Package 'bivrp' reference manual

Package 'bivrp'

Title:	Bivariate Residual Plots with Simulation Polygons
Description:	Generates bivariate residual plots with simulation polygons for any diagnostics and bivariate model from which functions to extract the desired diagnostics, simulate new data and refit the models are available.
Authors:	Rafael de Andrade Moral [aut, cre], John Hinde [aut]
Maintainer:	Rafael de Andrade Moral <[email protected]>
License:	GPL (>= 2)
Version:	1.2-2
Built:	2024-12-16 06:46:29 UTC
Source:	CRAN

Title:

Bivariate Residual Plots with Simulation Polygons

Description:

Generates bivariate residual plots with simulation polygons for any diagnostics and bivariate model from which functions to extract the desired diagnostics, simulate new data and refit the models are available.

Authors:

Rafael de Andrade Moral [aut, cre], John Hinde [aut]

Maintainer:

Rafael de Andrade Moral <[email protected]>

License:

GPL (>= 2)

Version:

1.2-2

Built:

2024-12-16 06:46:29 UTC

Source:

CRAN

Help Index

Bivariate Residual Plots with Simulation Polygons

Description

Details

Package:	bivrp
Type:	Package
Title:	Bivariate Residual Plots with Simulation Polygons
Version:	1.2-2
Date:	2020-04-01
Authors@R:	c(person("Rafael", "de Andrade Moral", role = c("aut", "cre"), email = "[email protected]"), person("John", "Hinde", role = "aut"))
Author:	Rafael de Andrade Moral [aut, cre], John Hinde [aut]
Maintainer:	Rafael de Andrade Moral <[email protected]>
Depends:	R (>= 3.0.0), MASS (>= 7.3-35), methods, graphics, stats
Suggests:	mvtnorm (>= 1.0-3), mrfDepth (>= 1.0.10)
Description:	Generates bivariate residual plots with simulation polygons for any diagnostics and bivariate model from which functions to extract the desired diagnostics, simulate new data and refit the models are available.
License:	GPL (>= 2)
NeedsCompilation:	no
Packaged:	2020-04-01 12:27:57 UTC; rafael
Repository:	CRAN
Date/Publication:	2020-04-01 13:00:02 UTC

Index of help topics:

bivrp                   Bivariate Residual Plots with Simulation
                        Polygons
bivrp-package           Bivariate Residual Plots with Simulation
                        Polygons
is_point_inside         Determine if point is inside or outside a
                        simple polygon area
plot.bivrp              Plot Method for bivrp Objects
polygon_area            Polygon operations

Author(s)

Rafael de Andrade Moral [aut, cre], John Hinde [aut]

Maintainer: Rafael de Andrade Moral <[email protected]>

Bivariate Residual Plots with Simulation Polygons

Description

Produces a bivariate residual plot with simulation polygons to assess goodness-of-fit of bivariate statistical models, provided the user supplies three functions: one to obtain model diagnostics, one to simulate data from a fitted model object, and one to refit the model to simulated data.

Usage

bivrp(obj, sim = 99, conf = .95, diagfun, simfun, fitfun, verb = FALSE,
      sort.res = TRUE, closest.angle = TRUE, angle.ref = - pi,
      counter.clockwise = TRUE, xlab, ylab, main,
      clear.device = FALSE, point.col, point.pch, ...)
      
## S3 method for class 'bivrp'
print(x, ...)
bivrp(obj, sim = 99, conf = .95, diagfun, simfun, fitfun, verb = FALSE,
      sort.res = TRUE, closest.angle = TRUE, angle.ref = - pi,
      counter.clockwise = TRUE, xlab, ylab, main,
      clear.device = FALSE, point.col, point.pch, ...)
      
## S3 method for class 'bivrp'
print(x, ...)

Arguments

`obj`	fitted model object
`sim`	number of simulations used to compute envelope. Default is 99
`conf`	confidence level of the simulated polygons. Default is 0.95
`diagfun`	user-defined function used to obtain the diagnostic measures from the fitted model object
`simfun`	user-defined function used to simulate a random sample from the model estimated parameters
`fitfun`	user-defined function used to re-fit the model to simulated data
`verb`	logical. If `TRUE`, prints each step of the simulation procedure
`sort.res`	logical. If `TRUE`, points will be sorted using angles formed with the origin (type of ordering can be fine-tuned with arguments `closest.angle`, `angle.ref` and `counter.clockwise`).
`closest.angle`	logical. If `FALSE`, points will be sorted starting from the angle defined in `angle.ref`, if `TRUE`, points will be sorted starting from the closest angle to the observed bivariate sample ranked as first
`angle.ref`	the reference angle from which points will be sorted starting from the closest angle to the input (in radians). Defaults to `- pi`
`counter.clockwise`	logical. Should the points be ordered counter-clockwise or clockwise from the reference angle?
`xlab`	argument passed to `par`
`ylab`	argument passed to `par`
`main`	argument passed to `par`
`clear.device`	logical. If `TRUE`, clears the plotting device after producing the bivariate residual plot with simulation polygons
`point.col`	a vector of length 2 with the colors of the points that are inside and outside of the simulated polygons
`point.pch`	a vector of length 2 with the point characters of the points that are inside and outside of the simulated polygons
`...`	further arguments passed to `plot.bivrp`
`x`	an object of class `bivrp`

Details

This approach relies on the same strategy used for producing half-normal plots with simulation envelopes. Given a vector of bivariate model diagnostics, the angle each point makes with the origin is calculated to order them. This can be fine-tuned using the logical arguments closest.angle, angle.ref, and counter.clockwise, see the Arguments section above.

Then, sim bivariate response variables are simulated from the fitted model, using the same model matrices, error distribution and fitted parameters, using the function defined as simfun. The model is refitted to each simulated sample, using the function defined as fitfun. Next, we obtain the same type of model diagnostics, using diagfun, again ordered the same way the original bivariate sample was. We have, for each bivariate diagnostic, sim simulated bivariate diagnostics forming the whole cloud of simulated diagnostics.

By default, we then obtain the convex hulls of each set of the $s$ sets of points and obtain a reduced polygon whose area is (conf * 100)% of the original convex hull's area, forming the simulated polygon. This is equivalent to passing the argument reduce.polygon = "proportional" to plot.bivrp. The argument reduce.polygon = "bag" can be used to obtain a (conf * 100)% bagplot as the simulated polygon instead of a convex hull. The points are then connected to the centroids of their respective simulated polygons and, if they lie outside the polygons, they are drawn in red. For the final display, the polygons are erased so as to ease visualization.

There is no automatic implementation of a bivariate model in this function, and hence users must provide three functions for bivrp. The first function, diagfun, must extract the desired model diagnostics from a model fit object. The second function, simfun, must return the response variable, simulated using the same error distributions and estimated parameters from the fitted model. The third and final function, fitfun, must return a fitted model object. See the Examples section.

This function produces a plot by passing the computed object to plot.bivrp. The print method returns a data.frame containing all ordered simulated bivariate diagnostics.

Value

The function returns an object of class "bivrp", which is a list containing the following components:

`reslist.ord`	list of ordered diagnostics from model refitting to each simulated dataset
`res.original.ord`	original model diagnostics
`res1`	diagnostics from variable 1
`res2`	diagnostics from variable 2
`res.original1`	original model diagnostics for variable 1
`res.original2`	original model diagnostics for variable 2
`conf`	confidence level of the simulated polygons

Author(s)

Rafael A. Moral <[email protected]> and John Hinde

Examples

## simulating a bivariate normal response variable

require(mvtnorm)

n <- 40
beta1 <- c(2, .4)
beta2 <- c(.2, .2)
x <- seq(1, 10, length = n)
X <- model.matrix(~ x)
mu1 <- X%*%beta1
mu2 <- X%*%beta2
sig1 <- 2
sig2 <- 3
sig12 <- -1.7
Sig1 <- diag(rep(sig1), n)
Sig2 <- diag(rep(sig2), n)
Sig12 <- diag(rep(sig12), n)
V <- rbind(cbind(Sig1, Sig12),
           cbind(Sig12, Sig2))

set.seed(2016)
Y <- as.numeric(rmvnorm(1, c(mu1, mu2), V))

## code for fitting the model estimating covariance or not
bivnormfit <- function(Y, X, covariance) {
  n <- nrow(X)
  p <- ncol(X)
  y <- cbind(Y[1:n],Y[(n+1):(2*n)])
  XtXinv <- solve(crossprod(X, X))
  beta.hat <- XtXinv %*% crossprod(X, y)
  mu.hat <- X%*%beta.hat
  sigma.hat <- 1/n * t(y - mu.hat) %*% (y - mu.hat)
  if(!covariance) sigma.hat <- diag(diag(sigma.hat))
  cov.betas <- sigma.hat %x% XtXinv
  se.s1 <- sqrt(2*sigma.hat[1]^2/(n-p+1))
  se.s2 <- sqrt(2*sigma.hat[4]^2/(n-p+1))
  if(!covariance) se.s12 <- NA else {
    rho <- sigma.hat[2]/sqrt(sigma.hat[1]*sigma.hat[4])
    se.s12 <- sqrt((1+rho^2)*sigma.hat[1]*sigma.hat[4]/(n-p+1))
  }
  se.betas <- sqrt(diag(cov.betas))
  se.sigma <- c(se.s1, se.s2, se.s12)
  coefs <- c(beta.hat, sigma.hat[1], sigma.hat[4], sigma.hat[2])
  names(coefs) <- c("beta1.0", "beta1.1", "beta2.0", "beta2.1", "sig1", "sig2", "sig12")
  fitted <- c(mu.hat)
  resid <- Y - fitted
  Sig1 <- diag(rep(sigma.hat[1]), n)
  Sig2 <- diag(rep(sigma.hat[4]), n)
  Sig12 <- diag(rep(sigma.hat[2]), n)
  V <- rbind(cbind(Sig1, Sig12),
             cbind(Sig12, Sig2))
  llik <- dmvnorm(Y, c(mu.hat), V, log = TRUE)
  ret <- list("coefs" = coefs, "covariance" = covariance, "n" = n, 
              "X" = X, "fitted" = fitted, "resid" = resid, "loglik" = llik,
              "Y" = Y, "se" = c(se.betas, se.sigma))
  class(ret) <- "bivnormfit"
  return(ret)
}

## fitting bivariate models with and without estimating covariance
fit0 <- bivnormfit(Y, X, covariance=FALSE)
fit1 <- bivnormfit(Y, X, covariance=TRUE)
## likelihood-ratio test
2*(fit0$loglik - fit1$loglik)
pchisq(54.24, 1, lower=FALSE)

## function for extracting diagnostics (raw residuals)
dfun <- function(obj) {
  r <- obj$resid
  n <- obj$n
  return(list(r[1:n], r[(n+1):(2*n)]))
}

## function for simulating new response variables
sfun <- function(obj) {
  n <- obj$n
  fitted <- obj$fitted
  sig1 <- obj$coefs[5]
  sig2 <- obj$coefs[6]
  if(obj$covariance) sig12 <- obj$coefs[7] else sig12 <- 0
  Sig1 <- diag(rep(sig1), n)
  Sig2 <- diag(rep(sig2), n)
  Sig12 <- diag(rep(sig12), n)
  V <- rbind(cbind(Sig1, Sig12),
             cbind(Sig12, Sig2))
  Y <- as.numeric(rmvnorm(1, c(mu1, mu2), V))
  return(list(Y[1:n], Y[(n+1):(2*n)], "X" = obj$X, 
              "covariance" = obj$covariance))
}

## function for refitting the model to simulated data
ffun <- function(new.obj) {
  Ynew <- c(new.obj[[1]], new.obj[[2]])
  bivnormfit(Ynew, new.obj$X, new.obj$covariance)
}

## Bivariate residual plot for model 1 (without estimating covariance)
plot1 <- bivrp(fit0, diagfun=dfun, simfun=sfun, fitfun=ffun, verb=TRUE)
## without polygon area reduction
plot(plot1, conf=1)
## drawing polygons
plot(plot1, add.polygon=TRUE)
## without ordering
plot(plot1, theta.sort=FALSE, kernel=TRUE, add.dplots=TRUE, superpose=TRUE)

## Bivariate residual plot for model 2 (estimating covariance)
plot2 <- bivrp(fit1, diagfun=dfun, simfun=sfun, fitfun=ffun, verb=TRUE)
## without polygon area reduction
plot(plot2, conf=1)
## drawing polygons
plot(plot2, add.polygon=TRUE, conf=1)
## without ordering
plot(plot2, theta.sort=FALSE, kernel=TRUE, add.dplots=TRUE, superpose=TRUE)
## simulating a bivariate normal response variable

require(mvtnorm)

n <- 40
beta1 <- c(2, .4)
beta2 <- c(.2, .2)
x <- seq(1, 10, length = n)
X <- model.matrix(~ x)
mu1 <- X%*%beta1
mu2 <- X%*%beta2
sig1 <- 2
sig2 <- 3
sig12 <- -1.7
Sig1 <- diag(rep(sig1), n)
Sig2 <- diag(rep(sig2), n)
Sig12 <- diag(rep(sig12), n)
V <- rbind(cbind(Sig1, Sig12),
           cbind(Sig12, Sig2))

set.seed(2016)
Y <- as.numeric(rmvnorm(1, c(mu1, mu2), V))

## code for fitting the model estimating covariance or not
bivnormfit <- function(Y, X, covariance) {
  n <- nrow(X)
  p <- ncol(X)
  y <- cbind(Y[1:n],Y[(n+1):(2*n)])
  XtXinv <- solve(crossprod(X, X))
  beta.hat <- XtXinv %*% crossprod(X, y)
  mu.hat <- X%*%beta.hat
  sigma.hat <- 1/n * t(y - mu.hat) %*% (y - mu.hat)
  if(!covariance) sigma.hat <- diag(diag(sigma.hat))
  cov.betas <- sigma.hat %x% XtXinv
  se.s1 <- sqrt(2*sigma.hat[1]^2/(n-p+1))
  se.s2 <- sqrt(2*sigma.hat[4]^2/(n-p+1))
  if(!covariance) se.s12 <- NA else {
    rho <- sigma.hat[2]/sqrt(sigma.hat[1]*sigma.hat[4])
    se.s12 <- sqrt((1+rho^2)*sigma.hat[1]*sigma.hat[4]/(n-p+1))
  }
  se.betas <- sqrt(diag(cov.betas))
  se.sigma <- c(se.s1, se.s2, se.s12)
  coefs <- c(beta.hat, sigma.hat[1], sigma.hat[4], sigma.hat[2])
  names(coefs) <- c("beta1.0", "beta1.1", "beta2.0", "beta2.1", "sig1", "sig2", "sig12")
  fitted <- c(mu.hat)
  resid <- Y - fitted
  Sig1 <- diag(rep(sigma.hat[1]), n)
  Sig2 <- diag(rep(sigma.hat[4]), n)
  Sig12 <- diag(rep(sigma.hat[2]), n)
  V <- rbind(cbind(Sig1, Sig12),
             cbind(Sig12, Sig2))
  llik <- dmvnorm(Y, c(mu.hat), V, log = TRUE)
  ret <- list("coefs" = coefs, "covariance" = covariance, "n" = n, 
              "X" = X, "fitted" = fitted, "resid" = resid, "loglik" = llik,
              "Y" = Y, "se" = c(se.betas, se.sigma))
  class(ret) <- "bivnormfit"
  return(ret)
}

## fitting bivariate models with and without estimating covariance
fit0 <- bivnormfit(Y, X, covariance=FALSE)
fit1 <- bivnormfit(Y, X, covariance=TRUE)
## likelihood-ratio test
2*(fit0$loglik - fit1$loglik)
pchisq(54.24, 1, lower=FALSE)

## function for extracting diagnostics (raw residuals)
dfun <- function(obj) {
  r <- obj$resid
  n <- obj$n
  return(list(r[1:n], r[(n+1):(2*n)]))
}

## function for simulating new response variables
sfun <- function(obj) {
  n <- obj$n
  fitted <- obj$fitted
  sig1 <- obj$coefs[5]
  sig2 <- obj$coefs[6]
  if(obj$covariance) sig12 <- obj$coefs[7] else sig12 <- 0
  Sig1 <- diag(rep(sig1), n)
  Sig2 <- diag(rep(sig2), n)
  Sig12 <- diag(rep(sig12), n)
  V <- rbind(cbind(Sig1, Sig12),
             cbind(Sig12, Sig2))
  Y <- as.numeric(rmvnorm(1, c(mu1, mu2), V))
  return(list(Y[1:n], Y[(n+1):(2*n)], "X" = obj$X, 
              "covariance" = obj$covariance))
}

## function for refitting the model to simulated data
ffun <- function(new.obj) {
  Ynew <- c(new.obj[[1]], new.obj[[2]])
  bivnormfit(Ynew, new.obj$X, new.obj$covariance)
}

## Bivariate residual plot for model 1 (without estimating covariance)
plot1 <- bivrp(fit0, diagfun=dfun, simfun=sfun, fitfun=ffun, verb=TRUE)
## without polygon area reduction
plot(plot1, conf=1)
## drawing polygons
plot(plot1, add.polygon=TRUE)
## without ordering
plot(plot1, theta.sort=FALSE, kernel=TRUE, add.dplots=TRUE, superpose=TRUE)

## Bivariate residual plot for model 2 (estimating covariance)
plot2 <- bivrp(fit1, diagfun=dfun, simfun=sfun, fitfun=ffun, verb=TRUE)
## without polygon area reduction
plot(plot2, conf=1)
## drawing polygons
plot(plot2, add.polygon=TRUE, conf=1)
## without ordering
plot(plot2, theta.sort=FALSE, kernel=TRUE, add.dplots=TRUE, superpose=TRUE)

Determine if point is inside or outside a simple polygon area

Description

Returns whether a point is inside or outside the convex polygon formed with the coordinates in a data frame or matrix

Usage

is_point_inside(point, polyg)
is_point_inside(point, polyg)

Arguments

`point`	vector of two values for a point in the Cartesian plane
`polyg`	data frame or matrix with the coordinates forming the convex polygon

Details

The algorithm used here draws a ray from the point and counts the number of intersections made with the polygon. If the number of intersections is only one, then this means the point is inside the convex polygon.

Value

This function returns TRUE, if the point is inside and FALSE, otherwise.

Author(s)

Rafael A. Moral <[email protected]> and John Hinde

Examples

my_polygon <- data.frame(c(1, 2, 3, 4, 3),
                         c(1, 0, .5, 3, 4))
points_to_test <- list(c(0, 0), c(2.5, 1), c(3.5, 4))

unlist(lapply(points_to_test, is_point_inside, my_polygon))

my_polygon <- data.frame(c(1, 2, 3, 4, 3),
                         c(1, 0, .5, 3, 4))
points_to_test <- list(c(0, 0), c(2.5, 1), c(3.5, 4))

unlist(lapply(points_to_test, is_point_inside, my_polygon))

Plot Method for bivrp Objects

Description

Plots the bivariate residual plot with simulation polygons from a bivrp object

Usage

## S3 method for class 'bivrp'
plot(x, kernel, superpose.points, chp, add.dplots, 
     theta.sort, add.polygon, reduce.polygon, one.dim, pch = 16, cex = 0.8, 
     conf, xlab, ylab, main, point.col, point.pch, transparent.colors,
     density.bw, ...)
## S3 method for class 'bivrp'
plot(x, kernel, superpose.points, chp, add.dplots, 
     theta.sort, add.polygon, reduce.polygon, one.dim, pch = 16, cex = 0.8, 
     conf, xlab, ylab, main, point.col, point.pch, transparent.colors,
     density.bw, ...)

Arguments

`x`	object of class `bivrp`
`kernel`	logical. If TRUE, instead of using polygons for each point, computes 2d kernels and plots the contours
`superpose.points`	only used if `kernel` or `chp` is TRUE. Logical argument, if `TRUE`, plots all simulated bivariate diagnostics
`chp`	logical. If `TRUE`, instead of using polygons for each point, performs convex hull peeling over all simulated points
`add.dplots`	logical. If `TRUE`, adds the marginal density plots
`theta.sort`	logical. If `TRUE`, produces a simulated polygon for each point
`add.polygon`	logical. If `TRUE`, plots the simulated polygons as well
`reduce.polygon`	method used to reduce the polygon area. Defaults to `proportional`, see `get_newpolygon` for details. If `reduce.polygon = "peel"`, performs convex hull peeling to reduce the area; if `reduce.polygon = "bag"`, computes a (`conf * 100`)% bagplot of the points
`one.dim`	logical. If `TRUE`, plots only the marginal density plots (only works with `theta.sort = FALSE`)
`pch`	argument passed to `par`
`cex`	argument passed to `par`
`conf`	confidence level of the simulated polygons. Default is 0.95
`xlab`	argument passed to `par`
`ylab`	argument passed to `par`
`main`	argument passed to `par`
`point.col`	a vector of length 2 with the colors of the points that are inside and outside of the simulated polygons
`point.pch`	a vector of length 2 with the point characters of the points that are inside and outside of the simulated polygons
`transparent.colors`	logical. If `TRUE`, adds transparency to the marginal density plots; if `FALSE`, only the border lines are drawn
`density.bw`	the smoothing bandwidth to be used for the marginal densities. Defaults to `"SJ"` (see `density`)
`...`	further arguments passed to `par`

Author(s)

Rafael A. Moral <[email protected]> and John Hinde

Polygon operations

Description

Convex polygon operations - determination of area, centre of mass, and area reduction

Usage

polygon_area(P)
get_k(P, conf)
get_newpolygon(conf, P, method)
get_reduced_bag(x, y, conf)
compute_bagplot(x, y, conf)
polygon_area(P)
get_k(P, conf)
get_newpolygon(conf, P, method)
get_reduced_bag(x, y, conf)
compute_bagplot(x, y, conf)

Arguments

`P`	2-column `matrix` or `data.frame` with the coordinates of the vertices of the convex polygon
`conf`	proportion of the area of polygon `P`
`method`	method used to reduce the area of the polygon. Use `method = "proportional"` to scale the distances between the centroid and the vertices by `sqrt(conf)`; use `method = "get_k"` to subtract the same distance `k` from the centroid to each vertex.
`x`	x coordinates (of raw data) used to obtain the reduced bag
`y`	y coordinates (of raw data) used to obtain the reduced bag

Details

The function compute_bagplot uses an adapted version of the code written by P. Segaert to obtain the bagplot, that uses the Fortran subroutine written by P.J. Rousseeuw, I. Ruts and A. Struyf.

Author(s)

Rafael A. Moral <[email protected]> and John Hinde

References

Rousseeuw P.J., Ruts I., Tukey J.W. (1999). The bagplot: A bivariate boxplot. The American Statistician, 53, 382–387.

Examples

  oldPolygon <- data.frame(x=c(2,1,3,4.5,5), y=c(1,3,5,4.5,2))
  
  # area
  polygon_area(oldPolygon)$area
  # centre of mass
  polygon_area(oldPolygon)$centre
  
  # get a new polygon with 50% of the area of the old one
  newPolygon <- get_newpolygon(conf=.5, P=oldPolygon, method="proportional")
  polygon_area(newPolygon)$area/polygon_area(oldPolygon)$area
  
  # second method
  newPolygon2 <- get_newpolygon(conf=.5, P=oldPolygon, method="get.k")
  polygon_area(newPolygon2)$area/polygon_area(oldPolygon)$area
  
  # illustration
  plot(oldPolygon, xlim=c(0,6), ylim=c(0,6), main="(a)", pch=16)
  polygon(oldPolygon, lwd=2, col="#00000033")
  text(oldPolygon, c(expression(P[1]), expression(P[2]),
                     expression(P[3]), expression(P[4]),
                     expression(P[5])), pos=c(1,2,3,4,4), cex=2)
  polygon(newPolygon, border=4, lwd=2, col="#52A3E199")
  points(newPolygon, pch=16, col=4)
  text(newPolygon, c(expression(paste(P[1],minute)), expression(paste(P[2],minute)),
             expression(paste(P[3],minute)), expression(paste(P[4],minute)),
             expression(paste(P[5],minute))), pos=c(1,3,2,4,4), col=4, cex=2)

  C <- polygon_area(oldPolygon)$centre
  text(C[1], C[2], "C", pos=4, cex=2)
  for(i in 1:5) lines(c(C[1], oldPolygon[i,1]), 
                      c(C[2], oldPolygon[i,2]), lty=2, lwd=2, type="b")
oldPolygon <- data.frame(x=c(2,1,3,4.5,5), y=c(1,3,5,4.5,2))
  
  # area
  polygon_area(oldPolygon)$area
  # centre of mass
  polygon_area(oldPolygon)$centre
  
  # get a new polygon with 50% of the area of the old one
  newPolygon <- get_newpolygon(conf=.5, P=oldPolygon, method="proportional")
  polygon_area(newPolygon)$area/polygon_area(oldPolygon)$area
  
  # second method
  newPolygon2 <- get_newpolygon(conf=.5, P=oldPolygon, method="get.k")
  polygon_area(newPolygon2)$area/polygon_area(oldPolygon)$area
  
  # illustration
  plot(oldPolygon, xlim=c(0,6), ylim=c(0,6), main="(a)", pch=16)
  polygon(oldPolygon, lwd=2, col="#00000033")
  text(oldPolygon, c(expression(P[1]), expression(P[2]),
                     expression(P[3]), expression(P[4]),
                     expression(P[5])), pos=c(1,2,3,4,4), cex=2)
  polygon(newPolygon, border=4, lwd=2, col="#52A3E199")
  points(newPolygon, pch=16, col=4)
  text(newPolygon, c(expression(paste(P[1],minute)), expression(paste(P[2],minute)),
             expression(paste(P[3],minute)), expression(paste(P[4],minute)),
             expression(paste(P[5],minute))), pos=c(1,3,2,4,4), col=4, cex=2)

  C <- polygon_area(oldPolygon)$centre
  text(C[1], C[2], "C", pos=4, cex=2)
  for(i in 1:5) lines(c(C[1], oldPolygon[i,1]), 
                      c(C[2], oldPolygon[i,2]), lty=2, lwd=2, type="b")

Package 'bivrp'

Help Index

Bivariate Residual Plots with Simulation Polygons

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Author(s)

Bivariate Residual Plots with Simulation Polygons

Description

Usage

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Details

Value

Author(s)

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Examples

Determine if point is inside or outside a simple polygon area

Description

Usage

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Value

Author(s)

Examples

Plot Method for bivrp Objects

Description

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Author(s)

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Polygon operations

Description

Usage

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Details

Author(s)

References

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Examples