Description Usage Arguments Details Value Author(s)

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).

1 2 | ```
## S4 method for signature 'sssFit'
testSurface(object, tol)
``` |

`object` |
an object of class |

`tol` |
numeric. Numeric tolerance to use for some inversion of matrices. Default to |

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 = Xβ* (linear model) against the alternative *H_1: g = Xβ + 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.

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.

Mario A. Martinez Araya, r@marioma.me

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