Q_theta: Objective function

In sahirbhatnagar/sail: Sparse Additive Interaction Learning

Description

calculates likelihood function. Used to assess convergence of fitting algorithm. This corresponds to the Q(theta) function in the paper

Usage

Q_theta(R, nobs, lambda, alpha, we, wj, wje, betaE, theta_list, gamma)

Arguments

R	residual
nobs	number of observations
lambda	a user supplied lambda sequence. Typically, by leaving this option unspecified users can have the program compute its own lambda sequence based on nlambda and lambda.factor. Supplying a value of lambda overrides this. It is better to supply a decreasing sequence of lambda values than a single (small) value, if not, the program will sort user-defined lambda sequence in decreasing order automatically. Default: NULL.
alpha	the mixing tuning parameter, with 0<α<1. It controls the penalization strength between the main effects and the interactions. The penalty is defined as λ(1-α)(w_e|β_e|+ ∑ w_j ||β_j||_2) + λα(∑ w_{je} |γ_j|) Larger values of alpha will favor selection of main effects over interactions. Smaller values of alpha will allow more interactions to enter the final model. Default: 0.5
we	penalty factor for exposure variable
wj	penalty factor for main effects
wje	penalty factor for interactions
betaE	estimate of exposure effect
theta_list	estimates of main effects
gamma	estimates of gamma parameter

Value

value of the objective function

sahirbhatnagar/sail documentation built on July 17, 2021, 5:10 a.m.