kappa4al: Sigmoidal curve fitting.

In mtloots/alR: Arc Lengths of Statistical Functions

Description

A framework for arc length fitting of the four-parameter kappa sigmoidal function.

Usage

kappa4al(formula, data = list(), lower, upper, q1, q2, tol, maxiter, ...)

## Default S3 method:
kappa4al(formula, data = list(), lower = c(0, -5, -5),
  upper = c(10, 1, 1), q1, q2, tol = 1e-15, maxiter = 50000, ...)

## S3 method for class 'kappa4al'
print(x, ...)

## S3 method for class 'kappa4al'
summary(object, ...)

## S3 method for class 'summary.kappa4al'
print(x, ...)

## S3 method for class 'formula'
kappa4al(formula, data = list(), lower = c(0, -5, -5),
  upper = c(10, 1, 1), q1, q2, tol = 1e-15, maxiter = 50000, ...)

## S3 method for class 'kappa4al'
predict(object, newdata = NULL, ...)

Arguments

formula	An LHS ~ RHS formula, specifying the linear model to be estimated.
data	A data.frame which contains the variables in formula.
lower	A vector of lower constraints for the parameters to be estimated; defaults to c(0, -5, -5).
upper	A vector of upper constraints for the parameters to be estimated; defaults to c(10, 1, 1).
q1, q2	Numeric vectors, for the lower and upper bounds of the intervals over which arc lengths are to be computed.
tol	Error tolerance level; defaults to 1e-15.
maxiter	The maximum number of iterations allowed; defaults to 50000.
...	Arguments to be passed on to the differential evolution function JDEoptim.
x	A kappa4al object.
object	A kappa4al object.
newdata	The data on which the estimated model is to be fitted.

Value

A generic S3 object with class kappa4al.

kappa4al.default: A list with all components from JDEoptim, as well as:

• intercept: Did the model contain an intercept TRUE/FALSE?

• coefficients: A vector of estimated coefficients.

• error: The value of the objective function.

• fitted.values: A vector of estimated values.

• residuals: The residuals resulting from the fitted model.

• call: The call to the function.

• ALFHat: Arc length segments of the empirical CDF (calculated from data).

• ALF: Arc length segments of the CDF of the four-parameter kappa distribution (theoretical). p1: The vector of sample quantiles in the data corresponding to q1. p2: The vector of sample quantiles in the data corresponding to q2.

summary.kappa4al: A list of class summary.kappa4al with the following components:

• call: Original call to the kappa4al function.

• coefficients: A vector with parameter estimates.

• arclengths: A matrix of the arc length segments of the dependent and independent variables that were matched.

• r.squared: The r^{2} coefficient.

• sigma: The residual standard error.

• error: Value of the objective function.

• residSum: Summary statistics for the distribution of the residuals.

print.summary.kappa4al: The object passed to the function is returned invisibly.

predict.kappa4al: A vector of predicted values resulting from the estimated model.

Methods (by class)

• default: default method for kappa4al.

• kappa4al: print method for kappa4al.

• kappa4al: summary method for kappa4al.

• summary.kappa4al: print method for summary.kappa4al.

• formula: formula method for kappa4al.

• kappa4al: predict method for kappa4al.

Examples

k <- kappa4tc(-4, 0, 1)$par
x <- seq(qkappa4(0, 4, 0.4, -4, k), qkappa4(0.7, 4, 0.4, -4, k), length.out=100)
y <- sapply(x, function(i) pkappa4(i, 4, 0.4, -4, k))
kappa4nls.default(y~x, q1=c(0.025, 0.5), q2=c(0.5, 0.975), tol=1e-5)

u <- seq(qkappa4(0.1, 4, 0.4, -4, k), qkappa4(0.8, 4, 0.4, -4, k), length.out=100)
v <- sapply(u, function(i) pkappa4(i, 4, 0.4, -4, k))
al <- kappa4al(y~x, q1=c(0.025, 0.5), q2=c(0.5, 0.975), tol=1e-5)
predict(al, newdata=data.frame(y=v, x=u))

mtloots/alR documentation built on May 23, 2019, 8:18 a.m.