QL_fun: Title: Gradient Descent Method for penalized likelihood this...

In Goodgolden/LDTM: Longitudinal Dirichlet Tree Multinomial Model

Title: Gradient Descent Method for penalized likelihood this is gradient descent methods for penalized likelihood

Description

Title: Gradient Descent Method for penalized likelihood this is gradient descent methods for penalized likelihood

Usage

QL_fun(Ytree, X, W, model, B1, grad, alpha, lambda, L)

Arguments

Ytree	is the tree information from the Ytree function. Input will be a set of n * 2 matrices, each of which represent the an interior knot and its children branches
X	matrix of nxp which is the number of subjects by number of covariates
W	matrix this will be the starting Beta used in the algorithm
model	character type of model to use for the Log Likelihood. Options are (Dirichlet Multinomial = "dirmult", Multinomial = "mult", or Dirichlet = "dir")
B1	the Beta values that will be updated in the loop using the gradient descent
grad	the gradient descent
alpha	numeric the desired lasso parameter. In paper they used (0, 0.25, 0,5, and 1) to investigate the covariate selection. Note: In the paper they noted this as Gamma
lambda	numeric the tuning parameter
L	numeric Lipschitz constant, instead of choosing a constant step size L. We can use the backtracking to choose a suitable L at each iteration. Note: This is noted at C in the Wang et al. paper

Details

Since the penalized likelihood function is non-smooth, we adopt the accelerated proximal gradient method to minimize the objective function (equation 4) which will estimate parameters and select covariates simultaneously. Tao Wang and Hongyu Zhao (2017)

Value

The smallest approximated negative likelihood obtained through the algorithm

Goodgolden/LDTM documentation built on May 25, 2022, 5:25 p.m.