What is the alpha argument of the ltsReg function of the robustbase package?

Question

I have a question about the use of the argument alpha of function ltsReg package robustbase.

As I understand it, it is responsible for determining the size of the subsets that will be used to adjust the model for these subsets by selecting the model of the subset that presented the smallest residues squared.

Generally, the value adopted for lts is 0.5, but the argument alpha allows you to provide a value between 0.5 and 1. So, if I use the value 1, my adjustment should be equivalent to the OLS adjustment? Or I’m misinterpreted the alpha argument?

Answer 1

Estimates should be equivalent when you use alpha = 1. See the example below:

> library(robustbase)
> data(heart)
> coef(ltsReg(clength ~ height + weight, data = heart, alpha = 1))
 Intercept     height     weight 
20.3757645  0.2107473  0.1910949 
> coef(lm(clength ~ height + weight, data = heart))
(Intercept)      height      weight 
 20.3757645   0.2107473   0.1910949 

What can happen is that for the ltsReg there is no closed form p/ get the estimates so they are obtained computationally unlike simple linear regression. Therefore, there may be differences of approximation.

See the functions that are minimized in simple linear regression:

and in linear trimmed Squares:

If k = n what happens to alpha = 1, functions are equal. Therefore estimates will also be equal.