Nlstools Example

# Loading package and dataset
library("nlstools")

## 
## 'nlstools' has been loaded.

## IMPORTANT NOTICE: Most nonlinear regression models and data set examples

## related to predictive microbiolgy have been moved to the package 'nlsMicrobio'

set.seed(405)

# Define the nonlinear model
formulaExp <- as.formula(VO2 ~ (t <= 5.883) * VO2rest + (t > 5.883) * 
  (VO2rest + (VO2peak - VO2rest) * (1 - exp(-(t - 5.883) / mu))))

# Graphical assessment of starting values
preview(formulaExp, data = O2K, 
  start = list(VO2rest = 400, VO2peak = 1600, mu = 1)) # figure 2

## 
## RSS:  149000

# Model fit, overview of the results, 
# plot of the fitted model superimposed to the data
O2K.nls1 <- nls(formulaExp, start = list(VO2rest = 400, VO2peak = 1600, 
                mu = 1), data = O2K)
overview(O2K.nls1)

## 
## ------
## Formula: VO2 ~ (t <= 5.883) * VO2rest + (t > 5.883) * (VO2rest + (VO2peak - 
##     VO2rest) * (1 - exp(-(t - 5.883)/mu)))
## 
## Parameters:
##          Estimate Std. Error t value Pr(>|t|)    
## VO2rest 3.568e+02  1.141e+01   31.26   <2e-16 ***
## VO2peak 1.631e+03  2.149e+01   75.88   <2e-16 ***
## mu      1.186e+00  7.661e-02   15.48   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 49.59 on 33 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.598e-06
## 
## ------
## Residual sum of squares: 81200 
## 
## ------
## t-based confidence interval:
##                2.5%       97.5%
## VO2rest  333.537401  379.980302
## VO2peak 1587.155300 1674.611703
## mu         1.030255    1.342002
## 
## ------
## Correlation matrix:
##            VO2rest    VO2peak        mu
## VO2rest 1.00000000 0.07907046 0.1995377
## VO2peak 0.07907046 1.00000000 0.7554924
## mu      0.19953773 0.75549241 1.0000000

plotfit(O2K.nls1, smooth = TRUE)