How do GDM knots relate to spline coefficients?

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How do GDM knots relate to spline coefficients?

Greg Guerin

I want to identify the sub-intervals of environmental gradients with the greatest species turnover rate from a fitted GDM (gdm::gdm) by calculating rise over run for each spline/segment.

I fitted models with 5 splines (default is 3) and allowed automatic definition of knots (via quantiles). The sum of spline coefficients for each predictor equals the height of the overall function on the y-axis.

However, GDM outputs include 5 knots and 5 spline coefficients per fitted predictor, with the lowest and highest values of the knots representing the extremes of the gradients in the predictor data. I had assumed each coefficient refers to the additional y-axis height attained in each segment/sub-interval along the gradients as defined by knots, but 5 knots only gives four segments (i.e. knot1 � function1 � knot2 � function2 � knot3 � function3 � knot4 � function4 � knot5).

Can anyone explain how individual splines are related to the knots (i.e. Given same number of knots as coefficients) so that I can work out which gradient sub-interval goes with each coefficient?

Greg Guerin

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