monpol: Monotone Polynomials

In MonoPoly: Functions to Fit Monotone Polynomials

Description

Determine the least-squares estimates of the parameters of a monotone polynomial

Usage

monpol(formula, data, subset, weights, na.action,
       degree = 3, K, start,
       a = -Inf, b=Inf,
       trace = FALSE, plot.it = FALSE,
       control = monpol.control(),
       algorithm = c("Full", "Hawkins", "BCD", "CD1", "CD2"),
       ptype = c("SOS", "Elphinstone", "EHH", "Penttila"),
       ctype = c("cge0", "c2"),
       monotone,
       model=FALSE, x=FALSE, y=FALSE)

Arguments

formula	an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.
data	an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which monpol is called.
subset	an optional vector specifying a subset of observations to be used in the fitting process.
weights	an optional vector of weights to be used in the fitting process. Should be NULL or a numeric vector.
na.action	a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. The ‘factory-fresh’ default is na.omit. Another possible value is NULL, no action. Value na.exclude can be useful.
degree	positive integer, a polynomial with highest power equal to degree will be fitted to the data.
K	non-negative integer, a polynomial with highest power 2K+1 will be fitted to the data.
start	optional starting value for the iterative fitting.
a,b	polynomial should be monotone on the interval from a to b. If either parameter is finite, parameterisation “SOS” has to be used.
trace	print out information about the progress of the interative fitting at the start and then every trace iterations.
plot.it	plot the data and initial fit, then plot current fit every plot.it iterations.
control	settings that control the iterative fit; see monpol.control for details.
algorithm	algorithm to be used. It is recommended to use either “Full” or “Hawkins”; see both papers in ‘References’ for details.
ptype	parameterisation to be used. It is recommended to use the “SOS” parameterisation; see the 2016 paper in ‘References’ for details.
ctype	parameterisation to be used; see paper in ‘References’ for details.
monotone	only used for parameterisation “SOS” to enforce the kind of monotonicity desired over the interval [a,b], should be “increasing” or “decreasing”.
model, x, y	logicals. If TRUE the corresponding components of the fit (the model frame, the model matrix, the response, the QR decomposition) are returned.

Details

A monpol object is a type of fitted model object. It has methods for the generic function coef, fitted, formula, logLik, model.matrix, predict, print, residuals.

The parameterisation type “SOS” with the “Full” algorithm is currently the recommended fitting procedure and is discussed in the 2016 paper in ‘References’. For this parameterisation the argument ctype is ignored.

The “Hawkins” algorithm is also recommended and discussed in both papers in the ‘References’.

The parameterisations “Elphinstone”, “EHH” and “Pentilla”, for which the argument “ctype” defines a further variation of parameterisation, work together with algorithms “Full”, “BCD”, “CD1” and “CD2”. These parameterisations and algorithms are discussed in the 2013 paper in ‘References’.

Value

monpol returns an object of class "monpol"

Author(s)

Berwin A Turlach <[e-mail]>

References

Murray, K., M<c3><bc>ller, S. and Turlach, B.A. (2016). Fast and flexible methods for monotone polynomial fitting, Journal of Statistical Computation and Simulation 86(15): 2946–2966, doi: 10.1080/00949655.2016.1139582.

Murray, K., M<c3><bc>ller, S. and Turlach, B.A. (2013). Revisiting fitting monotone polynomials to data, Computational Statistics 28(5): 1989–2005, doi: 10.1007/s00180-012-0390-5.

Examples

monpol(y~x, w0)

Example output

Loading required package: quadprog

Monotone polynomial model
Call:
monpol(formula = y ~ x, data = w0)

Coefficients:
    beta0      beta1      beta2      beta3  
-0.004059   0.015497   0.008259   0.072618  

MonoPoly documentation built on May 2, 2019, 7:59 a.m.