# Compare - Plots Plots 2-4 influence curves to the same model. methods ```r comparePlot(obj1, obj2, ... ) ## S4 method for signature 'IC,IC' comparePlot(obj1, obj2, obj3 = NULL, obj4 = NULL, data = NULL, ..., withSweave = getdistrOption("withSweave"), forceSameModel = FALSE, main = FALSE, inner = TRUE, sub = FALSE, col = par("col"), lwd = par("lwd"), lty, col.inner = par("col.main"), cex.inner = 0.8, bmar = par("mar")[1], tmar = par("mar")[3], with.automatic.grid = TRUE, with.legend = FALSE, legend = NULL, legend.bg = "white", legend.location = "bottomright", legend.cex = 0.8, withMBR = FALSE, MBRB = NA, MBR.fac = 2, col.MBR = par("col"), lty.MBR = "dashed", lwd.MBR = 0.8, x.vec = NULL, scaleX = FALSE, scaleX.fct, scaleX.inv, scaleY = FALSE, scaleY.fct = pnorm, scaleY.inv = qnorm, scaleN = 9, x.ticks = NULL, y.ticks = NULL, mfColRow = TRUE, to.draw.arg = NULL, cex.pts = 1, cex.pts.fun = NULL, col.pts = par("col"), pch.pts = 19, cex.npts = 1, cex.npts.fun = NULL, col.npts = par("col"), pch.npts = 20, jitter.fac = 1, with.lab = FALSE, cex.lbs = 1, adj.lbs = c(0, 0), col.lbs = col.pts, lab.pts = NULL, lab.font = NULL, alpha.trsp = NA, which.lbs = NULL, which.Order = NULL, which.nonlbs = NULL, attr.pre = FALSE, return.Order = FALSE, withSubst = TRUE) ``` ## Arguments - `obj1`: object of class `"InfluenceCurve"` - `obj2`: object of class `"InfluenceCurve"` to be compared with `obj1` - `obj3`: optional: object of class `"InfluenceCurve"` to be compared with `obj1` - `obj4`: optional: object of class `"InfluenceCurve"` to be compared with `obj1` - `data`: optional data argument --- for plotting observations into the plot; - `withSweave`: logical: if `TRUE` (for working with Sweave ) no extra device is opened - `forceSameModel`: logical; shall we check / enforce that the model of the ICs `obj1`, `obj2`, `obj3`, and `obj4` be the same? - `main`: logical: is a main title to be used? or just as argument `main` in `plot.default`. - `col`: color[s] of ICs in arguments `obj1` [, ,`obj4`]. - `lwd`: linewidth[s] of ICs in arguments `obj1` [, ,`obj4`]. - `lty`: line-type[s] of ICs in arguments `obj1` [, ,`obj4`]. - `inner`: logical: do panels have their own titles? or character vector of / cast to length 'number of plotted dimensions'; if argument `to.draw.arg` is used, this refers to a vector of length `length(to.draw.arg)`, the actually plotted dimensions. For further information, see also description of argument `main` in `plot.default`. - `sub`: logical: is a sub-title to be used? or just as argument `sub` in `plot.default`. - `tmar`: top margin -- useful for non-standard main title sizes - `bmar`: bottom margin -- useful for non-standard sub title sizes - `cex.inner`: magnification to be used for inner titles relative to the current setting of `cex`; as in `par` - `col.inner`: character or integer code; color for the inner title - `with.automatic.grid`: logical; should a grid be plotted alongside with the ticks of the axes, automatically? If `TRUE` a respective call to `grid` in argument `panel.first` is ignored. - `with.legend`: logical; shall a legend be plotted? - `legend`: either `NULL` or a list of length (number of plotted panels) of items which can be used as argument `legend` in command `legend`. - `legend.location`: a valid argument `x` for `legend` --- the place where to put the legend on the last issued plot - `legend.bg`: background color for the legend - `legend.cex`: magnification factor for the legend - `withMBR`: logical; shall horizontal lines with min and max of MBRE be plotted for comparison? - `MBRB`: matrix (or `NA`); coerced by usual recycling rules to a matrix with as many rows as plotted panels and with first column the lower bounds and the second column the upper bounds for the respective coordinates (ideally given by the MBR-IC). - `MBR.fac`: positive factor; scales the bounds given by argument `MBRB` - `col.MBR`: color for the MBR lines; as usual `col`-argument; - `lty.MBR`: line type for the MBR lines; as usual `lty`-argument; - `lwd.MBR`: line width for the MBR lines; as usual `lwd`-argument; - `x.vec`: a numeric vector of grid points to evaluate the influence curve; by default, `x.vec` is `NULL`; then the grid is produced automatically according to the distribution of the IC. `x.vec` can be useful for usage with a rescaling of the x-axis to avoid that the evaluation points be selected too unevenly (i.e. on an equally spaced grid in the original scale, but then, after rescaling non-equally). The grid has to be specified in original scale; i.e.; when used with rescaling, it should be chosen non-equally spaced. - `scaleX`: logical; shall X-axis be rescaled (by default according to the cdf of the underlying distribution)? - `scaleY`: logical; shall Y-axis be rescaled (by default according to a probit scale)? - `scaleX.fct`: an isotone, vectorized function mapping the domain of the IC to [0,1]; if `scaleX` is `TRUE` and `scaleX.fct` is missing, the cdf of the underlying observation distribution. - `scaleX.inv`: the inverse function to `scale.fct`, i.e., an isotone, vectorized function mapping [0,1] to the domain of the IC such that for any `x` in the domain, `scaleX.inv(scaleX.fct(x))==x`; if `scaleX` is `TRUE` and `scaleX.inv` is missing, the quantile function of the underlying observation distribution. - `scaleY.fct`: an isotone, vectorized function mapping for each coordinate the range of the respective coordinate of the IC to [0,1]; defaulting to the cdf of $N(0,1)$; can also be a list of functions with one list element for each of the panels to be plot. - `scaleY.inv`: an isotone, vectorized function mapping for each coordinate the range [0,1] into the range of the respective coordinate of the IC; defaulting to the quantile function of $N(0,1)$; can also be a list of functions with one list element for each of the panels to be plot. - `scaleN`: integer; defaults to 9; on rescaled axes, number of x and y ticks if drawn automatically; - `x.ticks`: numeric; defaults to NULL; (then ticks are chosen automatically); if non-NULL, user-given x-ticks (on original scale); - `y.ticks`: numeric; defaults to NULL; (then ticks are chosen automatically); if non-NULL, user-given y-ticks (on original scale); can be a list with one (numeric or NULL) item per panel - `mfColRow`: shall default partition in panels be used --- defaults to `TRUE` - `to.draw.arg`: Either `NULL` (default; everything is plotted) or a vector of either integers (the indices of the subplots to be drawn) or characters --- the names of the subplots to be drawn: these names are to be chosen either among the row names of the trafo matrix `rownames(trafo(eval(obj1@CallL2Fam)@param))` or if the last expression is `NULL` a vector `"dim"`, `dimnr` running through the number of rows of the trafo matrix. - `withSubst`: logical; if `TRUE` (default) pattern substitution for titles and lables is used; otherwise no substitution is used. - `col.pts`: color of the points of the `data` argument plotted; can be a vector or a matrix. More specifically, if argument `attr.pre` is `TRUE`, it is recycled to fill a matrix of dimension `n` by `nIC` (`n` the number of observations prior to any selection and `nIC` the number of ICs plotted) where filling is done in order column first. The columns are used for possibly different colors for the different ICs from arguments `obj1`, `obj2`, and, possibly `obj3` and `obj4`. The selection done via `which.lbs` and `which.Order` is then done afterwards and on this matrix; in this case, argument `col.npts` is ignored. If `attr.pre` is `FALSE`, `col.pts` is recycled to fill a matrix of dimension `n.s` by `nIC` where `n.s` is the number of observations selected for labelling and refers to the index ordering after the selection. Then argument `col.npts` deteremines the colors of the shown but non-labelled observations as given in argument `which.nonlbs`. - `pch.pts`: symbol of the points of the `data` argument plotted (may be a vector of length `nIC` or a matrix, see `col.pts`). - `cex.pts`: size of the points of the `data` argument plotted (may be a vector of length `nIC` or a matrix, see `col.pts`). - `cex.pts.fun`: rescaling function for the size of the points to be plotted; either `NULL` (default), then `log(1+abs(x))` is used for each of the rescalings, or a function which is then used for each of the rescalings, or a list of functions; if it is a function or a list of functions, if necessary it is recylced to length `nIC * dim` where `dim` is the number of dimensions of the pICs to be plotted; in the index of this list, `nIC` is incremented first; then `dim`. - `col.npts`: color of the non-labelled points of the `data` argument plotted; (may be a vector of length `nIC` the number of plotted pICs, i.e., one value for each pIC in arguments `obj1`, `obj2`, and, if available, `obj3` and `obj4`, or it can be a matrix `nnlb <- sum(which.nonlbs)` by `nIC`, `nnlb` the number of non-labelled observations. - `pch.npts`: symbol of the non-labelled points of the `data` argument plotted (may be a vector of length `nIC` or a matrix, see `col.npts`). - `cex.npts`: size of the non-labelled points of the `data` argument plotted (may be a vector of length `nIC` or a matrix, see `col.npts`). - `cex.npts.fun`: rescaling function for the size of the non-labelled points to be plotted; either `NULL` (default), then `log(1+abs(x))` is used for each of the rescalings, or a function which is then used for each of the rescalings, or a list of functions; if it is a function or a list of functions, if necessary it is recylced to length `nIC * dim` where `dim` is the number of dimensions of the pICs to be plotted; in the index of this list, `nIC` is incremented first; then `dim`. - `lab.pts`: character or NULL; labels to be plotted to the observations; can be a vector of length `n`, `n` the number of all observations prior to any selection with `which.lbs`, `which.Order`; if `lab.pts` is `NULL`, observation indices are used. - `with.lab`: logical; shall labels be plotted to the observations? (May be a vector of length `nIC`, see `col.pts` -- but not a matrix). - `cex.lbs`: size of the labels; can be vectorized to an array of dim nlbs x `nIC` x npnl where npnl is the number of plotted panels and nlbs the number of plotted labels; if it is a vector, it is recylced in order labels then plotted ICs then panels. - `col.lbs`: color of the labels; can be vectorized to a matrix of dim nlbs x `nIC` as `col.pts`. - `adj.lbs`: adjustment of the labels; can be vectorized to an array of dim 2 x `nIC` x npnl, npnl the number of plotted panels; if it is a vector, it is recycled in order (x,y)-coords then ICs then panels. - `lab.font`: font to be used for labels (may be a vector of length `nIC`, see `with.lab`). - `alpha.trsp`: alpha transparency to be added ex post to colors `col.pch` and `col.lbl`; if one-dim and NA all colors are left unchanged. Otherwise, with usual recycling rules `alpha.trsp` gets shorted/prolongated to length the data-symbols to be plotted. Coordinates of this vector `alpha.trsp` with NA are left unchanged, while for the remaining ones, the alpha channel in rgb space is set to the respective coordinate value of `alpha.trsp`. The non-NA entries must be integers in [0,255] (0 invisible, 255 opaque). - `jitter.fac`: jittering factor used in case of a `DiscreteDistribution` for plotting points of the `data` argument in a jittered fashion (may be a vector of length 2, see `with.lab`). - `attr.pre`: logical; do graphical attributes for plotted data refer to indices prior (`TRUE`) or posterior to selection via arguments `which.lbs`, `which.Order`, `which.nonlbs` (`FALSE`)? - `which.lbs`: either an integer vector with the indices of the observations to be plotted into graph or `NULL` --- then no observation is excluded. - `which.Order`: for each of the given ICs, we order the observations (descending) according to the norm given by the corresponding `normtype(object)`; then `which.Order` either is an integer vector with the indices of the **ordered** observations (remaining after a possible reduction by argument `which.lbs`) to be plotted into graph or `NULL` --- then no (further) observation is excluded. - `which.nonlbs`: indices of the observations which should be plotted but not labelled; either an integer vector with the indices of the observations to be plotted into graph or `NULL` --- then all non-labelled observations are plotted. - `return.Order`: logical; if `TRUE`, a list of length maximally four with order vectors is returned --- one for the ordering w.r.t. each of the given ICs; more specifically, the order of the (remaining) observations given by their original index is returned (remaining means: after a possible reduction by argument `which.lbs`, and ordering is according to the norm given by `normtype(object)`); othervise we return `invisible()` as usual. - ``...``: further arguments to be passed to `plot` ## Returns An S3 object of class `c("plotInfo","DiagnInfo")`, i.e., a list containing the information needed to produce the respective plot, which at a later stage could be used by different graphic engines (like, e.g. `ggplot`) to produce the plot in a different framework. A more detailed description will follow in a subsequent version. ## Details Any parameters of `plot.default` may be passed on to this particular `plot` method. For main-, inner, and subtitles given as arguments `main`, `inner`, and `sub`, top and bottom margins are enlarged to 5 resp. 6 by default but may also be specified by `tmar` / `bmar` arguments. If `main` / `inner` / `sub` are logical then if the respective argument is `FALSE` nothing is done/plotted, but if it is `TRUE`, we use a default main title taking up the calling arguments in case of `main`, default inner titles taking up the class and (named) parameter slots of arguments in case of `inner`, and a "generated on "-tag in case of `sub`. Of course, if `main` / `inner` / `sub` are `character`, this is used for the title; in case of `inner` it is then checked whether it has correct length. If argument `withSubst` is `TRUE`, in all title and axis lable arguments, the following patterns are substituted: - **`"%C1"`,`"%C2"`,[`"%C3"`,][`"%C4"`]**: class of argument `obj`, i=1,..4 - **`"%A1"`,`"%A2"`,[`"%A3"`,][`"%A4"`]**: deparsed argument `obj`, i=1,..4 - **`"%D"`**: time/date-string when the plot was generated If argument `...` contains argument `ylim`, this may either be as in `plot.default` (i.e. a vector of length 2) or a vector of length 2*(number of plotted dimensions); in the case of longer length, these are the values for `ylim` for the plotted dimensions of the IC, one pair for each dimension. In addition, argument `...` may contain arguments `panel.first`, `panel.last`, i.e., hook expressions to be evaluated at the very beginning and at the very end of each panel (within the then valid coordinates). To be able to use these hooks for each panel individually, they may also be lists of expressions (of the same length as the number of panels and run through in the same order as the panels). ## References Kohl, M. (2005) **Numerical Contributions to the Asymptotic Theory of Robustness**. Bayreuth: Dissertation. ## Author(s) Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de ## See Also `L2ParamFamily-class`, `IC-class`, `plot` ## Examples ```r if(require(ROptEst)){ N0 <- NormLocationScaleFamily(mean=0, sd=1) N0.Rob1 <- InfRobModel(center = N0, neighbor = ContNeighborhood(radius = 0.5)) IC1 <- optIC(model = N0, risk = asCov()) IC2 <- optIC(model = N0.Rob1, risk = asMSE()) comparePlot(IC1,IC2) set.seed(12); data <- r(N0)(20) comparePlot(IC1, IC2, data=data, with.lab = TRUE, which.lbs = c(1:4,15:20), which.Order = 1:6, return.Order = TRUE) ## don't test to reduce check time on CRAN ## selection of subpanels for plotting par(mfrow=c(1,1)) comparePlot(IC1, IC2 ,mfColRow = FALSE, to.draw.arg=c("mean"), panel.first= grid(),ylim=c(-4,4),xlim=c(-6,6)) ## matrix-valued ylim comparePlot(IC1, IC2, panel.first= grid(),ylim=c(-4,4,0,4),xlim=c(-6,6)) x <- c(data,-12,10) comparePlot(IC1, IC2, data=x, which.Order=10, panel.first= grid(), ylim=c(-4,4,0,4), xlim=c(-6,6)) Y <- Chisq(df=1)* DiscreteDistribution(c(-1,1)) comparePlot(IC1, IC2, data=x, which.Order=10, scaleX = TRUE, scaleX.fct=pnorm, scaleX.inv=qnorm, scaleY = TRUE, scaleY.fct=p(Y), scaleY.inv=q.l(Y), panel.first= grid(), ylim=c(-4,4,0,4), xlim=c(-6,6)) comparePlot(IC1, IC2, data=x, which.Order=10, scaleX = TRUE, scaleX.fct=pnorm, scaleX.inv=qnorm, scaleY = TRUE, scaleY.fct=p(Y), scaleY.inv=q.l(Y), x.ticks = c(-Inf, -10, -1,0,1,10,Inf), y.ticks = c(-Inf, -5, -1,0,1,5,Inf), panel.first= grid(), ylim=c(-4,4,0,4), xlim=c(-6,6)) ## with use of trafo-matrix: G <- GammaFamily(scale = 1, shape = 2) ## explicitely transforming to ## MASS parametrization: mtrafo <- function(x){ nms0 <- names(c(main(param(G)),nuisance(param(G)))) nms <- c("shape","rate") fval0 <- c(x[2], 1/x[1]) names(fval0) <- nms mat0 <- matrix( c(0, -1/x[1]^2, 1, 0), nrow = 2, ncol = 2, dimnames = list(nms,nms0)) list(fval = fval0, mat = mat0)} G2 <- G trafo(G2) <- mtrafo G2 G2.Rob1 <- InfRobModel(center = G2, neighbor = ContNeighborhood(radius = 0.5)) system.time(IC1 <- optIC(model = G2, risk = asCov())) system.time(IC2 <- optIC(model = G2.Rob1, risk = asMSE())) system.time(IC2.i <- optIC(model = G2.Rob1, risk = asMSE(normtype=InfoNorm()))) system.time(IC2.s <- optIC(model = G2.Rob1, risk = asMSE(normtype=SelfNorm()))) comparePlot(IC1,IC2, IC2.i, IC2.s) } ```

comparePlot function