4.1.2.1.1. statsmodels.base._constraints.fit_constrained

statsmodels.base._constraints.fit_constrained(model, constraint_matrix, constraint_values, start_params=None, fit_kwds=None)

fit model subject to linear equality constraints

The constraints are of the form R params = q where R is the constraint_matrix and q is the vector of constraint_values.

The estimation creates a new model with transformed design matrix, exog, and converts the results back to the original parameterization.

Parameters:

model: model instance

An instance of a model, see limitations in Notes section

constraint_matrix : array_like, 2D

This is R in the linear equality constraint R params = q. The number of columns needs to be the same as the number of columns in exog.

constraint_values :

This is q in the linear equality constraint R params = q If it is a tuple, then the constraint needs to be given by two arrays (constraint_matrix, constraint_value), i.e. (R, q). Otherwise, the constraints can be given as strings or list of strings. see t_test for details

start_params : None or array_like

starting values for the optimization. start_params needs to be given in the original parameter space and are internally transformed.

**fit_kwds : keyword arguments

fit_kwds are used in the optimization of the transformed model.

Returns:

params : ndarray ?

estimated parameters (in the original parameterization

cov_params : ndarray

covariance matrix of the parameter estimates. This is a reverse transformation of the covariance matrix of the transformed model given by cov_params() Note: fit_kwds can affect the choice of covariance, e.g. by specifying cov_type, which will be reflected in the returned covariance.

res_constr : results instance

This is the results instance for the created transformed model.

Notes

Limitations:

Models where the number of parameters is different from the number of columns of exog are not yet supported.

Requires a model that implement an offset option.