2.1.10. patsy.builtins.te

patsy.builtins.te(s1, .., sn, constraints=None)

Generates smooth of several covariates as a tensor product of the bases of marginal univariate smooths s1, .., sn. The marginal smooths are required to transform input univariate data into some kind of smooth functions basis producing a 2-d array output with the (i, j) element corresponding to the value of the j th basis function at the i th data point. The resulting basis dimension is the product of the basis dimensions of the marginal smooths. The usual usage is something like:

y ~ 1 + te(cr(x1, df=5), cc(x2, df=6), constraints='center')

to fit y as a smooth function of both x1 and x2, with a natural cubic spline for x1 marginal smooth and a cyclic cubic spline for x2 (and centering constraint absorbed in the resulting design matrix).

Parameters:constraints – Either a 2-d array defining general linear constraints (that is np.dot(constraints, betas) is zero, where betas denotes the array of initial parameters, corresponding to the initial unconstrained design matrix), or the string 'center' indicating that we should apply a centering constraint (this constraint will be computed from the input data, remembered and re-used for prediction from the fitted model). The constraints are absorbed in the resulting design matrix which means that the model is actually rewritten in terms of unconstrained parameters. For more details see spline-regression.

Using this function requires scipy be installed.

Note

This function reproduce the tensor product smooth ‘te’ as implemented in the R package ‘mgcv’ (GAM modelling). See also ‘Generalized Additive Models’, Simon N. Wood, 2006, pp 158-163

New in version 0.3.0.