Why does the fit get worse after adding the second explanatory variable?
require("VGAM")
df = data.frame(x = c(1,2,3,4,5,6,7,8,9,10), y = c(1,4,8,15,25,36,48,65,80,105), z = c(0,0,0,1,100,400,900,1600,1800,200) )
vgt1 = vgam(y~s(x, df=2), data=df,family=gaussianff, trace=TRUE)
vgt2 = vgam(y~cbind(s(x, df=2),s(z, df=2)), data=df,family=gaussianff, trace=TRUE)
plot(df$x, df$y, col="black")
lines(df$x, vgt1@predictors, col="red")
lines(df$x, vgt2@predictors, col="blue")
When you add a variable you use + not cbind.
vgam parses the formula using terms.formula to look for specials = 's', i.e. terms that are wrapped in s signifying a spline.
Therefore
vgt2 = vgam(y~s(x, df=2)+s(z, df=2), data=df,family=gaussianff, trace=TRUE)
will give you what you want (and this has a lower deviance than vgt1).
When you fit
vgt2 = vgam(y~cbind(s(x, df=2),s(z, df=2)), data=df,family=gaussianff, trace=TRUE)
terms.formula doesn't find any specials that start with s, as cbind is the function that identifies the term in the formula. Therefore
gam(y~cbind(s(x, df=2),s(z, df=2)), data=df,family=gaussianff, trace=TRUE)
is the equivalent of
gam(y~cbind(x,y), data=df,family=gaussianff, trace=TRUE)
which in term is the equivalent of
vgam(y~x+z, data=df,family=gaussianff, trace=TRUE)
i.e. no spline terms are fitted.