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From Mauro Talevi <mauro.tal...@aquilonia.org>
Subject Re: [math] Improving numerics in OLSMultipleLinearRegression
Date Thu, 12 Jun 2008 12:15:38 GMT
Phil Steitz wrote:

> Yes, and I would distinguish performance optimization from numerical 
> accuracy.  From my perspective, we can release a ".0" with room for 
> performance improvement, but at least decent numerics are required.

I agree that decent numerics are required.   I'm still rather surprised 
that the diagonal covariance case would yield such bad numerics wrt the 
GLS case - which has been tested with independent fortran code to a 
level of 10^-6.

>>> We have talked in the past about providing an implementation based on 
>>> QR decomposition.   Anyone up for  using the QR decomposition that we 
>>> now have to do this?  I really think we need to do it (or something 
>>> else to improve numerics) before releasing this class.  I will get to 
>>> it eventually, but am a little pegged at the moment. 

Are you proposing doing a QR decomposition of both the X and Y matrices 
and working out the formulas using the decomposed ones?

> Here are some initial ideas on what should be included in the multiple 
> regression API.  Other suggestions welcome!
> 
> 1.  Coefficients should be accompanied by standard errors, t-statistics, 
> two-sided t probablilities (can get these using t distribution from 
> distributions package) and ideally confidence intervals.
> 2.  F, R-square, adjusted R-square, F prob (again can use distributions 
> package to estimate)
> 3.  ANOVA table (Regression sum of squares, residual sum of squares)
> 4.  Residuals
> 
> R, SAS, SPSS and Excel all represent (or in the case of R, can 
> construct) these basic statistics in some way in their output.  We 
> should model them in classes representing properties of the computed model.

Perhaps we should put these on the wiki or even better in jira.
IMO, it's best to deal with the numerics and the new data input 
strategies, before adding new functionality in the frame.

>> And finally, how do you see the no/hasIntercept model working?
> As a configurable property - noIntercept means the model is estimated 
> without an intercept.   The point I was making was more how the data is 
> supplied via the API.  It is awkward to have to fill in a column of 1's 
> to get the linear algebra to work to estimate a model with intercept 
> (which should be the default).

ok - good point.

> I would recommend that we have setData or "newData" provide a n x m 
> matrix, where n is the number of observations and m-1 is the number of 
> independent variables.  Then either a) have the constructor take another 
> argument specifying which column holds the dependent variable b) assume 
> it is the first column c) support column labels and some form of model 
> specification such as what R provides (a lot of work) d) split off the y 
> vector, so setting data requires separate x and y vectors.  Probably a) 
> is easiest for users, who will most often be starting with a rectangular 
> array of data with the dependent variable in one of the columns.

Perhaps it would help if we had overloaded newData methods that accept 
different input strategies, but ultimately they will produce a n x m 
double array.  That way we can provide users with choice.

I'll get to it in the next week or so - ATM I'm a bit loaded myself.

Cheers


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