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I would like to know how can I be able to interpret the results from fitting splines with the scam package.

My data points are taken from the chileancredit dataset available in the package smbinning.

Here are my x and y data points:

library("scam")
library("zoo")
data(chileancredit, package = "smbinning")
chilean_clean <- na.omit(chileancredit)
x <- unique(sort(chilean_clean$TOB[1000:length(chilean_clean$TOB)]))
y_mav <- rollmean(chilean_clean$FlagGB, k = 1000)
y <- y_mav[(length(y_mav)-length(x)+1):length(y_mav)]

y is the moving average of a binary target variable.

With the scam function I could fit a convex spline to my datapoints (I specified 5 parameters in total):

spline_fit <- scam(y~ s(x,k=5,bs="cx",m=2),
                   family=gaussian(link="identity"), 
                   data=as.data.frame(x=x,y=y))

However, the five coefficients I could get from scam, I'm having trouble interpreting them:

(Intercept)      s(x).1      s(x).2      s(x).3      s(x).4 
   0.9275358  -4.3564887  -4.8378830  -4.8522646  -4.8950387 

The first term is the intercept, however I've lookup up in the results of scam for knots or cuts - seems like there is none. I don't know how I could interpret the smoothing parameters without the knots. Anyone has any idea? Thanks.

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    $\begingroup$ The s(x).i terms are the penalised regression coefficients for the 4 basis functions in the model, they're not smoothness parameters. You code isn't working for me; I get an error that the x and y lengths differ. Can you run your code in a clean session and update as needed? Then I'll take a closer look. $\endgroup$ – Reinstate Monica - G. Simpson Apr 28 '17 at 15:46
  • $\begingroup$ @GavinSimpson thank you I fixed the code and now it should be reproducible. $\endgroup$ – user95902 Apr 29 '17 at 7:45
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Well after reading this Wood S.N. (2006) Generalized Additive Models: An Introduction with R, the coefficients from the output are difficult in giving a valid interpretation. But with predict.gam from package mgcv they can be directly applied in prediction.

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