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Re: st: RE: Constrained Lowess

From   "Sergiy Radyakin" <>
Subject   Re: st: RE: Constrained Lowess
Date   Fri, 2 May 2008 12:40:31 -0400

Hello Nick,

I am sorry for being inprecise. Indeed, I smooth the rates (of e.g.
unemployment) by groups defined by age (which is truncated to
integers, and thus I concider it categorical).

So I start with a table like the following:

Age     Unemployment rate
10         0.01
11         0.02
99         0.01

Here unemployment rate is naturally between 0 and 1. It is the average
of the 0/1-responses within the group, defined by age.

If I just run lowess, it produces the picture similar to the one here:
sysuse auto
generate z=1/headroom^16
lowess z mpg
Note that the tails go below zero, and this is what I am trying to avoid.

Your advice of logit transformation before/after smoothing worked.

Thank you,
  Sergiy Radyakin

On 5/2/08, Nick Cox <> wrote:
> Quite how to get useful results from smoothing a binary response is not
> clear to me.
> If the data were proportions on (0,1) or even [0,1] I would suggest
> some kind of transformation approach. -lowess, logit- is presumably
> intended to help.
> Otherwise consider something like an angular or folded root
> transformation, applying -lowess- and then transforming back.
> But for binary data any transformation just maps two distinct values to
> two other distinct values and so cannot help, so far as I can see.
> In the case of unemployment data, presumably you are dealing with
> individuals? If they are aggregate data for lots of individuals I would
> collapse by age to get proportion of unemployed, and then smooth if
> necessary. It sounds as if you want something quite different, however.
> Also, as you regard -age- as categorical I probably don't understand
> what you are trying to do.
> Nick
> Sergiy Radyakin
> I am plotting a smoothed graph (-lowess-) of a binary variable (e.g.
> unemployed) by categorical (e.g. age). However the smoothed values are
> not necessarily in the [0;1] range, where unemployment must be by
> definition. I can save the smoothed values into a new variable with
> the option -generate(newvar)- and then truncate the negatives and
> values larger than one, but I believe smoothing must look differently
> if I could tell -lowess- to look for such a constrained value in the
> first place. As it follows from the description of -lowess- it doesn't
> have such a feature. Is there any user-written command or simple
> algorithm for this purpose?
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