Exponential curve fitting with nls using data.table groups

Question

I'd like to fit exponential curves to groups 1 & 2 in the data table shown below and obtain a new column containing the residual standard error corresponding to each group. The exponential curve should follow y=a*exp(b*x)+c

## Example data table
DT <- data.table(
x = c(1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8),
y = c(15.4,16,16.4,17.7,20,23,27,35,25.4,26,26.4,27.7,30,33,37,45),
groups = c(1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2)

However, I only know how to fit nls curves and obtain the residual standard error of single groups using the code below which estimates good starting parameters a, b, and c:

subsetDT <- DT[group == 1]
c.0 <- min(subsetDT[,y]) * 0.5
model.0 <- lm(log(y- c.0) ~ x, data=subsetDT)
start <- list(a=exp(coef(model.0)[1]), b=coef(model.0)[2], c=c.0)
model <- nls(y ~ a * exp(b * x) + c,
         data = subsetDT, start = start, 
         control = nls.control(maxiter=500))
sigma <- summary(model)$sigma

I don't want to subset DT by group in a loop to calculate sigma and other model information.

I know that if I was using lm, I'd be able to do the following to obtain new columns containing model information:

DT[, `:=` (r.squared=summary(lm(log(y)~x))$r.squared,
           int=coef(lm(log(y)~x))[1],
           coeff=coef(lm(log(y)~x))[2]
          ), by=c("groups")]

How can I use := to fit an exponential curve and incorporate my nls parameters a, b, and c?

chinsoon12 chinsoon12 · Accepted Answer · 2018-09-26T00:47:03

If you are looking for adding sigma, a, b, c as new columns in your original dataset, you can do the following:

DT[, c("sigma", "a", "b", "c") := {
        c.0 <- min(y) * 0.5
        model.0 <- lm(log(y - c.0) ~ x, data=.SD)
        start <- list(a=exp(coef(model.0)[1]), b=coef(model.0)[2], c=c.0)
        model <- nls(y ~ a * exp(b * x) + c,
            data=.SD, 
            start=start, 
            control=nls.control(maxiter=500))
        c(.(sigma=summary(model)$sigma), as.list(coef(model)))
    },
    by=.(groups)]

output:

    x    y groups     sigma         a         b        c
 1: 1 15.4      1 0.2986243 0.5265405 0.4565363 14.56728
 2: 2 16.0      1 0.2986243 0.5265405 0.4565363 14.56728
 3: 3 16.4      1 0.2986243 0.5265405 0.4565363 14.56728
 4: 4 17.7      1 0.2986243 0.5265405 0.4565363 14.56728
 5: 5 20.0      1 0.2986243 0.5265405 0.4565363 14.56728
 6: 6 23.0      1 0.2986243 0.5265405 0.4565363 14.56728
 7: 7 27.0      1 0.2986243 0.5265405 0.4565363 14.56728
 8: 8 35.0      1 0.2986243 0.5265405 0.4565363 14.56728
 9: 1 25.4      2 0.2986243 0.5265404 0.4565363 24.56728
10: 2 26.0      2 0.2986243 0.5265404 0.4565363 24.56728
11: 3 26.4      2 0.2986243 0.5265404 0.4565363 24.56728
12: 4 27.7      2 0.2986243 0.5265404 0.4565363 24.56728
13: 5 30.0      2 0.2986243 0.5265404 0.4565363 24.56728
14: 6 33.0      2 0.2986243 0.5265404 0.4565363 24.56728
15: 7 37.0      2 0.2986243 0.5265404 0.4565363 24.56728
16: 8 45.0      2 0.2986243 0.5265404 0.4565363 24.56728

Exponential curve fitting with nls using data.table groups

1 Answers