4.1.2.1.3. statsmodels.base._constraints.transform_params_constraint¶
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statsmodels.base._constraints.
transform_params_constraint
(params, Sinv, R, q)[source]¶ find the parameters that statisfy linear constraint from unconstraint
The linear constraint R params = q is imposed.
Parameters: params : array_like
unconstraint parameters
Sinv : ndarray, 2d, symmetric
covariance matrix of the parameter estimate
R : ndarray, 2d
constraint matrix
q : ndarray, 1d
values of the constraint
Returns: params_constraint : ndarray
parameters of the same length as params satisfying the constraint
Notes
This is the exact formula for OLS and other linear models. It will be a local approximation for nonlinear models.
TODO: Is Sinv always the covariance matrix? In the linear case it can be (X’X)^{-1} or sigmahat^2 (X’X)^{-1}.
My guess is that this is the point in the subspace that satisfies the constraint that has minimum Mahalanobis distance. Proof ?