Re: st: question about use of restricted cubic splines in regression

[Nick Cox <njcoxstata@gmail.com>]

I don't think there are many rules here. A downside of splines is
inevitably that you replace one predictor with a bunch, with the
side-effect that with interactions too all of a sudden there are many
more parameters. For conservative modellers like myself who like to
fit very parsimonious models whenever possible, this is scary; others
find that they now have the flexibility they want and need, and so
long as the number of observations is reasonable find the brave new
world very exciting.

I would tend strongly to use the same bunch for X and then interact
them with the groups. I'd also do lots of exploratory analysis for

smooth(mean(Y|X, each group))

to see what is going on.

I'd also study the examples closely in Harrell, F. 2001. Regression
modeling strategies. New York: Springer.

However, Frank Harrell has strategies that work very well when you are
as smart and knowledgeable as Frank Harrell....

Nick

On Fri, Oct 21, 2011 at 5:01 AM, Airey, David C
<david.airey@vanderbilt.edu> wrote:

> I have one continuous response Y and one continuous predictor X measured in 20 groups. One of the groups is a natural control, and I want to test whether each of the 19 other groups is different from the control. I'd like to fit the regression lines for each of the 20 groups using restricted cubic splines with 4 knots, because I know the response will not be linear but I don't want to assume a specific nonlinear function. I want to fit all 20 groups using fixed effects as the full model. I'm assuming equal variances across groups. I then want to fit a reduced model where the control group and one of the 19 other groups have the same coefficients, but the other 18 groups have different estimates. I then want to perform a likelihood ratio test for the difference. I will create reduced models for each of the other 18 groups and perform 18 more likelihood ratio tests to test whether the control group differs from one or more of the 19 other groups.
>
> I've not worked with restricted cubic splines before. Do I make a set of knots for each group? If I want coefficients shared between two groups I assume I recode the groups to have the same group identifier and make knot variables for the combined group? Do I also need indicator variables for group identification?

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