statsmodels.genmod.generalized_estimating_equations.OrdinalGEE.qic

OrdinalGEE.qic(params, scale, cov_params, n_step=1000)

Returns quasi-information criteria and quasi-likelihood values.

Parameters:
paramsarray_like

The GEE estimates of the regression parameters.

scalescalar

Estimated scale parameter

cov_paramsarray_like

An estimate of the covariance matrix for the model parameters. Conventionally this is the robust covariance matrix.

n_stepinteger

The number of points in the trapezoidal approximation to the quasi-likelihood function.

Returns:
qlscalar

The quasi-likelihood value

qicscalar

A QIC that can be used to compare the mean and covariance structures of the model.

qicuscalar

A simplified QIC that can be used to compare mean structures but not covariance structures

Notes

The quasi-likelihood used here is obtained by numerically evaluating Wedderburn’s integral representation of the quasi-likelihood function. This approach is valid for all families and links. Many other packages use analytical expressions for quasi-likelihoods that are valid in special cases where the link function is canonical. These analytical expressions may omit additive constants that only depend on the data. Therefore, the numerical values of our QL and QIC values will differ from the values reported by other packages. However only the differences between two QIC values calculated for different models using the same data are meaningful. Our QIC should produce the same QIC differences as other software.

When using the QIC for models with unknown scale parameter, use a common estimate of the scale parameter for all models being compared.

References