steinian_estimate: Perform Steinian Estimate for Model Risk (Only Applicable for...

In catalytic: Tools for Applying Catalytic Priors in Statistical Modeling

Perform Steinian Estimate for Model Risk (Only Applicable for Binomial Family)

Description

This function computes the Steinian estimate for model risk by fitting a sequence of Generalized Linear Models (GLMs) with varying values of tau. It combines the preliminary estimate from a model fitted with an initial tau_0 value with a penalty term that incorporates the in-sample prediction error and a covariance penalty, which is based on models fitted by inverting the response of individual observations.

Usage

steinian_estimate(formula, cat_init, tau_seq, tau_0, ...)

Arguments

formula	A formula specifying the GLMs. Should at least include response variables.
cat_init	A list generated from cat_glm_initialization.
tau_seq	A sequence of tuning parameter values (tau) over which the Steinian estimate will be computed. Each value of tau is used to weight the synthetic data during model fitting.
tau_0	A reference value for tau that is used in the calculation of the preliminary estimate model and the variance term.
...	Other arguments passed to other internal functions.

Details

1. Preliminary Estimate Model: The function first fits a GLM model using the observed and synthetic data with an initial value of tau_0 for the synthetic data weights.

2. In-sample Prediction Error: For each value of tau in tau_seq, the function computes the in-sample prediction error (logistic deviance).

3. Steinian Penalty: The function calculates the Steinian covariance penalty for each observation by fitting a modified model that inverts one observation at a time. The penalty is added to the in-sample prediction error to obtain the final risk estimate.

4. Steinian Risk Estimate: The final Steinian risk estimate is calculated by summing the in-sample prediction error and the Steinian penalty term for each value of tau in tau_seq.

Value

A numeric vector of Steinian risk estimates, one for each value of tau in tau_seq.

catalytic documentation built on April 4, 2025, 5:51 a.m.