statforbiology (version 0.9.9)

poly2: Simple polynomial regression functions

Description

These functions provide the simple polynomial (second order) regression model (poly2), the polynomial regression model with self-starter for the nls function (NLS.poly2) and the polynomial regression function with self-starter for the drm function in the drc package (DRC.poly2). Fitting linear functions with nonlinear least square regression is sub-optimal, but it might be useful for comparing alternative models.

Usage

poly2.fun(predictor, a, b, c)
  NLS.poly2(predictor, a, b, c)
  DRC.poly2(fixed = c(NA, NA, NA), names = c("a", "b", "c"))

Value

poly2.fun and NLS.poly2 return a numeric value, while DRC.poly2 returns a list containing the nonlinear function, the self starter function and the parameter names.

Arguments

predictor

a numeric vector of values at which to evaluate the model

a

numeric. The response when the predictor is equal to 0.

b

numeric. The slope at X = 0

c

numeric. Regression parameter

fixed

numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed.

names

a vector of character strings giving the names of the parameters. The default is reasonable.

Author

Andrea Onofri

Details

The simple polynomial (second order) regression model is given by the following equation: $$ f(x) = a + b x + c x^2$$

References

Ratkowsky, DA (1990) Handbook of nonlinear regression models. New York (USA): Marcel Dekker Inc.

Onofri, A. (2020). A collection of self-starters for nonlinear regression in R. See: https://www.statforbiology.com/2020/stat_nls_usefulfunctions/

Examples

# Polynomial regression
X <- seq(5, 50, 5)
Y <- c(12.6, 74.1, 157.6, 225.5, 303.4, 462.8,
       669.9, 805.3, 964.2, 1169)

model <- nls(Y ~ NLS.poly2(X, a, b, c))
summary(model)
model <- drm(Y ~ X, fct = DRC.poly2())
summary(model)