Re: Least Median Square Regression

Posted by Jon Peck on Oct 18, 2016; 11:23pm
URL: http://spssx-discussion.165.s1.nabble.com/Least-Median-Square-Regression-tp5733299p5733305.html

The .5 quantile regression minimizes the sum of absolute deviations around the median.  Least median of squares would indeed be something different.  I could cook up an extension command for this pretty easily, though if there is some general interest.

On Tue, Oct 18, 2016 at 5:09 PM, Bruce Weaver <[hidden email]> wrote:

Jon, are you sure about quantile regression with the .5 quantile?  That
produces Least (or Minimum) Absolute Deviations (LAD/MAD) regression, does
it not?

I think Bryan is asking about something different.  E.g., here is an excerpt
from
http://web.ipac.caltech.edu/staff/fmasci/home/astro_refs/LeastMedianOfSquares.pdf:

"Classical least squares regression consists of minimizing the sum of the
squared residuals. Many authors have produced more robust versions of this
estimator by replacing the square by something else, such as the absolute
value. In this article a different approach is introduced in which the sum
is replaced by the median of the squared residuals."

The first sentence describes OLS, the second LAD, and the third Least Median
of Squares (LMS) regression.

Cheers,
Bruce



Jon Peck wrote
> There are two ways to do this in Statistics, but both require that the
> (free) R Essentials be installed:
> SPSSINC ROBUST REGR (Analyze > Regression > Robust Regression) or SPSSINC
> QUANTREG (Analyze > Regression > Quantile Regression) specifying the .5
> quantile.  The latter is better if you have any categorical variables.
>
> On Tue, Oct 18, 2016 at 2:28 PM, Bryan Mac <

> bryanmac.24@

> > wrote:
>
>> Hi,
>>
>> I was wondering how to perform Least Median Square Regression in SPSS?
>> I have version 23. I also do not have any of the new modules installed.
>>
>> Thanks
>>
>> BM
>>
>>
>>
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> Jon K Peck

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-----
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Bruce Weaver
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