get_glm_log_density_grad

This function calculates the gradient of the log density with respect to the coefficients
for a given GLM family based on the provided predictors, response variable, and weights.

To improve estimation accuracy and stability in statistical modeling, catalytic prior distributions are employed, integrating observed data with synthetic data generated from a simpler model's predictive distribution. This approach enhances model robustness, stability, and flexibility in complex data scenarios. The catalytic prior distributions are introduced by 'Huang et al.' (2020, <doi:10.1073/pnas.1920913117>), Li and Huang (2023, <doi:10.48550/arXiv.2312.01411>).

Dongming Huang

catalytic

Tools for Applying Catalytic Priors in Statistical Modeling

Yitong Wu

Weihao Li

Ministry of Education, Singapore 

get_glm_log_density_grad function

<dl><dt>family_string</dt>
<dd>Character. The GLM family to use. Options are <code>"binomial"</code> or <code>"gaussian"</code>.</dd>
<dt>X</dt>
<dd>Matrix. The design matrix (predictors) for the GLM.</dd>
<dt>Y</dt>
<dd>Vector. The response variable.</dd>
<dt>coefs</dt>
<dd>Numeric vector. The coefficients for the GLM.</dd>
<dt>weights</dt>
<dd>Numeric vector. The weights for the GLM. Default is 1.</dd></dl>

Arguments

Compute Gradient of Log Density for GLM Families — get_glm_log_density_grad

<dl>

<dt>family_string</dt>
<dd>Character. The GLM family to use. Options are <code>"binomial"</code> or <code>"gaussian"</code>.</dd>


<dt>X</dt>
<dd>Matrix. The design matrix (predictors) for the GLM.</dd>


<dt>Y</dt>
<dd>Vector. The response variable.</dd>


<dt>coefs</dt>
<dd>Numeric vector. The coefficients for the GLM.</dd>


<dt>weights</dt>
<dd>Numeric vector. The weights for the GLM. Default is 1.</dd>

</dl>

get_glm_log_density_grad: Compute Gradient of Log Density for GLM Families

Description

Usage

Value

Arguments