that length, so col[i] is used for x[,i] (if x is 2 dimensional), with line type and width controlled by lty[i] and lwd[i], respectively. If ask==FALSE, these are all replicated to length = the number of plots to be superimposed. For more information on alternative values for these paramters, see 'col', 'lty', 'lwd', or 'cex' with par. axes Either a logical or a list or NULL. logical whether axes should be drawn on the plot list a list used to create custom axes used to create axes via do.call(x$axes[], x$axes[-1]). The primary example of this uses list("axesIntervals", ...), e.g., with Fourier bases to create CanadianWeather plots ...  additional arguments such as axis labels that may be used with other plot functions.

## Details

plotfit plots discrete data along with a functional data object for fitting the data. It is designed to be used after something like Data2fd, smooth.fd, smooth.basis or smoothe.basisPar to check the fit of the data offered by the fd object.

plotfit.fdSmooth calls plotfit for its 'fd' component.

The plot can be restricted to a subset of observations (i.e., second dimension of y) or variables (i.e., third dimension of y) by providing y with the dimnames for its second and third dimensions matching a subset of the dimnames of fdobj[['coef']] (for plotfit.fd or fdSm[['fdobj']][['coef']] for plotfit.fdSmooth). If only one observation or variable is to be plotted, y must include 'drop = TRUE', as, e.g., y[, 2, 3, drop=TRUE]. If y or fdobj[['coef']] does not have dimnames on its second or third dimension, subsetting is acheived by taking the first few colums so the second or third dimensions match. This is acheived using checkDims3(y, fdobj[['coef']], defaultNames = fdobj[['fdnames']]]).

## Value

A matrix of mean square deviations from predicted is returned invisibly. If fdobj[["coefs"]] is a 3-dimensional array, this is a matrix of dimensions equal to the last two dimensions of fdobj[["coefs"]]. This will typically be the case when x is also a 3-dimensional array with the last two dimensions matching those of fdobj[["coefs"]]. The second dimension is typically replications and the third different variables.

If x and fobj[["coefs"]] are vectors or 2-dimensional arrays, they are padded to three dimensions, and then MSE is computed as a matrix with the second dimension = 1; if x and fobj[["coefs"]] are vectors, the first dimension of the returned matrix will also be 1.

## Side Effects

a plot of the the data 'x' with the function or the deviations between observed and predicted, depending on whether residual is FALSE or TRUE.

plot, plot.fd, lines.fd plot.fdSmooth, lines.fdSmooth par smooth.fd smooth.basis smooth.basisPar Data2fd checkDims3
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 # set up a Fourier basis for smoothing temperature data daybasis65 <- create.fourier.basis(c(0, 365), 65, axes=list("axesIntervals")) # smooth the average temperature data using function Data2fd Daytempfd <- with(CanadianWeather, smooth.basis(day.5, dailyAv[,,"Temperature.C"], daybasis65)$fd ) daytempfd <- with(CanadianWeather, smooth.basis(day.5, dailyAv[,,"Temperature.C"], daybasis65, fdnames=list("Day", "Station", "Deg C"))$fd ) # Plot the temperature data along with the fit to the data for the first # station, St. John's Newfoundland # If you want only the fitted functions, use plot(daytempfd) # To plot only a single fit vs. observations, use argument index # to request which one you want. with(CanadianWeather, plotfit.fd(dailyAv[, , "Temperature.C", drop=FALSE], argvals= day.5, daytempfd, index=1, titles=place) ) # Default ylab = daytempfd[['fdnames']] with(CanadianWeather, plotfit.fd(dailyAv[, , "Temperature.C"], argvals= day.5, Daytempfd, index=1, titles=place) ) plot(daytempfd) ## Not run: # plot all the weather stations, one by one after a click on the plot # in response to a request. # This example is within the "dontrun" environment to prevent the # the R package checking process from pausing: without 'dontrun', the package # build process might encounter problems with the par(ask=TRUE) feature. with(CanadianWeather, plotfit.fd(dailyAv[,, "Temperature.C"], day.5, daytempfd, ask=TRUE) ) ## End(Not run) # Now plot results for two weather stations. op <- par(mfrow=c(2,1), xpd=NA, bty="n") # xpd=NA: clip lines to the device region, # not the plot or figure region # bty="n": Do not draw boxes around the plots. ylim <- range(CanadianWeather$dailyAv[,,"Temperature.C"]) # Force the two plots to have the same scale with(CanadianWeather, plotfit.fd(dailyAv[,,"Temperature.C"], day.5, daytempfd, index=2, titles=place, ylim=ylim) ) with(CanadianWeather, plotfit.fd(dailyAv[,,"Temperature.C"], day.5, daytempfd, index=35, titles=place, ylim=ylim) ) ## Not run: # Plot residuals with interactive display of stations one by one par(op) with(CanadianWeather, plotfit.fd(dailyAv[, , "Temperature.C"], day.5, daytempfd, residual=TRUE) ) ## End(Not run) # The gait data are bivariate, and this code illustrates how plotfit.fd # deals with the plotting of two variables at the same time # First define normalized times and their range gaittime <- as.numeric(dimnames(gait)[])*20 gaitrange <- c(0,20) # Define the harmonic acceleration differential operator harmaccelLfd <- vec2Lfd(c(0, (2*pi/20)^2, 0), rangeval=gaitrange) # Set up basis for representing gait data. gaitbasis <- create.fourier.basis(gaitrange, nbasis=21) # Smooth the data gaitfd <- smooth.basisPar(gaittime, gait, gaitbasis, Lfdobj=harmaccelLfd, lambda=1e-2)$fd # Assign names to the data names(gaitfd$fdnames) <- c("Normalized time", "Child", "Angle") gaitfd$fdnames[] <- c("Hip", "Knee") ## Not run: # plot each pair of curves interactively, two plots per page, the top # for hip angle, and the bottom for knee angle plotfit.fd(gait, gaittime, gaitfd) # Plot the residuals, sorting cases by residual sum of squares summed over # both hip and knee angles. # The first series of 39 plots are for hip angle, two plots per page, # and the second 39 are for knee angle. The plots are sorted by the # size of the total residual sum of squares, but RMS residual values # for specific angles are not all going to be in order. plotfit.fd(gait, gaittime, gaitfd, residual=TRUE, sort=TRUE) ## End(Not run)                                                               