plotting.rsa {RSAtools}

Plots the response surface of a polynomial model of first, second, or third degree

Description

Plots the response surface of a model based on polynomial families (37 families), saturated polynomials, or user-specific polynomials.

Usage

plotting.rsaCOEF(
  x = 0,
  y = 0,
  x2 = 0,
  y2 = 0,
  xy = 0,
  w = 0,
  wx = 0,
  wy = 0,
  x3 = 0,
  xy2 = 0,
  x2y = 0,
  y3 = 0,
  b0 = 0,
  type = "3d",
  model = "CUBIC",
  acceleration = c(0, 0),
  FAST = TRUE,
  n_sample = 100,
  xlim = NULL,
  ylim = NULL,
  zlim = NULL,
  xlab = NULL,
  ylab = NULL,
  zlab = NULL,
  main = "",
  surface = "predict",
  lambda = NULL,
  suppress.surface = FALSE,
  suppress.box = FALSE,
  suppress.grid = FALSE,
  suppress.ticklabels = FALSE,
  rotation = list(x = -63, y = 32, z = 15),
  label.rotation = list(x = 19, y = -40, z = 92),
  gridsize = 21,
  bw = FALSE,
  legend = TRUE,
  param = TRUE,
  coefs = FALSE,
  axes = c("LOC", "LOIC", "r1_LOC", "r2_LOC", "r1_LOIC", "r2_LOIC", "a1_LOC", "a2_LOC",
    "a1_LOIC", "a2_LOIC"),
  axesStyles = list(LOC = list(lty = "solid", lwd = 2, col = ifelse(bw == TRUE,
    "black", "blue")), LOIC = list(lty = "solid", lwd = 2, col = ifelse(bw == TRUE,
    "black", "blue")), PA1 = list(lty = "dotted", lwd = 2, col = ifelse(bw == TRUE,
    "black", "gray30")), PA2 = list(lty = "dotted", lwd = 2, col = ifelse(bw == TRUE,
    "black", "gray30")), r1_LOC = list(lty = "solid", lwd = 2, col = ifelse(bw == TRUE,
    "black", "green")), r2_LOC = list(lty = "solid", lwd = 2, col = ifelse(bw == TRUE,
    "black", "green")), r1_LOIC = list(lty = "solid",      lwd = 2, col = ifelse(bw ==
    TRUE, "black", "red")), r2_LOIC = list(lty = "solid", lwd = 2, col = ifelse(bw ==
    TRUE, "black", "red")), a1_LOC = list(lty = "twodash", lwd = 2, col = ifelse(bw ==
    TRUE, "black", "green")), a2_LOC = list(lty = "twodash", lwd = 2, col = ifelse(bw ==
    TRUE, "black", "green")), a1_LOIC = list(lty = "twodash", lwd = 2, col = ifelse(bw ==
    TRUE, "black", "red")), a2_LOIC = list(lty = "twodash", lwd = 2, col = ifelse(bw ==
    TRUE, "black", "red"))),
  project = c("contour"),
  maxlines = FALSE,
  cex.tickLabel = 1,
  cex.axesLabel = 1,
  cex.main = 1,
  points = list(data = NULL, n_random = NULL, show = NA, value = "raw", jitter = 0,
    color = "black", cex = 0.5, out.mark = FALSE),
  fit = NULL,
  link = "identity",
  tck = c(1.5, 1.5, 1.5),
  distance = c(1.3, 1.3, 1.4),
  border = FALSE,
  contour = list(show = FALSE, color = "grey40", highlight = c()),
  hull = NA,
  showSP = FALSE,
  showSP.CI = FALSE,
  pal = NULL,
  pal.range = "box",
  pad = 0,
  claxes.alpha = 0.05,
  demo = FALSE,
  ...
)

plotting.rsa(x, ...)

Arguments

x

Either an RSA object (returned by the RSAmodel function), or the coefficient for the X predictor

y

Y coefficient

x2

X^2 coefficient

y2

Y^2 coefficient

xy

XY interaction coefficient

w

W coefficient (for (un)constrained absolute difference model)

wx

WX coefficient (for (un)constrained absolute difference model)

wy

WY coefficient (for (un)constrained absolute difference model)

x3

X^3 coefficient

xy2

XY^2 coefficient

x2y

X^2Y coefficient

y3

Y^3 coefficient

b0

Intercept

type

3d for 3d surface plot, 2d for 2d contour plot, "interactive" for interactive rotatable plot.

model

If x is an RSA object: from which model should the response surface be computed?

acceleration

Rates of accelerations along the LOC and LOIC to be inspected (0< |rate| < 1). Passed on internally to ident.ext

FAST

If FALSE, will also project response over LOC and LOIC. If TRUE, will only project the response surface (faster option).

n_sample

Number of random draws to consider to find extrema. This option is used for large samples to increase speed in preliminary analyses, but it is not recommended for published results). Passed on internally to ident.ext

xlim

Limits of the x axis

ylim

Limits of the y axis

zlim

Limits of the z axis

xlab

Label for x axis

ylab

Label for y axis

zlab

Label for z axis

main

the main title of the plot

surface

Method for the calculation of the surface z values. "predict" takes the predicted values from the model, "smooth" uses a thin plate smoother (function Tps from the fields package) of the raw data

lambda

lambda parameter for the smoother. Default (NULL) means that it is estimated by the smoother function. Small lambdas around 1 lead to rugged surfaces, big lambdas to very smooth surfaces.

suppress.surface

Should the surface be suppressed (only for type="3d")? Useful for only showing the data points, or for didactic purposes (e.g., first show the cube, then fade in the surface).

suppress.box

Should the surrounding box be suppressed (only for type="3d")?

suppress.grid

Should the grid lines be suppressed (only for type="3d")?

suppress.ticklabels

Should the numbers on the axes be suppressed (only for type="3d")?

rotation

Rotation of the 3d surface plot (when type == "3d")

label.rotation

Rotation of the axis labls (when type == "3d")

gridsize

Number of grid nodes in each dimension

bw

Print surface in black and white instead of colors?

legend

Print color legend for z values?

param

Should the surface parameters a1 to a5 be shown on the plot? In case of a 3d plot a1 to a5 are printed on top of the plot; in case of a contour plot the principal axes are plotted. Surface parameters are not printed for cubic surfaces.

coefs

Should the regression coefficients b1 to b5 (b1 to b9 for cubic models) be shown on the plot? (Only for 3d plot)

axes

*A vector of strings specifying the axes that should be plotted. Can be any combination of c("LOC", "LOIC","r1_LOC","r2_LOC","r1_LOIC","r2_LOIC","a1_LOC","a2_LOC","a1_LOIC","a2_LOIC"). LOC = line of congruence, LOIC = line of incongruence, r1_LOC = first reversal point on LOC,r2_LOC = second reversal point on LOC,r1_LOIC = first reversal point on LOIC,r2_LOIC = second reversal point on LOIC,a1_LOC = first acceleration point on LOC,a2_LOC = second acceleration point on LOC,a1_LOIC = first acceleration point on LOIC,a2_LOIC = second acceleration point on LOIC.

axesStyles

*Define the visual styles of the axes LOC,LOIC,r1_LOC,r2_LOC,r1_LOIC,r2_LOIC,a1_LOC,a2_LOC,a1_LOIC,a2_LOIC. Provide a named list: axesStyles=list(LOC = list(lty="solid", lwd=2, col=ifelse(bw==TRUE, "black", "blue")). It recognizes three parameters: lty, lwd, and col. If you define a style for an axis, you have to provide all three parameters, otherwise a warning will be shown.

project

*A vector of graphic elements that should be projected on the floor of the cube. Can include any combination of c("LOC", "LOIC", "contour", "points"). Note that projected elements are plotted in the order given in the vector (first elements are plotted first and overplotted by later elements).

maxlines

Should the maximum lines be plotted? (red: maximum X for a given Y, blue: maximum Y for a given X). Works only in type="3d"

cex.tickLabel

Font size factor for tick labels

cex.axesLabel

Font size factor for axes labels

cex.main

Factor for main title size

points

A list of parameters which define the appearance of the raw scatter points:

• data: Data frame which contains the coordinates of the raw data points. First column = x, second = y, third = z. This data frame is automatically generated when the plot is based on a fitted RSA-object

• n_random *Number of randomly drawn data points to be plotted from data. Used to avoid cluttering in large datasets.

• show = TRUE: Should the original data points be overplotted?

• color = "black": Color of the points. Either a single value for all points, or a vector with the same size as data points provided. If parameter fill is also defined, color refers to the border of the points.

• fill = NULL: Fill of the points. Either a single value for all points, or a vector with the same size as data points provided. As a default, this is set to NULL, which means that all points simply have the color color.

• value="raw": Plot the original z value, "predicted": plot the predicted z value

• jitter = 0: Amount of jitter for the raw data points. For z values, a value of 0.005 is reasonable

• cex = .5: multiplication factor for point size. Either a single value for all points, or a vector with the same size as data points provided.

• stilt: Should stilts be drawn for selected data points (i.e., lines from raw data points to the floor)? A logical vector with the same size as data points provided, indicating which points should get a stilt.

• out.mark = FALSE: If set to TRUE, outliers according to Bollen & Jackman (1980) are printed as red X symbols, but only when they have been removed in the RSA function: RSAmodel(..., out.rm=TRUE).

  • If out.rm == TRUE (in RSAmodel()) and out.mark == FALSE (in plotting.rsa()), the outlier is removed from the model and *not plotted* in RSAplot.

  • If out.rm == TRUE (in RSAmodel()) and out.mark == TRUE (in plotting.rsa()), the outlier is removed from the model but plotted and marked in RSAplot.

  • If out.rm == FALSE (in RSAmodel()): Outliers are not removed and cannot be plotted.

  • Example syntax: plotting.rsa(r1, points=list(show=TRUE, out.mark=TRUE))

As a shortcut, you can also set points=TRUE to set the defaults.

fit

Do not change that parameter (internal use only)

link

Link function to transform the z axes. Implemented are "identity" (no transformation; default), "probit", and "logit"

tck

A vector of three values defining the position of labels to the axes (see ?wireframe)

distance

A vector of three values defining the distance of labels to the axes

border

Should a thicker border around the surface be plotted? Sometimes this border leaves the surrounding box, which does not look good. In this case the border can be suppressed by setting border=FALSE.

contour

A list defining the appearance of contour lines (aka. height lines). show=TRUE: Should the contour lines be plotted on the 3d wireframe plot? (Parameter only relevant for type="3d"). color = "grey40": Color of the contour lines. highlight = c(): A vector of heights which should be highlighted (i.e., printed in bold). Be careful: the highlighted line is not necessarily exactly at the specified height; instead the nearest height line is selected.

hull

Plot a bag plot on the surface (This is a bivariate extension of the boxplot. 50% of points are in the inner bag, 50% in the outer region). See Rousseeuw, Ruts, & Tukey (1999).

showSP

Plot the stationary point? (only relevant for type="contour")

showSP.CI

Plot the CI of the stationary point? (only relevant for type="contour")

pal

A palette for shading.

pal.range

Should the color range be scaled to the box (pal.range = "box", default), or to the min and max of the surface (pal.range = "surface")? If set to "box", different surface plots can be compared along their color, as long as the zlim is the same for both.

pad

Pad controls the margin around the figure (positive numbers: larger margin, negative numbers: smaller margin)

claxes.alpha

Alpha level that is used to determine the axes K1 and K2 that demarcate the regions of significance for the cubic models "CL" and "RRCL"

demo

Do not change that parameter (internal use only)

...

Additional parameters passed to the plotting function (e.g., sub="Title"). A useful title might be the R squared of the plotted model: sub = as.expression(bquote(R^2==.(round(getPar(x, "r2", model="CUBIC"), 3))))

Details

This function plots the response surface in 3D or 2D. The function was adapted from the function plot.RSA (RSA package), by adding features for new polynomial families (+27 families, +user-specific polynomial) and new curvature probing tests (+accelerations, +LOIC extrema; Núñez-Regueiro & Juhel, 2022, 2024b). When curvatures are found, lines are projected that intersect inflection points (i.e., reversal or acceleration points) along the lines of congruence (x=y; in green) and incongruence (x=-y; in red), following derivatives of response curvatures (Núñez-Regueiro & Juhel, 2024a).

Value

A plot of the response surface

References

Rousseeuw, P. J., Ruts, I., & Tukey, J. W. (1999). The Bagplot: A Bivariate Boxplot. The American Statistician, 53(4), 382-387. doi:10.1080/00031305.1999.10474494

Núñez-Regueiro, F., Juhel, J. (2022). Model-Building Strategies in Response Surface Analysis Manuscript submitted for publication.

Núñez-Regueiro, F., Juhel, J. (2024a). Response Surface Analysis for the Social Sciences I: Identifying Best-Fitting Polynomial Solutions Manuscript submitted for publication.

Núñez-Regueiro, F., Juhel, J. (2024b). Response Surface Analysis for the Social Sciences II: Combinatory Rationales for Complex Polynomial Models Manuscript submitted for publication.

See Also

plotting.ext, RSAmodel

Examples

######PLOT RESPONSE SURFACE OF FM26_PARALLELASYMWEAK
PLOTsim3D <- plotting.rsa(RSA_step1,model="FM26_PARALLELASYMWEAK",type="3d",
acceleration=c(0,-0.3),points=list(show=TRUE, value="predicted"),
legend = FALSE,distance = c(1.2, 1.2, 1.2),cex.tickLabel = 0.6,
cex.axesLabel = 0.8,xlim=c(-3,3),ylim=c(-3,3),zlim=c(-3,3),hull=FALSE)
PLOTsim3D