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rregressionnon-linear-regressionpmml

How to perform a non linear regression for my data

I have set of Temperature and Discomfort index value for each temperature data. When I plot a graph between temperature(x axis) and Calculated Discomfort index value( y axis) I get a reversed U-shape curve. I want to do non linear regression out of it and convert it into PMML model. My aim is to get the predicted discomfort value if I give certain temperature.

Please find the below dataset :

Temp <- c(0,5,10,6 ,9,13,15,16,20,21,24,26,29,30,32,34,36,38,40,43,44,45, 50,60)

Disc<-c(0.00,0.10,0.25,0.15,0.24,0.26,0.30,0.31,0.40,0.41,0.49,0.50,0.56, 0.80,0.90,1.00,1.00,1.00,0.80,0.50,0.40,0.20,0.15,0.00)

How to do non linear regression (possibly with nls??) for this dataset?

enter image description here

Solution

  • I did take a look at this, then I think it is not as simple as using nls as most of us first thought.

    nls fits a parametric model, but from your data (the scatter plot), it is hard to propose a reasonable model assumption. I would suggest using non-parametric smoothing for this.

    There are many scatter plot smoothing methods, like kernel smoothing ksmooth, smoothing spline smooth.spline and LOESS loess. I prefer to using smooth.spline, and here is what we can do with it:

    fit <- smooth.spline(Temp, Disc)

    Please read ?smooth.spline for what it takes and what it returns. We can check the fitted spline curve by

    plot(Temp, Disc)
lines(fit, col = 2)

    enter image description here

    Should you want to make prediction elsewhere, use predict function (predict.smooth.spline). For example, if we want to predict Temp = 20 and Temp = 44, we can use

    predict(fit, c(20,44))$y
# [1] 0.3940963 0.3752191

    Prediction outside range(Temp) is not recommended, as it suffers from potential bad extrapolation effect.

    Before I resort to non-parametric method, I also tried non-linear regression with regression splines and orthogonal polynomial basis, but they don't provide satisfying result. The major reason is that there is no penalty on the smoothness. As an example, I show some try with poly:

    try1 <- lm(Disc ~ poly(Temp, degree = 3))
try2 <- lm(Disc ~ poly(Temp, degree = 4))
try3 <- lm(Disc ~ poly(Temp, degree = 5))

plot(Temp, Disc, ylim = c(-0.3,1.0))
x<- seq(min(Temp), max(Temp), length = 50)
newdat <- list(Temp = x)
lines(x, predict(try1, newdat), col = 2)
lines(x, predict(try2, newdat), col = 3)
lines(x, predict(try3, newdat), col = 4)

    enter image description here

    We can see that the fitted curve is artificial.