rockchalk (version 1.8.111)

mcGraph1: Illustrate multicollinearity in regression, part 1.

Description

This is a set of functions that faciliates the examination of multicollinearity. Suppose the "true" relationship is y[i] = 0.2 * x1[i] + 0.2 * x2[i] + e where e is Normal(0, stde^2).

mcGraph1 draws the 3D regression space, but all of the points are illustrated "in" the flat plane of x1-x2 variables.

mcGraph2 draws a 3-D representation of a scatterplot with shadows in the x1-x2 plane. The observations are represented by blue points floating above the x1-x2 plane. If scaley=1, the end result is a scatterplot "cloud" of the y points above the x1-x2 plane, and gray shadows of the points are cast down from the cloud onto the x1-x2 plane itself. This uses persp to make the actual drawing.

With mcGraph3, the observations are scattered in 3-dimensions, the fitted values are represented by a mesh, and their shadows in the x1-x2 plane are also represented.

Usage

mcGraph1(x1, x2, y, x1lab, x2lab, ylab, ...)
mcGraph2(x1, x2, y, rescaley = 1, drawArrows = TRUE, x1lab, x2lab, ylab,
  ...)
mcGraph3(x1, x2, y, interaction = FALSE, drawArrows = TRUE, x1lab, x2lab,
  ylab, ...)

Arguments

x1

a predictor vector

x2

a predictor vector

y

the dependent variable

x1lab

label for the x1 axis, (the one called "xlab" inside persp)

x2lab

label for the x2 axis, (the one called "ylab" inside persp)

ylab

label for the y (vertical) axis (the one called "zlab" inside persp)

...

additional parameters passed to persp

rescaley

a single scalar value or a vector of the same length as y.

drawArrows

TRUE or FALSE, do you want arrows from the plane to observed y?

interaction

a TRUE or FALSE request for inclusion of the x1-x2 interaction in the regression calculation

Value

mcGraph1 and mcGraph2 return only the perspective matrix from persp. It is returned so that users can add additional embellishments on the 3D plot (can be used with trans3d)

mcGraph3 returns a list of 2 objects. 1) the fitted regression model2) the perspective matrix used with persp to draw the image.

Details

These functions are specialized to a particular purpose. If you just want to draw 3D regressions, look at plotPlane.

Examples

# NOT RUN {
set.seed(12345)
## Create data with x1 and x2 correlated at 0.10
dat <- genCorrelatedData(rho=.1, stde=7)

mcGraph1(dat$x1, dat$x2, dat$y, theta=20, phi=8, ticktype="detailed", nticks=10)

set.seed(12345)
## Create data with x1 and x2 correlated at 0.10
dat <- genCorrelatedData(rho=.1, stde=7)
## This will "grow" the "cloud" of points up from the
## x1-x2 axis
mcGraph2(dat$x1, dat$x2, dat$y, rescaley = 0.0, theta = 0)
mcGraph2(dat$x1, dat$x2, dat$y, rescaley = 0.1, theta = 0)
mcGraph2(dat$x1, dat$x2, dat$y, rescaley = 0.2, theta = 0)
mcGraph2(dat$x1, dat$x2, dat$y, rescaley = 0.3, theta = 0)
mcGraph2(dat$x1, dat$x2, dat$y, rescaley = 0.4, theta = 0)
mcGraph2(dat$x1, dat$x2, dat$y, rescaley = 0.5, theta = 0)
mcGraph2(dat$x1, dat$x2, dat$y, rescaley = 0.6, theta = 0)
mcGraph2(dat$x1, dat$x2, dat$y, rescaley = 0.7, theta = 0)
mcGraph2(dat$x1, dat$x2, dat$y, rescaley = 0.8, theta = 0)
mcGraph2(dat$x1, dat$x2, dat$y, rescaley = 0.9, theta = 0)
mcGraph2(dat$x1, dat$x2, dat$y, rescaley = 1, theta = 0)

##rotate this
mcGraph2(dat$x1, dat$x2, dat$y, rescaley = 1, theta = 20)
mcGraph2(dat$x1, dat$x2, dat$y, rescaley = 1, theta = 40)
mcGraph2(dat$x1, dat$x2, dat$y, rescaley = 1, theta = 60)
mcGraph2(dat$x1, dat$x2, dat$y, rescaley = 1, theta = 80)

## once they reach the top, make them glitter a while
for(i in 1:20){
  mcGraph2(dat$x1, dat$x2, dat$y, rescaley = runif(length(dat$x1), .9,1.1), theta = 0)
}

set.seed(12345)
## Create data with x1 and x2 correlated at 0.10
dat <- genCorrelatedData(rho=.1, stde=7)

mcGraph3(dat$x1, dat$x2, dat$y, theta = 0)

dat2 <- genCorrelatedData(rho = 0, stde = 7)

mcGraph3(dat2$x1, dat2$x2, dat2$y, theta = 0, phi = 10)
mcGraph3(dat2$x1, dat2$x2, dat2$y, theta = 30, phi = 10)
mcGraph3(dat2$x1, dat2$x2, dat2$y, theta = -30, phi = 10)
mcGraph3(dat2$x1, dat2$x2, dat2$y, theta = -30, phi = -10)
mcGraph3(dat2$x1, dat2$x2, dat2$y, theta = -30, phi = -15)

## Run regressions with not-strongly correlated data
modset1 <- list()
for(i in 1:20){
  dat2 <- genCorrelatedData(rho = .1, stde = 7)
  summary(lm( y ~ x1 + x2 , data = dat2))
  modset1[[i]] <- mcGraph3(dat2$x1, dat2$x2, dat2$y, theta = -30)
}


## Run regressions with strongly correlated data
modset2 <- list()
for(i in 1:20){
  dat2 <- genCorrelatedData(rho = .981, stde = 7)
  summary(lm( y ~ x1 + x2 , data = dat2))
  modset2[[i]] <- mcGraph3(dat2$x1, dat2$x2, dat2$y, theta = -30)
}

dat3 <- genCorrelatedData(rho = .981, stde = 100, beta=c(0.1, 0.2, 0.3, -0.1))
mcGraph3(dat3$x1, dat3$x2, dat3$y, theta=-10, interaction = TRUE)
# }