postGamma: Perform a Metropolis-Hastings Step for Drawing a New Gamma

In skipTrack: A Bayesian Hierarchical Model that Controls for Non-Adherence in Mobile Menstrual Cycle Tracking

Perform a Metropolis-Hastings Step for Drawing a New Gamma

Description

Our model assumes that tau_i ~ Gamma(alpha_i, phi) where alpha_i/phi = theta_i and g(theta_i) = Z_i^T Gamma, where g is the log-link function. Because of this GLM formulation we cannot simply draw from a posterior here and instead use a Metropolis-Hastings step with proposal distribution propGamma ~ MVNormal(currentGamma, rhoGamma*I)

Usage

postGamma(taui, Zi, currentGamma, phi = 1, rhoGamma = 1000)

Arguments

taui	A vector of length num_Individuals representing precision parameters for individuals.
Zi	A matrix of covariates, where each row represents an individual and each column represents a covariate.
currentGamma	A vector (or matrix with 1 row) representing the current Gamma value.
phi	A scalar, the prior rate for tau_i.
rhoGamma	A scalar representing the proposal distribution precision parameter.

Details

This draw step assumes a log-link function for the Gamma GLM that we are fitting.

Value

A list containing the new Gamma value and the corresponding thetai values.

skipTrack documentation built on April 3, 2025, 6:21 p.m.