# kappa4alBoot: Sigmoidal curve fitting. In mtloots/alR: Arc Lengths of Statistical Functions

## Description

Bootstrap estimates, along with standard errors and confidence intervals, of a nonlinear model, resulting from arc length fitting of the four-parameter kappa sigmoidal function.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```kappa4alBoot(formula, data = list(), xin, lower, upper, q1, q2, tol, maxiter, bootstraps, bootName, ...) ## Default S3 method: kappa4alBoot(formula, data = list(), xin, lower = c(0, -5, -5), upper = c(10, 1, 1), q1, q2, tol = 1e-15, maxiter = 50000, bootstraps, bootName, ...) ## S3 method for class 'kappa4alBoot' print(x, ...) ## S3 method for class 'kappa4alBoot' summary(object, ...) ## S3 method for class 'summary.kappa4alBoot' print(x, ...) ## S3 method for class 'formula' kappa4alBoot(formula, data = list(), xin, lower, upper, q1, q2, tol, maxiter, bootstraps, bootName, ...) ## S3 method for class 'kappa4alBoot' 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`. `xin` Numeric vector of length 3 containing initial values, for σ, h, and k. `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. `bootstraps` An integer giving the number of bootstrap samples. `bootName` The name of the .rds file to store the kappa4alBoot object. May include a path. `...` Arguments to be passed on to the differential evolution function `JDEoptim`. `x` A kappa4alBoot object. `object` A kappa4alBoot object. `newdata` The data on which the estimated model is to be fitted.

## Details

On systems where the pbMPI package is available, this code will run in parallel.

## Value

A generic S3 object with class kappa4alBoot.

kappa4alBoot.default: A list object (saved using `saveRDS` in the specified location) with the following components:

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

• coefficients: A vector of estimated coefficients.

• bcoefficients: A vector of bootstrap coefficients, resulting from bootstrap estimation.

• se: The standard errors for the estimates resulting from bootstrap estimation.

• error: The value of the objective function.

• errorList: A vector of values of the objective function for each bootstrap sample.

• fitted.values: A vector of estimated values.

• residuals: The residuals resulting from the fitted model.

• call: The call to the function.

• time: Min, mean and max time incurred by the computation, as obtained from `comm.timer`, or that obtained from `system.time`.

summary.kappa4alBoot: A list of class summary.kappa4alBoot with the following components:

• call: Original call to the `kappa4alBoot` function.

• coefficients: A matrix with estimates, estimated errors, and 95% parameter confidence intervals (based on the inverse empirical distribution function).

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

• r.squared: The r^{2} coefficient.

• sigma: The residual standard error.

• error: Value of the objective function.

• time: Min, mean and max time incurred by the computation, as obtained from `comm.timer`, or that obtained from `system.time`.

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

• errorSum: Summary statistics for the distribution of the value of the objective function.

print.summary.kappa4alBoot: The object passed to the function is returned invisibly.

predict.kappa4alBoot: A vector of predicted values resulting from the estimated model.

## Methods (by class)

• `default`: default method for kappa4alBoot.

• `kappa4alBoot`: print method for kappa4alBoot.

• `kappa4alBoot`: summary method for kappa4alBoot.

• `summary.kappa4alBoot`: print method for summary.kappa4alBoot.

• `formula`: formula method for kappa4alBoot.

• `kappa4alBoot`: predict method for kappa4alBoot.

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