The gam.check function first produces the smoothing parameter estimation convergence information. In this example, the smoothing parameter, Generalized Cross Validation/ Unbiased Risk Estimator (GCV/UBRE), score converges after seven iterations. The mean absolute gradient of the GCV/UBRE function at the minimum is 8.79622e-06 and the estimated rank is 10. The dimension check is to test whether the basis dimension for a smooth function is adequate. From this example, the low p-value indicates that the k is set too low. One may adjust the dimension choice for smooth by specifying the argument, k, by fitting gam to the data.

In addition to providing information regarding smoothing parameter estimation convergence, the function returns four diagnostic plots. The upper-left section of the plot in the screenshot shows a quantile-comparison plot. This plot is useful to identify outliers and heavy tails. The upper-right section of the plot shows residuals versus linear predictors, which are useful in finding nonconstant error variances. The bottom-left section of the plot shows a histogram of the residuals, which is helpful in detecting non-normality. The bottom-right section shows response versus the fitted value.