[RsR] Questions about interpreting lmRob output
The basic idea underlying the robust linear model is that some fraction (1-alpha > 0.5) of the data is distributed conditionally normal and the remaining fraction (alpha) comes from some arbitrary distribution (i.e., the outliers). The goal of a robust method is to estimate the parameters (beta and sigma^2) of this conditional normal distribution without giving the outliers too much influence. If the bulk of the data (aka the good data) is not distributed conditionally normal then a linear model is not appropriate regardless of whether it is fit robustly or not. Of course you can still use all of the standard linear modeling tricks. For instance a log transformation of the response sometimes helps with heteroskedasticity. Kjell
On 14 Nov 2007, at 15:24, Jenifer Larson-Hall wrote:
Thanks so much Kjell. Your response answers most of my questions. Actually, I figured the overlaid plots things out (and the cool fit.models function) by looking through the archives and finding your pdf presentation that showed it (www.stats.ox.ac.uk/~konis/robust/ROBCLA2006-konis.pdf) . That was very helpful! The documentation you sent me privately (Robust.pdf, documentation for S-PLUS library) was helpful in clearing up a few more lingering questions (I guess if others want it they can email you).
The Robust Library Users Guide (Robust.pdf) is included in the source version of the Robust Library.
Just one more question now: My sense of robust methods was that they returned values which did not make strict normality and homogeneity of variances assumptions. In the data set I gave in my previous email, there is heteroskedasticity and non-normality distribution of data. So from what I understand from my reading, robust methods will give me a better sense of what's going on in the bulk of my data than least- squares estimates. If this is true, then what is the reason for looking at diagnostic plots? If I find the data is still heteroskedastic and non-normal in the plots after the robust analysis, is this cause for worry? Dr. Jenifer Larson-Hall Assistant Professor of Linguistics University of North Texas (940)369-8950