constrained splines

[Andrew Azman]

Has anyone implemented splines from the Shape Constrained Additive Models (scam) package with brms? I am trying to fit a model and enforce monotonicity in a spline. Any help would be greatly appreciated. 

[Paul Buerkner]

I just tested it and surprisingly the model fitting seems to work. But when trying to plot the smooths, an error happens inside mgcv. Here is an example from the scam documentation:

library(scam)

set.seed(0)
n <- 200
x1 <- runif(n)*6-3
f1 <- 3*exp(-x1^2) # unconstrained term
f1 <- (f1-min(f1))/(max(f1)-min(f1)) # function scaled to have range [0,1]
x2 <- runif(n)*4-1;
f2 <- exp(4*x2)/(1+exp(4*x2)) # monotone increasing smooth
f2 <- (f2-min(f2))/(max(f2)-min(f2)) # function scaled to have range [0,1]
f <- f1+f2
y <- f+rnorm(n)*0.1
dat <- data.frame(x1=x1,x2=x2,y=y)
b <- scam(y~s(x1,k=15,bs="cr",m=2)+s(x2,k=25,bs="mpi",m=2),
          family=gaussian(link="identity"),data=dat,not.exp=FALSE)
print(b)
summary(b)
plot(b,pages=1)

library(brms)
fit <- brm(y~s(x1,k=15,bs="cr",m=2)+s(x2,k=25,bs="mpi",m=2), dat)

summary(fit)

marginal_smooths(fit)  # fails

I will report this error the the maintainer of scam. In the hope that he can fix this.

2018-02-19 19:56 GMT+01:00 Andrew Azman <andre...@gmail.com>:

Has anyone implemented splines from the Shape Constrained Additive Models (scam) package with brms? I am trying to fit a model and enforce monotonicity in a spline. Any help would be greatly appreciated. 

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[Andrew Azman]

Wow, thanks! Surprised it just worked.

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[Andrew Azman]

@Paul - It seems like that package has quite a few bugs actually. Any thoughts on enforcing montonicity through a strong prior instead?

[Paul Buerkner]

Can you describe your covariate, for which you want to enfore monotonicity?

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[Andrew Azman]

Sure, it is describing 'decay' within a biological system ranging from Inf to 0. 

[Paul Buerkner]

If your covariate can only take on not too many discrete values, you could use monotonic effects in brms (see vignette("brms_monotonic")), but your variable does rather look very much continuous.

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[Andrew Azman]

I had seen that vignette but its more of a continuous variable.

andrew azman

[Paul Buerkner]

After some email exchange with the author of the scam package, she sent me an updated version of one of the scam methods, which after being load into the global environment, will fix this problem. Just run the attached R script,
and post-processing of mpi splines should work.

Unfortunately, this updated version is unlikely to make it into the CRAN version of scam, since, for some reason, it interferes with the way post-processing is done in scam itself.

I hope this still helps and thanks to Natalya Pya for the fix!