nlregtol.int {tolerance}

Nonlinear Regression Tolerance Bounds, Version 2

Description

Provides 1-sided or 2-sided nonlinear regression tolerance bounds.

Usage

nlregtol.int(formula, xy.data = data.frame(), x.new = NULL, 
             side = 1, alpha = 0.05, P = 0.99, maxiter = 50, 
             new = FALSE, ...)

Arguments

formula

A nonlinear model formula including variables and parameters.

xy.data

A data frame in which to evaluate the formulas in formula. The first column of xy.data must be the response variable.

x.new

Any new levels of the predictor(s) for which to report the tolerance bounds. The number of columns must be 1 less than the number of columns for xy.data.

side

Whether a 1-sided or 2-sided tolerance bound is required (determined by side = 1 or side = 2, respectively).

alpha

The level chosen such that 1-alpha is the confidence level.

P

The proportion of the population to be covered by the tolerance bound(s).

maxiter

A positive integer specifying the maximum number of iterations that the nonlinear least squares routine (nls) should run.

new

When new = TRUE, the function shows updated version of outcomes.

...

Optional arguments passed to nls when estimating the nonlinear regression equation.

Details

It is highly recommended that the user specify starting values for the nls routine.

Value

npregtol.int2 returns a list with items:

tol

Data frame of original response varible y, fitted values y.hat, corresponding tolerance limits. The data frame is ordered by X values. If there are new data for prediction, predicted values are attached in the end.

alpha.P.side

Model specifications of critical level, content level and side.

reg.type

Type of regression model.

model

The linear regression model fitted.

newdata

X values of new data for prediction.

xy.data.original

Original data frame

References

Wallis, W. A. (1951), Tolerance Intervals for Linear Regression, in Second Berkeley Symposium on Mathematical Statistics and Probability, ed. J. Neyman, Berkeley: University of CA Press, 43–51.

Young, D. S. (2013), Regression Tolerance Intervals, Communications in Statistics - Simulation and Computation, 42, 2040–2055.

See Also

nls, nlregtol.int

Examples

 
## 95%/95% 2-sided nonlinear regression tolerance bounds
## for a sample of size 50.
set.seed(100)
x <- runif(50, 5, 45)
f1 <- function(x, b1, b2) b1 + (0.49 - b1)*exp(-b2*(x - 8)) +
  rnorm(50, sd = 0.01)
y <- f1(x, 0.39, 0.11)
formula <- as.formula(y ~ b1 + (0.49 - b1)*exp(-b2*(x - 8)))
out1 <- nlregtol.int(formula = formula,
                     xy.data = data.frame(cbind(y, x)),
                     x.new=c(10,20), side = 2,
                     alpha = 0.05, P = 0.95 , new = TRUE)
out1
#########
set.seed(100)
x1 <- runif(50, 5, 45)
x2 <- rnorm(50, 0, 10)
f1 <- function(x1, x2, b1, b2) {(0.49 - b1)*exp(-b2*(x1 + x2 - 8)) +
    rnorm(50, sd = 0.01)}
y <- f1(x1 , x2 , 0.25 , 0.39)
formula <- as.formula(y ~ (0.49 - b1)*exp(-b2*(x1 + x2 - 8)))
out2 <- nlregtol.int(formula = formula,
                     xy.data = data.frame(cbind(y, x1 , x2)),
                     x.new=cbind(c(10,20) , c(47 , 53)), side = 2,
                     alpha = 0.05, P = 0.95 , new = TRUE)
out2