Friday, February 03, 2006

st: RE: median cubic spline assumptions

On the contrary, this is strongly Stata-related.

It depends what you claimed in your paper, but on this report the reviewer and you are at cross-purposes.

Stata's -mspline- chops a scatter plot into vertical bands, calculates bivariate medians for each and then interpolates the median points using cubic splines. It is not any variety of cubic spline smoothing as usually discussed in any literature I have sampled. It is an idiosyncratic, but often quite useful, exploratory or heuristic smoothing technique. Personally I wouldn't include it in anything I tried to publish outside the Stata community, as to explain it properly would entail spelling all this out. (And a reviewer might reasonably ask Why this way?)

I don't think the issue of assumptions really arises. The main criterion worth discussing is to think about the graphical patterns produced and whether you can relate them to what you think is going in scientific or practical terms. I don't think that even in formal mood or mode anyone should want to formalise this in a terms of a model or data generating process.

The reviewer seems to want something much more formal. Also, the reviewer may not be understanding quite what the method does. His or her specific assertions seem incorrect or irrelevant to me, but there are checks that transcend verbal debate. Your results should be robust over a variety of choices of numbers of bands and also match what other smoothers suggest.

Nick n.j.cox@durham.ac.uk

Tim Wade > A statistics question, not really Stata related: > > In a recent paper, I used median cubic splines to graphically explore > non-linearity in the relationship between two continuous variables. > The independent variable, although continuous, was slightly clustered > and as a result there were some gaps where no data were available. The > reviewer said that because of this, the median cubic spline is not > appropriate beacuse it is adapted from time series approaches and > requires equidistant data of equal weight for meaningful > interpretation. I did not find this prerequisite for this approach in > any of my references, or in the Stata documentation. Has anyone else > encountered this issue? Is the median cubic spline transformation only > appropriate when responses are equidistant?

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