statsmodels.genmod.cov_struct.Autoregressive.covariance_matrix_solve¶

Autoregressive.covariance_matrix_solve(expval, index, stdev, rhs)[source]¶

Solves matrix equations of the form covmat * soln = rhs and returns the values of soln, where covmat is the covariance matrix represented by this class.

Parameters:¶

expvalarray_like

The expected value of endog for each observed value in the group.

indexint

The group index.

stdevarray_like

The standard deviation of endog for each observation in the group.

rhslist/tuple of array_like

A set of right-hand sides; each defines a matrix equation to be solved.

Returns:¶

solnlist/tuple of array_like

The solutions to the matrix equations.

Notes

Returns None if the solver fails.

Some dependence structures do not use expval and/or index to determine the correlation matrix. Some families (e.g. binomial) do not use the stdev parameter when forming the covariance matrix.

If the covariance matrix is singular or not SPD, it is projected to the nearest such matrix. These projection events are recorded in the fit_history attribute of the GEE model.

Systems of linear equations with the covariance matrix as the left hand side (LHS) are solved for different right hand sides (RHS); the LHS is only factorized once to save time.

This is a default implementation, it can be reimplemented in subclasses to optimize the linear algebra according to the structure of the covariance matrix.