Objective function

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

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 \(0<\alpha<1\). It controls the penalization strength between the main effects and the interactions. The penalty is defined as $$\lambda(1-\alpha)(w_e|\beta_e|+ \sum w_j ||\beta_j||_2) + \lambda\alpha(\sum w_{je} |\gamma_j|)$$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