lmCalib: Calibration in regression.

In tsieger/tsiMisc: Miscelaneous utility functions, mostly related to exploratory statistical analysis

Calibration in regression.

Description

lmCalib computes the estimate of x_0 in which the regression of y ~ x reaches given y0, and the related confidence interval.

Usage

lmCalib(x, y, y0, fixed = FALSE, 
    approx = FALSE, alpha = 0.05)

Arguments

x	independent variable
y	dependent variable
y0	dependent variable for which to compute the expected independent variable
fixed	is y0 fixed, or random?
approx	use approximation, or Fieller method?
alpha	confidence interval significance level

Details

The code is taken from Appendix A.4.5 in Zvara2008. The estimation is based on chapter 4.4. in Zvara2008

Value

A vector of the estimate of 'x0', and lower and upper limits of related confidence interval.

Author(s)

Tomas Sieger

References

Karel Zv\'ara: Regrese, Matfyzpress Praha 2008, J.A. Neter, W. Wasserman, M. Kutner: Applied Linear Statistical Models, Irwin, Homewood, Illinois (1985).

See Also

lmInt

Examples

iris.setosa<-iris[iris$Species=='setosa',]
attach(iris.setosa)

plot(Sepal.Length, Sepal.Width, xlim=c(min(3.5,min(Sepal.Length)),max(Sepal.Length)))
abline(coef(lm(Sepal.Width ~ Sepal.Length)))

y0 <- 3
abline(h = y0, col='gray')

# Fieller method with y0 fixed
calib <- lmCalib(Sepal.Length, Sepal.Width, y0, fixed = TRUE, approx = TRUE)
lines(calib[2:3],rep(y0,2)*1.01,col='red',lwd=3)
points(calib[1],y0*1.01,pch=19,cex=1.3,col='red')
# Fieller method with y0 random
calib <- lmCalib(Sepal.Length, Sepal.Width, y0, fixed = FALSE, approx = TRUE)
lines(calib[2:3],rep(y0,2)*1.03,col='red',lwd=1)
points(calib[1],y0*1.03,pch=19,cex=.8,col='red')

# approximate method with y0 fixed
calib <- lmCalib(Sepal.Length, Sepal.Width, y0, fixed = TRUE, approx = FALSE)
lines(calib[2:3],rep(y0,2)/1.01,lwd=3,col='blue')
points(calib[1],y0/1.01,pch=19,cex=1.2,col='blue')
# approximate method with y0 random
calib <- lmCalib(Sepal.Length, Sepal.Width, y0, fixed = FALSE, approx = FALSE)
lines(calib[2:3],rep(y0,2)/1.03,lwd=1,col='blue')
points(calib[1],y0/1.03,pch=19,cex=.8,col='blue')

legend('topleft', bg='white',
  c(paste0('Fieller method with y0=',y0,' fixed'),
    paste0('Fieller method with y0=',y0,' random'),
    paste0('approximate m. with y0=',y0,' fixed'),
    paste0('approximate m. with y0=',y0,'  random'),
    '(vertical offsets for visualization',
    ' purposes only)'),
  col = c('red', 'red', 'blue', 'blue', 'black'),
  lwd = c(3, 1, 3, 1, NA, NA))

detach(iris.setosa)

tsieger/tsiMisc documentation built on Oct. 10, 2023, 10:24 p.m.