|
Greetings, I'm performing research that will help determine the size of observed space and the time elapsed since the big bang. Hopefully you can help! I have data conforming to a piecewise linear function on which I want to perform two linear regressions. There is a point at which the slope and intercept change, and I need to (write a program to) find this point. Thoughts? |
|||||
|
|
R package strucchange might help you. Look at the vignette, it has a nice overview how to solve similar problems. |
|||
|
|
|
This is an (offline) changepoint detection problem. Our previous discussion provides references to journal articles and R code. Look first at the Barry and Hartigan "product partition model," because it handles changes in slope and has efficient implementations. |
|||
|
|
|
If the number of points is not too big, you may try all possibilities. Let's assume that the points are $X_i=(x_i,y_i)$ where $i=1,..,N$. Than, you may loop with $j$ from $2$ to $N-2$ and fit two lines to both $\{X_1,...,X_j\}$ and $\{X_{(j+1)},...,X_N\}$. Finally, you pick $j$ for which the sum of sum of squared residuals for both lines is minimal. |
|||
|
|
|
Also the segmented package has helped me with similar problems in the past. |
||||
|
|
|
What is wrong with doing simple non-linear least squares in this case? Am I missing something obvious? |
|||||
|
