I have observed data $y$. And I have a function that gives me estimated $\hat{y} = f(x,\hat{P})$ where P is the parameter I want to estimate. I was able to optim() command in R to get maximized log-likelihood estimate $\hat{P}$ using the residuals, assuming a normal distribution.

My question is: If I have multiple dataset and all of them should have the same $P$ but x is on a different scale for each dataset. Now I want to maximize the overall log-likelihood to find the overall $\hat{P}$ and its standard error. Can I just simply compute all the residuals from each data and assume they all have the same distribution so that I can use optim() to maximize the log-likelihood of that?


1 Answer 1


If they have all the same $P$, and the scale of the error term is the same for each, and they're independent across data sets, then you could just combine (stack) them all into a single set of (x,y) data.

(Which will then mean, yes, if you're using an optimizer (like optim in R) on residuals you should be able to combine the residuals into a single big set of residuals.)

(If you're less than certain they'll all be the same, other things can be done to address whether they might be different)


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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