quasi_rsq_nls: R squared statistic for non linear models

In padpadpadpad/nlsTools: Methods for Finding the Best Estimated Fits for Non-Least Squares Regression over the Level of a Factor

Description

Calculates a quasi-rsquared value for non linear least squares regression models.

Usage

quasi_rsq_nls(mdl, y, param)

Arguments

mdl	model object from which R^2 is desired. Used to calculate the residual sum of squares.
y	a vector of the response variable from the model.
param	the number of parameters of the non-linear model

Details

cautionary notes of whether its useful are provided here. A personal highlight of which is 'If someone asks for rope to hang themselves, its fine to give it to them (while performing due diligence by asking "are you sure you want to do this?")'

Calculated as :

1 - (n-1)/(n-param) * (1 - R^2)

where R^2 = 1 - RSS/TSS

RSS is the residual sum of squares given by deviance(mdl)

TSS is given by how much variance there is in the dependent variable:

(n - 1)*var(y)

Value

value of r squared for specific non-linear model object

Author(s)

Daniel Padfield

References

Spiess, A.N. & Neumeyer, N. (2010) An evaluation of R2 as an inadequate measure for nonlinear models in pharmacological and biochemical research: a Monte Carlo approach. BMC pharmacology, 10, 6.

A StackOverflow discussion

Examples

data(Chlorella_TRC)

# define the Sharpe-Schoolfield equation
schoolfield_high <- function(lnc, E, Eh, Th, temp, Tc) {
 Tc <- 273.15 + Tc
 k <- 8.62e-5
 boltzmann.term <- lnc + log(exp(E/k*(1/Tc - 1/temp)))
 inactivation.term <- log(1/(1 + exp(Eh/k*(1/Th - 1/temp))))
 return(boltzmann.term + inactivation.term)
}

fit <- minpack.lm::nlsLM(ln.rate ~ schoolfield_high(lnc, E, Eh, Th, temp = K, Tc = 20),
                data = Chlorella_TRC[Chlorella_TRC$curve_id == 1,],
                start = c(lnc = -1.2, E = 0.95, Eh = 5, Th = 315))

quasi_rsq_nls(fit, Chlorella_TRC[Chlorella_TRC$curve_id == 1,]$ln.rate, 4)

0.4608054

padpadpadpad/nlsTools documentation built on May 24, 2019, 5:59 p.m.