mallowian_estimate {catalytic} | R Documentation |
Perform Mallowian Estimate for Model Risk (Only Applicable for Gaussian Family)
Description
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.
Usage
mallowian_estimate(formula, cat_init, tau_seq, ...)
Arguments
formula |
A formula specifying the GLMs. Should at least include response variables. |
cat_init |
A list generated from |
tau_seq |
A sequence of tuning parameter values ( |
... |
Other arguments passed to other internal functions. |
Details
-
Model Fitting: For each value of
tau
intau_seq
, the function fits a GLM model using the observed and synthetic data. The synthetic data is weighted by the correspondingtau
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
intau_seq
.
Value
A numeric vector of Mallowian risk estimates, one for each value of tau
in tau_seq
.