gam object produced by gam() and produces some diagnostic information
about the fitting procedure and results. The default is to produce 4 residual
plots, and some information about the convergence of the smoothness selection optimization.gam.check(b)gam object as produced by gam().For mgcv based fits (not the default), the first plot shows the GCV or UBRE score against model
degrees of freedom, given the final estimates of the relative smoothing
parameters for the model. This is a slice through the
GCV/UBRE score function that passes through the minimum found during fitting. Although not conclusive (except in the single
smoothing parameter case), a lack of multiple local minima on this plot is
suggestive of a lack of multiple local minima
in the GCV/UBRE function and is therefore a good thing. Multiple local minima on this plot indicates that the GCV/UBRE function
may have multiple local minima, but in a multiple smoothing parameter case this is not conclusive - multiple local minima on one slice
through a function do not necessarily imply that the function has multiple local minima. A `good' plot here is a smooth curve with
only one local minimum (which is therefore its global minimum).
The location of the minimum used for the fitted model is also marked on the first plot. Sometimes this location may be a local minimum
that is not the global minimum on the plot. There is a legitimate reason for this to happen, and it does not always indicate problems.
Smoothing parameter selection is based on applying GCV/UBRE to the approximating linear model produced by the GLM IRLS fitting method
employed in gam.fit(). It is sometimes possible for these approximating models to develop `phantom' minima in their GCV/UBRE scores. These
minima usually imply a big change in model parameters, and have the characteristic that the minimia will not be present in the GCV/UBRE score
of the approximating model that would result from actually applying this parameter change. In other words, these are spurious minima in regions
of parameter space well beyond those for which the weighted least squares problem can be expected to represent the real underlying likelihood well.
Such minima can lead to convergence problems. To help ensure convergence even in the presence of phantom minima,
gam.fit switches to a cautious optimization mode after a user controlled number of iterations of the IRLS algorithm (see gam.control).
In the presence of local minima in the GCV/UBRE score, this method selects the minimum that leads to the smallest change in
model estimated degrees of freedom. This approach is usually sufficient to deal with phantom minima. Setting trace to TRUE in
gam.control will allow you to check exactly what is happening.
If the location of the point indicating the minimum is not on the curve showing the GCV/UBRE function then there are numerical problems with the estimation of the effective degrees of freedom: this usually reflects problems with the relative scaling of covariates that are arguments of a single smooth. In this circumstance reported estimated degrees of freedom can not be trusted, although the fitted model and term estimates are likely to be quite acceptable.
If the fit method is based on magic or gam.fit2 or
gam.fit3then there is no global search and the problems with
phantom local minima are much reduced. These more recent methods are also much
more robust than the mgcv based methods.
choose.k, gam, mgcv, magiclibrary(mgcv)
set.seed(0)
n<-200
sig<-2
x0 <- runif(n, 0, 1)
x1 <- runif(n, 0, 1)
x2 <- runif(n, 0, 1)
x3 <- runif(n, 0, 1)
y <- 2 * sin(pi * x0)
y <- y + exp(2 * x1) - 3.75887
y <- y+0.2*x2^11*(10*(1-x2))^6+10*(10*x2)^3*(1-x2)^10-1.396
e <- rnorm(n, 0, sig)
y <- y + e
b<-gam(y~s(x0)+s(x1)+s(x2)+s(x3))
plot(b,pages=1)
gam.check(b)Run the code above in your browser using DataLab