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I'm estimating a Non-Linear system (via seemingly unrelated regressions - SUR), using systemfit (nlsystemfit() function) package with 4 equations, 32 parameters to estimate (!) and 412 observations. But my code is taking forever (my laptop it's not a super-powerful one tho). So far, the process was on a 13 hours run. I'm not an expert in computational stuff, but someone explained me some time ago the concept of Time Complexity of the algorithms (or big-o), then depending on this concept the time to compute a certain algorithm could rely on specific functional relation on the number of observations and/or coefficients.

Hence, I'm thinking of just stopping my process, and trying to simplify the model (temporarily) and trying to run something simpler, only to check-up if the estimated parameters had sens so far. And then, run a whole model.

But all this has a sense if I can change key elements in my model, which can reduce the time of processing significantly. That's why I was looking on google about the time complexity of nlm-package (nlsystemfit() function relies on nlm) but unsuccessfully. So, this is my question: Anybody knows where I can find that info, or at least give me advice on how test non-linear systems before run a whole model?

Ariel
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    Sorry to hear your process has been running for over 13 hours. With only 412 observations, I would guess the fitting would happen quicker. If it was me, I would re-start and `microbenchmark` my code - maybe 1 equation and 8 parameters, then 2 and 8, then 1 and 16 - to get a feel for the limits and maybe find some optimization or tweaks (ex. `solvtol=`, `maxiter=`). – M.Viking Feb 13 '20 at 15:37
  • Thank you @M.Viking, that's a really good starting point. – Ariel Feb 13 '20 at 15:43
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    Provide the model or a reproducible example of the same. Jumping into computation for an entire dataset/model is not a wise step - you must benchmark your code (function/algorithm) from a modular extent and move incrementally if runtime is reasonable. –  Feb 13 '20 at 15:53

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Since you didn't provide any substantial information regarding your model or some code for the same, its hard to express a betterment for your situation.

From what you said:

Hence, I'm thinking of just stopping my process, and trying to simplify the model (temporarily) and trying to run something simpler, only to check-up if the estimated parameters had sens so far. And then, run a whole model.

It seems you require benchmarking or to obtain the measured time taken to execute, as in your case. (although it can deal with memory usage or some other performance metric as well)

There are quite a few ways to benchmark code in R, which include the use of Sys.time() or system.time() just before and right after your algorithm/function executes, or libraries such as rbenchmark (which is a simple wrapper around the system.time function), tictoc, bench and microbenchmark.

Among these the last two are preferable options, as bench::mark includes system_time(), a higher precision alternative to system.time() and microbenchmark is known to be a reliable source to accurately measure and compare the execution time of R expressions/algorithms.