rgp (R genetic programming) package - not able to do regression

Question

I am trying to do non-linear regression using R genetic package (rgp) using technique used here: Fitting a curve to specific data (see second method). I am using R package drc for heartrate data:

library(drc)

head(heartrate)
#  pressure   rate
#1    50.85 348.76
#2    54.92 344.45
#3    59.23 343.05
#4    61.91 332.92
#5    65.22 315.31
#6    67.79 313.50

library(rgp)

res <- symbolicRegression(rate ~ pressure, data=heartrate)

(symbreg <- res$population[[which.min(sapply(res$population, res$fitnessFunction))]])
#function (pressure) 
#pressure + (pressure/0.853106872646055 + pressure)

ggplot() + 
    geom_point(data=heartrate, aes(pressure,rate), size = 3) +
    geom_line(data=data.frame(symbx=heartrate$pressure, 
                              symby=sapply(heartrate$pressure, symbreg)), 
              aes(symbx, symby), colour = "red")

However, the resulting regression line that I am getting is clearly incorrect. The distribution of data points indicate a curvilinear relation with rate reducing as pressure increases (inverse association). However, the regression line generated is linear and in the wrong direction.

Where is the error?

Edit:

Using increased steps as suggested by @cuttlefish44 in comments:

res = symbolicRegression(rate ~ pressure, data = heartrate, stopCondition = makeStepsStopCondition(45000))

(symbreg <- res$population[[which.min(sapply(res$population, res$fitnessFunction))]])
#function (pressure) 
#exp(exp(exp(cos(cos(-9.23878724686801/pressure)))))

It took 8 minutes to complete. The plot is:

The direction of regression line is better than above (!), but it indicates that it will take a really long time to reach the obvious direction. The regression line with the function obtained by @cuttlefish44 is also similar and not a really good fit.

Answer 1

You may have already read this but I think your answer is hidden somewhere inside this introduction to RGP package written by Oliver Flasch.

I don't know anything about rgppackage but if you only want a linear regression, why don't you use lm()function from the base package ?

At least you would be able to estimate parameters of β₀ and β₁ for Ordinary least squares regression :

rate = β₁*pressure + β₀

     linear.model <- lm(rate ~ pressure, data=heartrate)

     ggplot(data=heartrate, aes(x=pressure,y=rate)) + 
         geom_point() + 
         geom_smooth(method="lm", col="red")

linear regression with ggplot2

You can access the coeficcients with linear.model$coefficients

You can still manipulate the predicted values with linear.model$fitted.values

You have access to the residual with : linear.model$residuals

If you want to fit the curve with more accuracy the linear model might be not sufficient, you can try glm, or a polynomial regression and select the best model with AIC or BIC criteria.