# How to choose between different methods of linear regression?

I find following commonly mentioned linear regression methods:

OLS: ordinary least squares

GLS: generalized least squares

WLS: weighted least squaes

RLM: robust linear model

OLS is usually the default. I believe robust model is to be used to correctly handle outliers, but I am not clear about others.

What are the criteria to choose one over the other?

Edit: It is mentioned in the comments that it is a very broad question (I did not know that!). However, I would like to have a one or two lines on each of above to know the "indications" or when to use them.

OLS: default

RLM: if outliers are important and cannot be ignored.

That leaves only GLS and WLS. What would be most important reasons to use them?

• This is very general, and whole books are needed for an answer. Could you limit the scope somewhat? Linear regression methods for ... ? – kjetil b halvorsen Jul 12 '20 at 17:35
• I have tried to specify that I need only a general indication on when to use each of these. – rnso Jul 12 '20 at 17:40
• OLS is useful as pedagogically to generally introduce regression and it's concepts and assumptions, but I am not sure if or when I actually have used OLS in research. Regression methods permitting creative violation of OLS regression's assumptions permit us to model the complexities with which the world behaves with more fidelity. – Alexis Jul 12 '20 at 17:49

## 1 Answer

Your links goes to statsmodels program web pages, a software I do not know. I will assume their use of terms is the standard. A very general indication, just as a starter, what you really need is a book on regression.

• OLS is the starting point, many other models can be seen as extensions or generalization. Assumptions is continuous response, linear effects and constant variance + independence (of residuals.)

• GLS weakens assumption, do not assume constant variance nor independence. So you will need somehow to model the variance and covariances.

• WLS is GLS but with covariances zero, so really an assumption of independence of residuals.

• RLM is really a huge class of models and methods. Especially think about this for routine or automatized analyses.