statsmodels.gam.smooth_basis.BSplines¶

class
statsmodels.gam.smooth_basis.
BSplines
(x, df, degree, include_intercept=False, constraints=None, variable_names=None, knot_kwds=None)[source]¶ additive smooth components using BSplines
This creates and holds the BSpline basis function for several components.
 Parameters
 xarray_like, 1D or 2D
underlying explanatory variable for smooth terms. If 2dimensional, then observations should be in rows and explanatory variables in columns.
 dfint
numer of basis functions or degrees of freedom
 degreeint
degree of the spline
 include_interceptbool
If False, then the basis functions are transformed so that they do not include a constant. This avoids perfect collinearity if a constant or several components are included in the model.
 constraintsNone, string or array
Constraints are used to transform the basis functions to satisfy those constraints. constraints = ‘center’ applies a linear transform to remove the constant and center the basis functions.
 variable_namesNone or list of strings
The names for the underlying explanatory variables, x used in for creating the column and parameter names for the basis functions. If
x
is a pandas object, then the names will be taken from it. knot_kwdsNone or list of dict
option for the knot selection. By default knots are selected in the same way as in patsy, however the number of knots is independent of keeping or removing the constant. Interior knot selection is based on quantiles of the data and is the same in patsy and mgcv. Boundary points are at the limits of the data range. The available options use with get_knots_bsplines are
knots : None or array interior knots
spacing : ‘quantile’ or ‘equal’
lower_bound : None or float location of lower boundary knots, all boundary knots are at the same point
upper_bound : None or float location of upper boundary knots, all boundary knots are at the same point
all_knots : None or array If all knots are provided, then those will be taken as given and all other options will be ignored.
Notes
A constant in the spline basis function can be removed in two different ways. The first is by dropping one basis column and normalizing the remaining columns. This is obtained by the default
include_intercept=False, constraints=None
The second option is by using the centering transform which is a linear transformation of all basis functions. As a consequence of the transformation, the Bspline basis functions do not have locally bounded support anymore. This is obtainedconstraints='center'
. In this caseinclude_intercept
will be automatically set to True to avoid dropping an additional column. Attributes
 smootherslist of univariate smooth component instances
 basisdesign matrix, array of spline bases columns for all components
 penalty_matriceslist of penalty matrices, one for each smooth term
 dim_basisnumber of columns in the basis
 k_variablesnumber of smooth components
 col_namescreated names for the basis columns
 There are additional attributes about the specification of the splines
 and some attributes mainly for internal use.
Methods
transform
(x_new)create the spline basis for new observations