CalOptimalDecision {aihuman}

Calculate optimal decision & utility

Description

(1) Calculate optimal decision for each observation given each of c0 (cost of an outcome) and c1 (cost of an unnecessarily harsh decision) from the lists. (2) Calculate difference in the expected utility between binary version of judge's decisions and DMF recommendations given each of c0 (cost of an outcome) and c1 (cost of an unnecessarily harsh decision) from the lists.

Usage

CalOptimalDecision(
  data,
  mcmc.re,
  c0.ls,
  c1.ls,
  dmf = NULL,
  rho = 0,
  burnin = 0,
  out.length = 500,
  ZX = NULL,
  size = 5,
  include.utility.diff.mcmc = FALSE
)

Arguments

data

A data.frame or matrix of which columns consists of pre-treatment covariates, a binary treatment (Z), an ordinal decision (D), and an outcome variable (Y). The column names of the latter three should be specified as "Z", "D", and "Y" respectively.

mcmc.re

A mcmc object generated by AiEvalmcmc() function.

c0.ls

The list of cost of an outcome. See Section 3.7 for more details.

c1.ls

The list of cost of an unnecessarily harsh decision. See Section 3.7 for more details.

dmf

A numeric vector of binary DMF recommendations. If null, use judge's decisions (0 if the decision is 0 and 1 o.w; e.g., signature or cash bond).

rho

A sensitivity parameter. The default is 0 which implies the unconfoundedness assumption (Assumption 4).

burnin

A proportion of burnin for the Markov chain. The default is 0.

out.length

An integer to specify the progress on the screen. Every out.length-th iteration is printed on the screen. The default is 500.

ZX

The data matrix for interaction terms. The default is the interaction between Z and all of the pre-treatment covariates (X).

size

The number of parallel computing. The default is 5.

include.utility.diff.mcmc

A logical argument specifying whether to save Utility.diff.control.mcmc and Utility.diff.treated.mcmc for Figure S17. The default is FALSE.

Value

A data.frame of (1) the probability that the optimal decision for each observation being d in 0,1,...,k, (2) expected utility of binary version of judge's decision (g_d), (3) expected utility of binary DMF recommendation, and (4) the difference between (2) and (3). If include.utility.diff.mcmc = TRUE, returns a list of such data.frame and a data.frame that includes the result for mean and quantile of Utility.diff.control.mcmc and Utility.diff.treated.mcmc across mcmc samples.

Examples

data(synth)
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 10)
sample_optd = CalOptimalDecision(data = synth, mcmc.re = sample_mcmc, 
                                 c0.ls = seq(0,5,1), c1.ls = seq(0,5,1), 
                                 size = 1) # adjust the size