Are absolute values of GCV meaningful for GAMs fit to different data? Say I make a couple of GAMs, like this:
# Load data
data(mtcars)

# Model for mpg
mpg.gam <- gam(mpg ~ s(hp) + s(wt), data = mtcars)

# Model for qsec
qsec.gam <- gam(qsec ~ s(hp) + s(wt), data = mtcars)

Would comparing GCV values between these models tell me anything at all? Or are GCV values only meaningful in a relative sense when comparing models fit to the same data?
 A: The GCV score is an estimator of mean squared error of the model fit, which for a Gaussian model is given by (using the notation of Wood, 2017)
$$\mathcal{V}_g = \frac{n||\mathbf{y} - \hat{\boldsymbol{\mu}} ||^2}{[n - \mathrm{tr}(\mathbf{A})]^2}$$
where $\mathbf{y}$ is the observed response vector, $\hat{\boldsymbol{\mu}}$ is the vector of fitted values, $n$ the number of observations, and $\mathbf{A}$ the influence matrix.
(For generalized models, measuring the lack of fit via squared errors, as shown above, is generally not meaningful, and the deviance of the model, $D(\hat{\boldsymbol{\beta}})$ is used in place of $||\mathbf{y} - \hat{\boldsymbol{\mu}} ||^2$, and the trace of the influence matrix is replaced by the effective degrees of freedom of the model [possibly weighted by  $\gamma$].)
The GCV score, $\mathcal{V}_g$, therefore depends on the units of the response and/or on the specific data used in the model. As such you cannot compare, in a meaningful way, the GCV scores for the two models you showed in your example.
The absolute value of the GCV score is interpretable as an estimation of the lack of fit of the model.
