tolerance (version 2.0.0)

nlregtol.int: Nonlinear Regression Tolerance Bounds

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, 
             ...)

Value

nlregtol.int returns a data frame with items:

alpha

The specified significance level.

P

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

y.hat

The predicted value of the response for the fitted nonlinear regression model.

y

The value of the response given in the first column of xy.data. This data frame is sorted by this value.

1-sided.lower

The 1-sided lower tolerance bound. This is given only if side = 1.

1-sided.upper

The 1-sided upper tolerance bound. This is given only if side = 1.

2-sided.lower

The 2-sided lower tolerance bound. This is given only if side = 2.

2-sided.upper

The 2-sided upper tolerance bound. This is given only if side = 2.

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.

...

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.

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

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)))
out <- nlregtol.int(formula = formula, 
                    xy.data = data.frame(cbind(y, x)), 
                    x.new=cbind(c(10, 20)), side = 2, 
                    alpha = 0.05, P = 0.95)
out

plottol(out, x = x, y = y, side = "two", x.lab = "X", 
         y.lab = "Y")