strucplot: Structured Trellis Plots

Description Usage Arguments Details Value Methods (by class) Overview How does strucplot() work? Panel spacing Effective xyLayout specification 2 level designs with a center point – the 'center' argument Note See Also Examples

View source: R/main.R

Description

Structured Trellis Plots Without Strip Labels

Usage

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strucplot(obj, ...)

## S3 method for class 'formula'
strucplot(obj, data = list(), groups = NULL,
  xyLayout = list(), spacings = list(x = 0:9, y = 0:9), center = FALSE,
  ...)

## Default S3 method:
strucplot(...)

## S3 method for class 'data.frame'
strucplot(obj, col = "darkblue", groups = NULL, ...)

## S3 method for class 'list'
strucplot(obj, ...)

## S3 method for class 'matrix'
strucplot(obj, ...)

## S3 method for class 'lm'
strucplot(obj, newdata = model.frame(obj)[-1],
  ylab = "Predicted Response", predictArgs = NULL, ...)

Arguments

obj

Argument determining method dispatch. For the formula method, a xyplot type formula of the form ~y|f1*f2*...*fn or y~x|f1*f2*...*fn (where "..." means the actual variable names). Instead of explicitly specifying the conditioning variables, i.e. the variables after the |, you can instead use a "." after |. This is interpreted to mean "all variables in the data argument except those to the left of the |". For example, the second formula above could be written as y~x|. where f1, f2, ..., fn and possibly x and y are the variables in data (typically columns of a data frame).

Note 1: Extended formulas and 3-d formulas (see xyplot) are not implemented.

Note 2: For the lm method, the model object should contain a model component. See predict.lm and Help pages for predict methods for classes inheriting from "lm" for other arguments and for exactly what is plotted.

It is preferable that this be the the first argument of the call.

data

For the formula method, a data frame (or more precisely, anything that is a valid envir argument in eval, e.g., a list or an environment) containing values for any variables in the formula, as well as groups and subset if applicable. If not found in data, or if data is unspecified, the variables are looked for in the environment of the formula.

groups

The groups parameter of xyplot

xyLayout

In its most general form, a list with named "x" and "y" components, either or both of which can be missing (or NULL). If there are n conditioning factors and both x and y are given, then the combined components (e.g. via unlist) must be a permutation of the sequence 1, 2,..., n (with no duplicates).

The integers in x specify the indices of the conditioning factors and their levels in the x direction hierarchy. Correspondingly for y. For a fuller explanation of how this controls the plot layout, see the Overview section and the examples.

For convenience, the xyLayout argument can be specified in several other ways. The basic idea is that the full list will be filled in "appropriately" if possible. Specifically, this means:

  • If both components are missing, NULL, or of zero length the list is constructed by splitting the conditioning factors equally in the horizontal and vertical directions, with horizontal gettting one more if the number of conditioning variables is odd;

  • If only one component of the list is given, the missing component gets the remaining factors, if any, in order(note that this means if both directions are not in order low to high, then both must be explicitly specified in the xyLayout list);

  • If component names are missing or empty(i.e. ""), the first one is "x" and the second is "y". Nonmissing component names must be "x" and/or "y" and must be unique;

  • A 1 or 2 column matrix can be used instead of a list with an even number of conditioning variables. If the column names are "x" or "y", they will be used. Otherwise, the x component is first and y second;

  • An unnamed vector can be given in place of a list with a single unnamed component (which would be assumed to be the "x" component)

As a result, all the following would produce exactly the same layout for n = 5 conditioning factors when used as the xyLayout argument:

  • list(x = 1:3, y = 4:5)

  • list (x = 1:3)

  • list (y = 4:5)

  • argument missing or NULL

  • 1:3

  • cbind(y = 4:5)

  • matrix(1:3,ncol=1)

Note that arbitrary integer vectors can be used, not just (ordered) sequences; e.g. the following are correct and equivalent when there are 6 conditioning factors:

  • list(y = c(1,5,3), x = c(2,4,6))

  • cbind(y=c(1,5,3), x=c(2,4,6))

  • cbind(y = c(1,5,3))

But be careful: xyLayout = c(2,4,6) is equivalent to xyLayout = list(x = c(2,4,6), y = c(1,3,5)), which is different than the previous, since order matters!

spacings

A list with x and y components that are nondecreasing sequences of positive vaues. The ith value in the sequence gives the spacing in character heights between the sets of panels at each level for the ith conditioning variable in the component's direction. If either a single vector or a list with single component is given, it is replicated. See the Overview for further explanation. Default is list(x=0:9, y=0:9)

center

Logical, default FALSE. If the conditioning factors constitute a 2-level design with a center point and center is TRUE, a compact trellis plot that omits panels for the missing settings of the factors is drawn. If FALSE or the design is not of this form, all panels are shown, which may be informative in any case to better visualize the design sparsity.

col

Fill color for the data frame method.

newdata

For the lm method and objects inheriting from the lm class. The 'newdata' argument for the associated predict method. Consult predict.lm for details.

ylab

For the lm method. Optional y axis label for predicted values.

predictArgs

For the lm method. A list of optional named arguments for the relevant predict method. These are will be used as part of the args list when invoking the relevant predict method using do.call.

...

Further arguments to panel functions, methods, or xyplot.

Details

A structured display is a trellis display without strip labels. The factors and levels are encoded by plot layout and spacing and decoded by a separate legend. See the Overview below for a detailed explanation.

Value

The formula method returns an object of type c("structured", "trellis"); or c("doe","structured","trellis") for 2-level designs with a center point. This is a trellis object with additional structure and formula attributes. The lm method returns a class of c("modelFit","structured","trellis"). At present, this extension is ignored, but future print/plot methods may take advantage of it. The other methods return the same object as the formula method.

The structure attribute provides xyLayout information. It is a list with x and y components, each of which in turn is a list, one of which may be empty (i.e. of length 0). The components of the x list have names of the conditioning variables in the horizontal direction of the layout with values the variable values; analogously for the y list.

The formula attribute gives the actual formula used in the trellis call, i.e. with the actual conditioning variable names substituted for ".".

Methods (by class)

Overview

The trellis display paradigm breaks down when there are more than 2 or 3 conditioning variables, because the plotting area becomes cluttered with multiple layers of strip labels identifying the panel settings. This is especially a problem if one wants to show the structure or results of studies that are (fractions of) factorial designs with the design factors as conditioning variables. For example, in industrial type experiments, it is not uncommon to have 5 or more experimental factors.

It is also often the case that there are multiple responses – e.g. several different characteristics of a product or a functional response like an IR spectrum, MRI scan, or surface plot. It can be desirable to display such results so that direct visual comparison of the complex responses can be made.

The strucplot function enables such functionality by omitting the strip labels and laying out the panels in a regular array, a 'xyLayout' in which the position of the panels rather than their strip labels identifies the variable settings.

Because the lattice package already has these capabilities, strucplot is implemented as a wrapper to lattice's xyplot function. This provides a convenient interface, simplifies the code and, most importantly, allows the user to access all of lattice's (and the underlying grid graphics') functionality in the usual way. Only two extra arguments – 'xyLayout' and 'spacings' – are used to do this, although the default 'spacings' argument normally need not be changed. (There is also a third 'center' argument for 2 level factorial designs, which are commonly used in industrial experiments, that is explained below.)

How does strucplot() work?

Suppose that the data consist of a numeric vector response y for 4 conditioning factors, f1, f2, f3, and f4, where f1 and f2 each have 2 levels, f3 has 3 levels, and f4 has 4 levels. (Because the conditioning variables are coerced to factors by factor, if level orderings other than that given by these coercions are wanted, the user should do them explicitly before calling strucplot).

Then the call, strucplot(~y|f1*f2*f3*f4) would produce a trellis plot without strip labels with 12 (= 3 x 4) rows and 4 (= 2 x 2) columns of panels, some of which may be empty if the corresponding factor settings are missing. The default xyLayout argument that produces this is: xyLayout = list(x = 1:2, y = 3:4). It splits the conditioning variables as evenly as possible into 2 groups with the x component getting the first 2 variables, f1 and f2, and the y component getting the second 2 variables, f3 and f4. (if there are an odd number of variables, the x component gets one more variable than the y). This means the levels of the x variables, f1 and f2, vary from left to right across each row. For the y variables, if as.table = TRUE, the default, the levels of the y variables, f3 and f4, vary from top to bottom down each column; otherwise if as.table = FALSE, from bottom to top up each column. Since there are 4 combinations of levels for the x variables and 12 for y, this gives a 12 row by 4 column display.

The panels are displayed in each direction in reverse lexicographic order, where the 'alphabets' are the factor levels. This means that the first variable changes the fastest; the second the next fastest, and so on. Using (i,j) to denote setting in which the first factor is at the ith level and the second is at the jth, this translates to (for as.table = TRUE):

Row ordering

(f1,f2): (1,1), (2,1), (1,2), (2,2)

Column ordering from top down

(f3, f4): ((1,1), (2,1), (3,1), (1,2), (2,2), ... , (1,4), (2,4), (3,4)

If one component is missing, if it is x, there will only be 1 column; if it is y, only 1 row. The nonmissing component must still be correctly specified to provide the panel ordering.

Panel spacing

Variable spacing between the panels hierarchically groups them to identify their settings. The default spacing for both x and y directions is 0:9. This means that panels corresponding to the first, fastest changing, variable are separated by 0 units (= character heights); groups of panels at each fixed level of the second next fastest changing variable are separated by 1 unit; groups of groups of panels at fixed levels of the third are separated by 2 units; and so forth.

For the example, this means that the row spacing would look like ('X' indicates a panel): XX XX . And for columns it would be going down: XXX XXX XXX XXX . The spacings can be different for x and y, but this is usually unnecessary.

Effective xyLayout specification

The default layout is often enhanced by changing the order of the factors and the xyLayout; for example, ordering the factors from those with the least change among levels to the most, or vice-versa; or setting the "most important" factors along rows to facilitate visual comparison.

The order of the variables – and hence which vary in the x or y direction – is given both by the left to right order of the conditioning in the formula and the xyLayout argument. Thus, in the example, conditioning with ~|f3*f1*f2*f4 and setting the layout with xyLayout = list(x=4, y=3:1) is equivalent to ~|f4*f2*f1*f3 and xyLayout = list(x=1,y=2:4) and produces a display with 12 rows and 4 columns in which the row panels now correspond to the 4 f4 levels and the column panels to the levels of f2, f1, and f3. This redundancy is deliberate: it allows changing layouts via the xyLayout argument to avoid rewriting a formula with long names in a different order.

2 level designs with a center point – the 'center' argument

Finally, the 'center' argument, a logical with default = TRUE, controls the display when the conditioning factors are arranged as a 2 level factorial design with a single "pseudo"-center point. "pseudo" here means that the settings of the factors at the center need not be exactly in the middle for numeric factors. If the design is not of this form, the 'center' argument is ignored.

For such designs, when center = TRUE, a more compact display will be drawn in which a center panel corresponding to the center point is shown as the single panel in its row and column, but all other empty panels corresponding to settings where some of the conditioning variables are at their mid levels and some are not, are omitted. Examples are given below.

If it is desired to show all the empty panels, which can be useful to informatively represent the actual design sparsity, set center = FALSE.

Note

Because 'xyLayout' and the number of levels in the conditioning variables determine the plot structure, a 'layout' argument in the call will be ignored. Other xyplot arguments that are ignored are 'skip','between', 'drop.unused.levels', 'strip','perm.cond',and 'index.cond'. All other xyplot should work as expected.

See Also

lattice

Examples

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 # Compare standard xyplot vs. strucplot of quakes data in datasets package.
 #  Cut depth into 6 groups and magitude into 5.

 require(datasets)
 # Note that as.table = TRUE is used to make depths increase
 # down the page. For strucplot(), this is the default.

 xyplot(lat ~ long|cut(mag,5)*cut(depth,6),  data = quakes, col="blue",
  as.table = TRUE,type = c("g","p"))

 # Compare to:
 strucplot(lat ~ long|cut(mag,5)*cut(depth,6), data = quakes, col="blue",
    type = c("g", "p"))

 # Visualizing designs:

 # A half fraction of a 2^5 (a 2^(5-1)) design

 # Build the design matrix
  ff <- do.call(expand.grid,rep(list(c(-1,1)),4))
  ff[[5]] <- do.call(mapply,c(FUN = prod,ff))
   names(ff) <- LETTERS[1:5]

 # Show the design
 strucplot(ff)

 # Plotting a 2 level design with a center point

 # Add a center point to ff and plot
  ffCenter <- rbind(ff,rep(0,5))
  strucplot(ffCenter)

 # Use center = TRUE for a more compact display and show legend below.
  print(strucplot(ffCenter, center = TRUE),legendLoc = "bottom")

 # The "npk" data. See help("npk") for details.
 # Visualize design with blocks the vertical factor and the rest horizontal
  strucplot(npk[,-5], xyLay = list(x = 2:4, y =1))

  # Plot the yield
  strucplot(~yield |., xyLay = list(x=2:4, y=1),data = npk, col = "darkblue",
    panel = function(...){
      panel.grid(h = -1, v = 0)
      panel.xyplot(...)}
    )

 # It may be more informative to plot bars instead of points.
 # See help(panel.bars) for details.
 #
 # Note also "shortcut" ways to specify the xyLayout
  strucplot(~yield |., xyLay = list(x=2:4),data = npk,
            panel = panel.bars)

 # Include a conditioning variable in the formula to reduce the
 # dimensionality of conditioning. Show legend on right of plot.
  print(strucplot(yield ~ N|., xyLay = 2:3, data = npk,
            panel = panel.bars), legendLoc = "right")

 # Use the horizontal = TRUE argument of panel.bars to plot the bars
 # horizontally. The left and right hand sides of the formula must also
 # be switched for 2-sided formulas (not for 1-sided).
  strucplot( N ~ yield |., xyLay = list(y=1), data = npk,
            panel = panel.bars, horizontal = TRUE)

 # Fit a linear model with all main effects and 2 factor interactions in N,P,K
 # and plot the fits, using the "newdata" argument to plot predictions at
 # non-design points).
  require("stats")
    npk.aov <- aov(yield ~ block + (N+P+K)^2, data = npk)
    full <- do.call(expand.grid,lapply(npk[,-5],levels))
    plot(strucplot(npk.aov,  xyLay = list(x = 2:4),panel = panel.bars,
            newdata = full),legendLoc = "bottom")

   # Compare to a grouped plot:
   ypred <- predict(npk.aov, new = full)
    plot(
      strucplot(ypred ~ N|K*block, groups = full$P, data = full,
        panel= function(x,y, groups, subscripts,cex=1.25,...){
          panel.grid(h=-1, v=0)
          panel.superpose(x,y,cex= cex, type = c("p","l"),...,
                    panel.groups = panel.xyplot,
                    groups=groups, subscripts =subscripts)},
        auto.key = list(points=FALSE,lines=TRUE, columns = 2,
                title = "P",cex.title=1), ylab = "Predicted Response" ),
      legendLoc = "right")

## Cleanup
rm(full, npk.aov, ypred,ff,ffCenter)

stripless documentation built on May 30, 2017, 2:05 a.m.