Linear hypotheses testing
- Hypothesis `L*B*M = C` to be tested where B is the parameters in
- regression Y = X*B. Each element is a tuple of length 2, 3, or 4:
(name, contrast_L, transform_M)
(name, contrast_L, transform_M, constant_C)
- containing a string `name`, the contrast matrix L, the transform
- matrix M (for transforming dependent variables), and right-hand side
- constant matrix constant_C, respectively.
Left-hand side contrast matrix for hypotheses testing. If 2D array, each row is an hypotheses and each column is an independent variable. At least 1 row (1 by k_exog, the number of independent variables) is required. If an array of strings, it will be passed to patsy.DesignInfo().linear_constraint.
Left hand side transform matrix. If None or left out, it is set to a k_endog by k_endog identity matrix (i.e. do not transform y matrix). If an array of strings, it will be passed to patsy.DesignInfo().linear_constraint.
Right-hand side constant matrix. if None or left out it is set to a matrix of zeros Must has the same number of rows as contrast_L and the same number of columns as transform_M
- If `hypotheses` is None: 1) the effect of each independent variable
- on the dependent variables will be tested. Or 2) if model is created
- using a formula, `hypotheses` will be created according to
- `design_info`. 1) and 2) is equivalent if no additional variables
- are created by the formula (e.g. dummy variables for categorical
- variables and interaction terms)
Testing the linear hypotheses
L * params * M = 0
where params is the regression coefficient matrix for the linear model y = x * params
If the model is not specified using the formula interfact, then the hypotheses test each included exogenous variable, one at a time. In most applications with categorical variables, the
from_formulainterface should be preferred when specifying a model since it provides knowledge about the model when specifying the hypotheses.