Test the model for the surface of response. The null hypothesis is assumed as a linear model defined by the coordinates while the alternative hypothesis is assumed a bivariate spline (tensor product or thin-plate spline).
# S4 method for sssFit
testSurface(object, tol)an object of class sssFit from command scp.
numeric. Numeric tolerance to use for some inversion of matrices. Default to .Machine$double.neg.eps*1.0e-10.
Returns a table with the degrees of freedom, sum of squares and mean squares from different sources and the F test and its associated p-value.
If we have defined a bivariate spline using s2D in the formula of scp then the model is an spatial semiparametric model based on splines (tensor products or thin-plate splines). In this case testSurface performs a test for the null hypothesis \(H_0: g = X\beta\) (linear model) against the alternative \(H_1: g = X\beta + Zr\) (spline model). When \(g\) is assumed as a thin-plate spline then this test is equivalent to test the null hypothesis \(H_0:\) the pattern of response in the space is a plane against the alternative \(H_1:\) the pattern of response in the space is a bivariate thin-plate spline. In one dimension this test is equivalent to a test for linearity in the pattern of response.