Normalized Root Mean Square (NRMS) vs Root Mean Square (RMS)? I am trying to find the best-fit model from my observation and model predicated data. I came across these two different approach which have been used in the literature: Normalized Root Mean Square and Root Mean Square.
Can someone shedsome light on which of these two is a better measure of the model fitting? When to use which approach? I would appreciate any references on a comparison of these.
 A: Why does NRMS exist?
The purpose of normalisation is to allow direct comparison of two variables that exist on different scales, so that the magnitude of errors can be compared more meaningfully. 
There are different flavours of NRMS out there which fall into two main camps


*

*normalisation to a central moment of the data such as mean or median

*normalisation to the variance of the data (standard deviation, range, interquartile range).
The first is basically a transformation of the coefficicent of variation, the second is a transformation of $R^2$.
References
https://en.wikipedia.org/wiki/Root-mean-square_deviation
http://www.academia.edu/4303409/Why_you_dont_need_to_use_RPD (this one is based on a specific implementation of NRMS, but its principles are extendable to all variance based normalisation)
Answers

Can someone shed some light on which of these two is a better measure
  of the model fitting?

Neither is universally better, it depends on the information you want as they give different information

When to use which approach?

Use RMS if you are comparing different models on the same data. Use NRMS or one of its cousins if comparing different data that exists on different scales. Normalise by mean/median if % error is useful, by range if you want the equivalent of a correlation coefficient. 
