This function calculates the Mallowian estimate for model risk by fitting a sequence of
Generalized Linear Models (GLMs) with varying values of tau. It uses the in-sample prediction
error along with a regularized projection matrix to estimate the model risk. The tau parameter
influences the weighting of synthetic data during model fitting.
mallowian_estimate(formula, cat_init, tau_seq, ...)A numeric vector of Mallowian risk estimates, one for each value of tau in tau_seq.
A formula specifying the GLMs. Should at least include response variables.
A list generated from cat_glm_initialization.
A sequence of tuning parameter values (tau) over which
the Mallowian estimate will be computed. Each value of tau is used to weight the
synthetic data during model fitting.
Other arguments passed to other internal functions.
Model Fitting: For each value of tau in tau_seq, the function fits a GLM model
using the observed and synthetic data. The synthetic data is weighted by the corresponding
tau value during the fitting process.
In-sample Prediction Error: After fitting the model, the function computes the in-sample prediction error (Mean Squared Error) to assess the model's performance.
Regularized Projection Matrix: The function calculates a regularized projection matrix using the observed and synthetic data, which influences the covariance matrix used in risk estimation.
Mallowian Risk Estimate: The final Mallowian risk estimate is computed by combining the
in-sample prediction error with a penalty term involving the projection matrix and a variance term.
This estimate is calculated for each value of tau in tau_seq.