Least trimmed squared for regression

Question

I'm new in statistics. Hope you can help me on the following:

I want to use least trimmed squared (LTS) for regression. Below is the coding in R:

lts2_M1 <- function(failure)
{
library(MASS)
y_log <- failure[, 1]
x11 <- failure[, 4]
x2 <- failure[, 3]
fit0 <- lqs(y_log ~ x11+x2, method = "lts", nsamp = "exact")
list(fit0)
}

the result is:

lqs.formula(formula = y_log ~ x11 + x2, nsamp = "exact", 
            method = "lts")
Coefficients:
(Intercept)          x11           x2  
  -5.234269    -0.002685     0.110067  
Scale estimates 0.2065 0.2301 

Question:

1. Is that the correct way to perform LTS for regression?
2. In some of R example, i saw that they are using 'ltsReg'. what is the difference with the above method then?
3. From the result, residual standard error=0.2065. what is the formula used to calculate that?

Answer 1

Answer for your questions:

1) Is that the correct way to perform LTS for regression?

-> I would say yes, But if you want to know method behind model, then you can refer following(from help page): "In lqs The first three methods minimize some function of the sorted squared residuals. For methods "lqs" and "lms" is the quantile squared residual, and for "lts" it is the sum of the quantile smallest squared residuals. "lqs" and "lms" differ in the defaults for quantile, which are floor((n+p+1)/2) and floor((n+1)/2) respectively. For "lts" the default is floor(n/2) + floor((p+1)/2). The "S" estimation method solves for the scale s such that the average of a function chi of the residuals divided by s is equal to a given constant.

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2) In some of R example, i saw that they are using 'ltsReg'. what is the difference with the above method then?

-> Both are developed by different developers and based on different packages, but ltsReg will give you more information in returned object.