Plot method for regvec3d objects

The plot method for regvec3d objects uses the low-level graphics tools in this package to draw 3D and 3D vector diagrams reflecting the partial and marginal relations of y to x1 and x2 in a bivariate multiple linear regression model, lm(y ~ x1 + x2).

The summary method prints the vectors and their vector lengths, followed by the summary for the model.

Usage

# S3 method for class 'regvec3d'
plot(
  x,
  y,
  dimension = 3,
  col = c("black", "red", "blue", "brown", "lightgray"),
  col.plane = "gray",
  cex.lab = 1.2,
  show.base = 2,
  show.marginal = FALSE,
  show.hplane = TRUE,
  show.angles = TRUE,
  error.sphere = c("none", "e", "y.hat"),
  scale.error.sphere = x$scale,
  level.error.sphere = 0.95,
  grid = FALSE,
  add = FALSE,
  ...
)

# S3 method for class 'regvec3d'
summary(object, ...)

# S3 method for class 'regvec3d'
print(x, ...)

Arguments

x: A “regvec3d” object
y: Ignored; only included for compatibility with the S3 generic
dimension: Number of dimensions to plot: 3 (default) or 2
col: A vector of 5 colors. col[1] is used for the y and residual (e) vectors, and for x1 and x2; col[2] is used for the vectors y -> yhat and y -> e; col[3] is used for the vectors yhat -> b1 and yhat -> b2;
col.plane: Color of the base plane in a 3D plot or axes in a 2D plot
cex.lab: character expansion applied to vector labels. May be a number or numeric vector corresponding to the the rows of X, recycled as necessary.
show.base: If show.base > 0, draws the base plane in a 3D plot; if show.base > 1, the plane is drawn thicker
show.marginal: If TRUE also draws lines showing the marginal relations of y on x1 and on x2
show.hplane: If TRUE, draws the plane defined by y, yhat and the origin in the 3D
show.angles: If TRUE, draw and label the angle between the x1 and x2 and between y and yhat, corresponding respectively to the correlation between the xs and the multiple correlation
error.sphere: Plot a sphere (or in 2D, a circle) of radius proportional to the length of the residual vector, centered either at the origin ("e") or at the fitted-values vector ("y.hat"; the default is "none".)
scale.error.sphere: Whether to scale the error sphere if error.sphere="y.hat"; defaults to TRUE if the vectors representing the variables are scaled, in which case the oblique projections of the error spheres can represent confidence intervals for the coefficients; otherwise defaults to FALSE.
level.error.sphere: The confidence level for the error sphere, applied if scale.error.sphere=TRUE.
grid: If TRUE, draws a light grid on the base plane
add: If TRUE, add to the current plot; otherwise start a new rgl or plot window
...: Parameters passed down to functions [unused now]
object: A regvec3d object for the summary method

Value

None

Details

A 3D diagram shows the vector y and the plane formed by the predictors, x1 and x2, where all variables are represented in deviation form, so that the intercept need not be included.

A 2D diagram, using the first two columns of the result, can be used to show the projection of the space in the x1, x2 plane.

The drawing functions vectors and link{vectors3d} used by the plot.regvec3d method only work reasonably well if the variables are shown on commensurate scales, i.e., with either scale=TRUE or normalize=TRUE.

References

Fox, J. (2016). Applied Regression Analysis and Generalized Linear Models, 3rd ed., Sage, Chapter 10.

Examples

if (require(carData)) {
   data("Duncan", package="carData")
   dunc.reg <- regvec3d(prestige ~ income + education, data=Duncan)
   plot(dunc.reg)
   plot(dunc.reg, dimension=2)
   plot(dunc.reg, error.sphere="e")
   summary(dunc.reg)

   # Example showing Simpson's paradox
   data("States", package="carData")
   states.vec <- regvec3d(SATM ~ pay + percent, data=States, scale=TRUE)
   plot(states.vec, show.marginal=TRUE)
   plot(states.vec, show.marginal=TRUE, dimension=2)
   summary(states.vec)
}
#> Loading required package: carData

#>                        x         y         z    length
#> income         0.7754622 0.0000000 0.0000000 0.7754622
#> education      0.6842863 0.6509930 0.0000000 0.9444785
#> prestige       0.8378014 0.3553340 0.4145197 1.0000000
#> residuals      0.0000000 0.0000000 0.4145197 0.4145197
#> prestige hat   0.8378014 0.3553340 0.0000000 0.9100403
#> b1 income      0.4642947 0.0000000 0.0000000 0.4642947
#> b2 education   0.3735067 0.3553340 0.0000000 0.5155284
#> prestige hat 1 0.8378014 0.0000000 0.0000000 0.8378014
#> prestige hat 2 0.6172234 0.5871929 0.0000000 0.8519156
#> 
#> Call:
#> lm(formula = formula, data = Data)
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -29.538  -6.417   0.655   6.605  34.641 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept) -6.06466    4.27194  -1.420    0.163    
#> income.      0.59873    0.11967   5.003 1.05e-05 ***
#> education.   0.54583    0.09825   5.555 1.73e-06 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 13.37 on 42 degrees of freedom
#> Multiple R-squared:  0.8282,	Adjusted R-squared:   0.82 
#> F-statistic: 101.2 on 2 and 42 DF,  p-value: < 2.2e-16
#> 

#>                      x          y        z    length
#> pay          1.0000000  0.0000000 0.000000 1.0000000
#> percent      0.6630098  0.7486108 0.000000 1.0000000
#> SATM        -0.4853306 -0.7164880 0.501098 1.0000000
#> residuals    0.0000000  0.0000000 0.501098 0.5010980
#> SATM hat    -0.4853306 -0.7164880 0.000000 0.8653905
#> b1 pay       0.1492295  0.0000000 0.000000 0.1492295
#> b2 percent  -0.6345601 -0.7164880 0.000000 0.9570901
#> SATM hat 1  -0.4853306  0.0000000 0.000000 0.4853306
#> SATM hat 2  -0.5689615 -0.6424199 0.000000 0.8581495
#> 
#> Call:
#> lm(formula = formula, data = Data)
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -29.697 -13.788   0.701   9.988  42.961 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept) 513.6990    16.9174  30.365  < 2e-16 ***
#> pay.          0.9718     0.6292   1.545    0.129    
#> percent.     -1.3743     0.1387  -9.906 3.45e-13 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 17.68 on 48 degrees of freedom
#> Multiple R-squared:  0.7489,	Adjusted R-squared:  0.7384 
#> F-statistic: 71.58 on 2 and 48 DF,  p-value: 3.947e-15
#>