0
$\begingroup$

I have an exponential regression equation that I use to predict the condition of roads.

The equation can be found on page 53 of the original master's thesis: Development of a Flexible Framework for Deterioration Modelling in Infrastructure Asset Management

From page 53:

enter image description here

The equation has some IF statements which deal with specific roads-related scenarios. For the purpose of this question, I'll boil it down to it's simplest form:

condition = 21 - EXP(0.072*age)


Question:

The equation was developed for my organization back in 2012. At that time, the roads had only been inspected once. Now, fast-forward to 2017, and we have a lot more data to work with.

So, I think it would be wise to update the equation. If we were able to redo the analysis with the new data, I suspect we'd be able to predict the future condition of roads more accurately.

However, as non-stats guy, I'm finding this to be rather difficult.

How can I update the coefficient in the exponential regression equation?

$\endgroup$
  • $\begingroup$ Do you need it to be of the form $y=a+be^{cx}$ necessarily? Is there any reason for that? $\endgroup$ – Anna SdTC Dec 13 '17 at 4:38
1
$\begingroup$

If you want to follow the same curve form, you set the y-intercept to 21 like the original author did. Then, the equation you need to estimate is $$y=21-e^{ax},$$

which is equivalent to

$$21-y=e^{ax}.$$

If you take logarithms both sides (you can do it because $y<21$), then $$log(21-y)=ax.$$

Renaming $log(21-y)=z$, this is of the form $$z=ax,$$

which is a linear regression with no intercept that can be estimated with many standard software packages.

For the lower bound you would, instead of the 21, use the 21-1.282-8.277 (the worst-case condition in the conditionals) as a y-intercept, and apply the same estimation method.

$\endgroup$
  • 1
    $\begingroup$ So at age 0, $e^{ax}=e^0=1$, and we want to find an intercept such that at age $x=0$ we have $y=20$. If the intercept was $20$, then, at age 0, $y=20-e^{0}=20-1=19$, which is not the state of new roads. $\endgroup$ – Anna SdTC Dec 13 '17 at 5:09
  • 1
    $\begingroup$ A more general approach to estimate the y-intercept, if it is not as explicitly determined by the context as in this case, would be to compute the average of the $y$ conditional on $x=0$ (so the average condition for all roads of age=0 but only those) and add 1 for the same reason we add 1 to make the 20-score be an intercept of 21. Or, if you want upper-lower bounds like in the example, the average for the best-case roads at $x=0$, and of the worst-case roads at $x=0$ will give you two the two intercepts. $\endgroup$ – Anna SdTC Dec 13 '17 at 5:28

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.