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Topic: "Piecewise overlapped regression"
Replies: 3   Last Post: Feb 4, 2006 12:46 PM

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Ken Starks

Posts: 20
Registered: 12/6/04
Re: "Piecewise overlapped regression"
Posted: Feb 4, 2006 12:46 PM
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Ross Clement (Email address invalid - do not use) wrote:

> For reasons that are lengthy to explain, I'm now looking at tracking
> pitch of human speech. When people speak, the pitch of their voices
> rises and lowers in, it is presumed AFAIK, a fairly smooth pattern.
> However since even a single sentence can have a number of rises and
> falls, fitting a single polynomial to pitch across a whole sentence
> will require (I'm guessing) too high an order polynomial. At present
> I'm fitting cubic splines, but am not happy since the splines always go
> through the relatively few (compared to the number of samples at
> 44.1khz sampling) places where I get estimates of frequency. Since
> these are estimates, I'd like to see what happens if I fit a regression
> line rather than a spline. I could do this with lowess() and similar
> methods, but as it is early days, I would like to have a fit that's an
> equation, particularly one easy to differentiate, where I can apply
> Newton-Rhapson to find zeroes, etc., solely because I think "that might
> be useful some day".
> The book reference you give and the additional key-words for putting
> into my favourite search engine will be a great leg-up. Thanks.
> Cheers,
> Ross-c

It sounds like 'Tree-based Models' as described in the
'R' (stats package) documentation:

Rather than seek an explicit global linear model for prediction or
interpretation, tree-based models seek to bi-furcate the data,
recursively, at critical points of the determining variables in
order to partition the data ultimately into groups that are as homogeneous
as possible within and as heterogeneous as possible between.

The term 'hierachical model' may also work.

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