hes_ll_ls: Hessian Matrix

In zthuang0422/PURM-2021-Latent-Stratification: Maximum Likelihood Latent Stratification

Description

Computes the second order partial derivative with respect to each of the par variables, resulting in a Hessian matrix.

Usage

hes_ll_ls(par, data, trans = FALSE)

Arguments

par	vector c(piA, piB, muA1, muA0, muB1, sigma), c(piA, piB/(1-piA), muA1, muA0, muB1, sigma) if trans=TRUE.
data	data frame containing columns y (positive outcome with zeros) and z (treatment).
trans	boolean signifying if piB has been transformed.

Details

For the input data frame, column z is the dummy variable for treatment. If z = 1, then the observation has received treatment. If z = 0, then the observation has not received treatment.
Sometimes piB is transformed to relative proportions from absolute proportions. This transformation allows the reparameterization of the piA and piB to allow constraint bounds between 0 and 1 in the optimization procedure.
The returned Hessian is the second order derivative with respect to θ where θ is in the order of piA, piB, muA1, muA0, muB1, and sigma.

Value

Hessian matrix for the latent stratification model.

Examples

sim = sim_latent_strat(n=10000, piA=0.2, piB=0.1, muA1=5, muA0=4.5, muB1=3, sigma=0.3)
hes_ll_ls(sim$par, sim$data)

# if the strata proportions are in relative sizes
hes_ll_ls(sim$par, sim$data, trans=TRUE)

zthuang0422/PURM-2021-Latent-Stratification documentation built on Dec. 23, 2021, 10:12 p.m.