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Re: st: Looking for courses in non-linear modelling and imputation techniques

From   Nick Cox <>
Subject   Re: st: Looking for courses in non-linear modelling and imputation techniques
Date   Mon, 10 Oct 2011 21:00:09 +0100

Whenever I use cubic splines, my expectation is that the choice of
knots is not especially important. Knots aren't necessarily thresholds
which need to be matched one to one to a theoretically plausible
story. However, most of the systems I deal with show fairly smooth
behaviour, and things could easily be different with processes
involving e.g. key ages.

The best ways I know to convince a sceptic are

1. to change the knot positions a bit and show insensitivity (if this
fails, the sceptic has a point)

2. to compare with a quite different method, e.g. fractional polynomials

3. to plot a relationship when possible and show that splines give
good summaries


On Mon, Oct 10, 2011 at 7:46 PM, Jacobs, David
<> wrote:

> Splines seem extremely useful, but referees (in sociology at least) often give me trouble about the theoretical justification for particular cut points when I use this specification.  And sociological theory isn't terribly informative about such issues.
> I certainly agree that quadratics or for that matter cubics (which soc. referees also don't like) are procrustean, while dummies throw away information.
> Does anyone on the list have advice about how to justify splines when theory in one's discipline (and others) is mute about cut points?
> -----Original Message-----
> From: [] On Behalf Of Maarten Buis
> Sent: Monday, October 10, 2011 12:56 PM
> To:
> Subject: Re: st: Looking for courses in non-linear modelling and imputation techniques
> On Mon, Oct 10, 2011 at 6:02 PM, Sofia Ramiro wrote:
>> I want to explore non-linear relationships between outcomes that have so far
>> been analyzed as if their relationship was linear. For this, I need to learn
>> some statistical techniques to explore these relationships (besides normal
>> regression, or even generalized estimation equations), if I am not wrong.
>> This is more difficult to find in normal courses, at least the ones I have
>> been finding, as they focus on linear relationships between variables...
> This is actually routinely discussed in introductory regression
> courses. The standard remedies depends on the discipline: either one
> splits the linear variable up in categories and adds dummies/indicator
> variables for those categories or one adds a square term. These
> standard remedies tend to either trow away too much information
> (dummies) or impose too much structure and thus not fit very well
> (square term). Personally, I like adding linear splines (see: -help
> mkspline-) as a nice compromise between adding a non-linear effect and
> interpretable coefficients. Another option is fractional polynomials
> (see: -help fracpoly- and Royston and Sauerbrei 2008).
> Hope this helps,
> Maarten
> Royston, P., and W. Sauerbrei. 2008. Multivariable Model-building: A
> Pragmatic Approach to Regression Analysis
> Based on Fractional Polynomials for Modelling Continuous Variables.
> Chichester, UK: Wiley.

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