Add a Confidence Region or Bayesian Credible Region for Regression Lines to a Scatterplot

Produce a confidence or credible region for regression lines based on a sample of bootstrap beta values or posterior beta values. The beta parameters are the intercept and slope from a simple linear regression.

Usage

regcr(beta, x, em.beta = NULL, em.sigma = NULL, alpha = .05, 
      nonparametric = FALSE, plot = FALSE, xyaxes = TRUE, ...)

Arguments

beta

An nx2 matrix of regression parameters. The first column gives the intercepts and the second column gives the slopes.

x

An n-vector of the predictor variable which is necessary when nonparametric = TRUE.

em.beta

The estimates for beta required when obtaining confidence regions. This is required for performing the standardization necessary when obtaining nonparametric confidence regions.

em.sigma

The estimates for the regression standard deviation required when obtaining confidence regions. This is required for performing the standardization necessary when obtaining nonparametric confidence regions.

alpha

The proportion of the beta sample to remove. In other words, 1-alpha is the level of the credible region.

nonparametric

If nonparametric = TRUE, then the region is based on the convex hull of the remaining beta after trimming, which is accomplished using a data depth technique. If nonparametric = FALSE, then the region is based on the asymptotic normal approximation.

plot

If plot = TRUE, lines are added to the existing plot. The type of plot created depends on the value of xyaxes.

xyaxes

If xyaxes = TRUE and plot = TRUE, then a confidence or credible region for the regression lines is plotted on the x-y axes, presumably overlaid on a scatterplot of the data. If xyaxes = FALSE and plot = TRUE, the (convex) credible region for the regression line is plotted on the beta, or intercept-slope, axes, presumably overlaid on a scatterplot of beta.

...

Graphical parameters passed to lines or plot command.

Value

regcr returns a list containing the following items:

boundary

A matrix of points in beta, or intercept-slope, space arrayed along the boundary of the confidence or credible region.

upper

A matrix of points in x-y space arrayed along the upper confidence or credible limit for the regression line.

lower

A matrix of points in x-y space arrayed along the lower confidence or credible limit for the regression line.

See also

regmixEM, regmixMH

Examples

## Nonparametric credible regions fit to NOdata. 

data(NOdata)
attach(NOdata)
#> The following objects are masked from NOdata (pos = 6):
#> 
#>     Equivalence, NO
#> The following objects are masked from NOdata (pos = 7):
#> 
#>     Equivalence, NO
set.seed(100)
beta <- matrix(c(1.3, -0.1, 0.6, 0.1), 2, 2)
sigma <- c(.02, .05)
MH.out <- regmixMH(Equivalence, NO, beta = beta, s = sigma, 
                   sampsize = 2500, omega = .0013)
#> Acceptance rate: 39.48%
attach(data.frame(MH.out$theta))
beta.c1 <- cbind(beta0.1[2400:2499], beta1.1[2400:2499])
beta.c2 <- cbind(beta0.2[2400:2499], beta1.2[2400:2499])
plot(NO, Equivalence)
regcr(beta.c1, x = NO, nonparametric = TRUE, plot = TRUE, 
      col = 2)
regcr(beta.c2, x = NO, nonparametric = TRUE, plot = TRUE, 
      col = 3)