Presenting results of regression analysis with splines

[Kjell Weyde]

Dear all,

I would like to do a linear regression analysis with splines in Stata 14. My goal is inference (what is the effect of x), not prediction. Something like this:

mkspline2 x_spline = x, nknots(4) cubic
regress y x_spline* cov1 cov2 cov3

My questions are:
1) What is the best way to assess Statistical significance of x? Is it by looking at each of the 95%CIs for the x_splines, or should I do some test of overall effect, lincom etc?
2) What is the "best" way to report the estimates for x_spline*? Is it to make a graph and comment on it, and/or report predicted values of y at certain values of x?


Best regards,
Kjell Weyde

[Maarten Buis]

ad 1) you first need to specify what null hypothesis you want to test; the concept of significance is meaningless when one does not explicitly specify the null-hypothesis (and there is a growing movement in statistics that claims that the concept of significance is always meaningless). After that you translate that null hypothesis to the parameters.

ad 2) I noticed you used mkspline2 and not mkspline, so you also have access to adjustrcspline and mfxrcspline. Depending on the purpose of the analysis and the role your spline variable plays in that analysis, you could use those to present your results. If you want to report a table, then cubic splines are not intuitive. Instead I often use linear splines for that as it gives more sensible numbers than cubic splines. Alternatively, you could look at (Newson 2012).

Newson R. B. 2012. Sensible parameters for univariate and multivariate splines. The Stata Journal 12(3): 479-504.
http://www.stata-journal.com/article...rticle=sg151_2.

[Kjell Weyde]

Dear Dr Buis, thank you for your answers. Much appreciated!

Regarding 1): my hypothesis is that x is positively associated with the outcome. Not more specific than that.
2) I am not very familiar with splines. Linear splines seem more appealing in that they have more sensible coefficients, but does this come at the cost of precision? And are tables of spline estimates normally presented, or will it suffice to present the plots?

[Kjell Weyde]

When I am interested in whether x has some association with the outcome, could I use, for example, testparm and do as in the example below, and conclude that x is significantly associated with y if the testparm result is stat sign?

testparm x_spline1 x_spline2 x_spline3