Package 'aihuman' reference manual

Title:	Experimental Evaluation of Algorithm-Assisted Human Decision-Making
Description:	Provides statistical methods for analyzing experimental evaluation of the causal impacts of algorithmic recommendations on human decisions developed by Imai, Jiang, Greiner, Halen, and Shin (2023) <doi:10.1093/jrsssa/qnad010>. The data used for this paper, and made available here, are interim, based on only half of the observations in the study and (for those observations) only half of the study follow-up period. We use them only to illustrate methods, not to draw substantive conclusions.
Authors:	Sooahn Shin [aut, cre] , Zhichao Jiang [aut], Kosuke Imai [aut]
Maintainer:	Sooahn Shin <[email protected]>
License:	GPL (>= 2)
Version:	0.1.0
Built:	2024-11-28 06:41:25 UTC
Source:	CRAN

Experimental Evaluation of Algorithm-Assisted Human Decision-Making

Description

Provides statistical methods for analyzing experimental evaluation of the causal impacts of algorithmic recommendations on human decisions developed by Imai, Jiang, Greiner, Halen, and Shin (2023) <doi:10.1093/jrsssa/qnad010>. The data used for this paper, and made available here, are interim, based on only half of the observations in the study and (for those observations) only half of the study follow-up period. We use them only to illustrate methods, not to draw substantive conclusions.

Package Content

Index of help topics:

APCEsummary             Summary of APCE
APCEsummaryipw          Summary of APCE for frequentist analysis
AiEvalmcmc              Gibbs sampler for the main analysis
BootstrapAPCEipw        Bootstrap for estimating variance of APCE
BootstrapAPCEipwRE      Bootstrap for estimating variance of APCE with
                        random effects
BootstrapAPCEipwREparallel
                        Bootstrap for estimating variance of APCE with
                        random effects
CalAPCE                 Calculate APCE
CalAPCEipw              Compute APCE using frequentist analysis
CalAPCEipwRE            Compute APCE using frequentist analysis with
                        random effects
CalAPCEparallel         Calculate APCE using parallel computing
CalDIM                  Calculate diff-in-means estimates
CalDIMsubgroup          Calculate diff-in-means estimates
CalDelta                Calculate the delta given the principal stratum
CalFairness             Calculate the principal fairness
CalOptimalDecision      Calculate optimal decision & utility
CalPS                   Calculate the proportion of principal strata
                        (R)
FTAdata                 Interim Dane data with failure to appear (FTA)
                        as an outcome
HearingDate             Interim court event hearing date
NCAdata                 Interim Dane data with new criminal activity
                        (NCA) as an outcome
NVCAdata                Interim Dane data with new violent criminal
                        activity (NVCA) as an outcome
PSAdata                 Interim Dane PSA data
PlotAPCE                Plot APCE
PlotDIMdecisions        Plot diff-in-means estimates
PlotDIMoutcomes         Plot diff-in-means estimates
PlotFairness            Plot the principal fairness
PlotOptimalDecision     Plot optimal decision
PlotPS                  Plot the proportion of principal strata (R)
PlotSpilloverCRT        Plot conditional randomization test
PlotSpilloverCRTpower   Plot power analysis of conditional
                        randomization test
PlotStackedBar          Stacked barplot for the distribution of the
                        decision given psa
PlotStackedBarDMF       Stacked barplot for the distribution of the
                        decision given DMF recommendation
PlotUtilityDiff         Plot utility difference
PlotUtilityDiffCI       Plot utility difference with 95
                        interval
SpilloverCRT            Conduct conditional randomization test
SpilloverCRTpower       Conduct power analysis of conditional
                        randomization test
TestMonotonicity        Test monotonicity
TestMonotonicityRE      Test monotonicity with random effects
aihuman-package         Experimental Evaluation of Algorithm-Assisted
                        Human Decision-Making
g_legend                Pulling ggplot legend
hearingdate_synth       Synthetic court event hearing date
psa_synth               Synthetic PSA data
synth                   Synthetic data

Further information is available in the following vignettes:

`aihuman`	aihuman (source, pdf)

Maintainer

Sooahn Shin <[email protected]>

Author(s)

Sooahn Shin [aut, cre] (<https://orcid.org/0000-0001-6213-2197>), Zhichao Jiang [aut], Kosuke Imai [aut]

Gibbs sampler for the main analysis

Description

See Appendix S5 for more details.

Usage

AiEvalmcmc(
  data,
  rho = 0,
  Sigma0.beta.inv = NULL,
  Sigma0.alpha.inv = NULL,
  sigma0 = NULL,
  beta = NULL,
  alpha = NULL,
  theta = NULL,
  delta = NULL,
  n.mcmc = 5 * 10,
  verbose = FALSE,
  out.length = 10,
  beta.zx.off = FALSE,
  theta.z.off = FALSE
)
AiEvalmcmc(
  data,
  rho = 0,
  Sigma0.beta.inv = NULL,
  Sigma0.alpha.inv = NULL,
  sigma0 = NULL,
  beta = NULL,
  alpha = NULL,
  theta = NULL,
  delta = NULL,
  n.mcmc = 5 * 10,
  verbose = FALSE,
  out.length = 10,
  beta.zx.off = FALSE,
  theta.z.off = 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.
`rho`	A sensitivity parameter. The default is `0` which implies the unconfoundedness assumption (Assumption 4).
`Sigma0.beta.inv`	Inverse of the prior covariance matrix of beta. The default is a diagonal matrix with `0.01` diagonal entries.
`Sigma0.alpha.inv`	Inverse of the prior covariance matrix of alpha. The default is a diagonal matrix with `0.01` diagonal entries.
`sigma0`	Prior variance of the cutoff points (theta and delta)
`beta`	Initial value for beta.
`alpha`	Initial value for alpha.
`theta`	Initial value for theta.
`delta`	Initial value for delta.
`n.mcmc`	The total number of MCMC iterations. The default is `50`.
`verbose`	A logical argument specified to print the progress on the screen. The default is `FALSE`.
`out.length`	An integer to specify the progress on the screen. If `verbose = TRUE`, every `out.length`-th iteration is printed on the screen. The default is `10`.
`beta.zx.off`	A logical argument specified to exclude the interaction terms (Z by X) from the model. The default is `FALSE`.
`theta.z.off`	A logical argument specified to set same cutoffs theta for treatment and control group. The default is `FALSE`.

Value

An object of class mcmc containing the posterior samples.

Examples

data(synth)
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 2)

data(synth)
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 2)

Summary of APCE

Description

Summary of average principal causal effects (APCE) with ordinal decision.

Usage

APCEsummary(apce.mcmc)
APCEsummary(apce.mcmc)

Arguments

apce.mcmc

APCE.mcmc array generated from CalAPCE or CalAPCEparallel.

Value

A data.frame that consists of mean and quantiles (2.5

Examples


data(synth)
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 10)
subgroup_synth = list(1:nrow(synth),which(synth$Sex==0),which(synth$Sex==1),
                      which(synth$Sex==1&synth$White==0),which(synth$Sex==1&synth$White==1))
sample_apce = CalAPCE(data = synth, mcmc.re = sample_mcmc, subgroup = subgroup_synth)
sample_apce_summary = APCEsummary(sample_apce[["APCE.mcmc"]])


data(synth)
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 10)
subgroup_synth = list(1:nrow(synth),which(synth$Sex==0),which(synth$Sex==1),
                      which(synth$Sex==1&synth$White==0),which(synth$Sex==1&synth$White==1))
sample_apce = CalAPCE(data = synth, mcmc.re = sample_mcmc, subgroup = subgroup_synth)
sample_apce_summary = APCEsummary(sample_apce[["APCE.mcmc"]])

Summary of APCE for frequentist analysis

Description

Summary of average principal causal effects (APCE) with ordinal decision with frequentist results.

Usage

APCEsummaryipw(
  G1_est,
  G2_est,
  G3_est,
  G4_est,
  G5_est,
  G1_boot,
  G2_boot,
  G3_boot,
  G4_boot,
  G5_boot,
  name.group = c("Overall", "Female", "Male", "Non-white\nMale", "White\nMale")
)
APCEsummaryipw(
  G1_est,
  G2_est,
  G3_est,
  G4_est,
  G5_est,
  G1_boot,
  G2_boot,
  G3_boot,
  G4_boot,
  G5_boot,
  name.group = c("Overall", "Female", "Male", "Non-white\nMale", "White\nMale")
)

Arguments

`G1_est`	List generated from `CalAPCEipw` for the first subgroup.
`G2_est`	List generated from `CalAPCEipw` for the second subgroup.
`G3_est`	List generated from `CalAPCEipw` for the third subgroup.
`G4_est`	List generated from `CalAPCEipw` for the fourth subgroup.
`G5_est`	List generated from `CalAPCEipw` for the fifth subgroup.
`G1_boot`	List generated from `BootstrapAPCEipw` for the first subgroup.
`G2_boot`	List generated from `BootstrapAPCEipw` for the second subgroup.
`G3_boot`	List generated from `BootstrapAPCEipw` for the third subgroup.
`G4_boot`	List generated from `BootstrapAPCEipw` for the fourth subgroup.
`G5_boot`	List generated from `BootstrapAPCEipw` for the fifth subgroup.
`name.group`	A list of character vectors for the label of five subgroups.

Value

A data.frame that consists of mean and quantiles (2.5

Examples

data(synth)
synth$SexWhite = synth$Sex * synth$White
freq_apce = CalAPCEipw(synth)
boot_apce = BootstrapAPCEipw(synth, rep = 10)
# subgroup analysis
data_s0 = subset(synth, synth$Sex==0,select=-c(Sex,SexWhite))
freq_s0 = CalAPCEipw(data_s0)
boot_s0 = BootstrapAPCEipw(data_s0, rep = 10)
data_s1 = subset(synth, synth$Sex==1,select=-c(Sex,SexWhite))
freq_s1 = CalAPCEipw(data_s1)
boot_s1 = BootstrapAPCEipw(data_s1, rep = 10)
data_s1w0 = subset(synth, synth$Sex==1&synth$White==0,select=-c(Sex,White,SexWhite))
freq_s1w0 = CalAPCEipw(data_s1w0)
boot_s1w0 = BootstrapAPCEipw(data_s1w0, rep = 10)
data_s1w1 = subset(synth, synth$Sex==1&synth$White==1,select=-c(Sex,White,SexWhite))
freq_s1w1 = CalAPCEipw(data_s1w1)
boot_s1w1 = BootstrapAPCEipw(data_s1w1, rep = 10)

freq_apce_summary <- APCEsummaryipw(freq_apce, freq_s0, freq_s1, freq_s1w0, freq_s1w1,
                                    boot_apce, boot_s0, boot_s1, boot_s1w0, boot_s1w0)
PlotAPCE(freq_apce_summary, y.max = 0.25, decision.labels = c("signature","small cash",
         "middle cash","large cash"), shape.values = c(16, 17, 15, 18), 
         col.values = c("blue", "black", "red", "brown", "purple"), label = FALSE)

data(synth)
synth$SexWhite = synth$Sex * synth$White
freq_apce = CalAPCEipw(synth)
boot_apce = BootstrapAPCEipw(synth, rep = 10)
# subgroup analysis
data_s0 = subset(synth, synth$Sex==0,select=-c(Sex,SexWhite))
freq_s0 = CalAPCEipw(data_s0)
boot_s0 = BootstrapAPCEipw(data_s0, rep = 10)
data_s1 = subset(synth, synth$Sex==1,select=-c(Sex,SexWhite))
freq_s1 = CalAPCEipw(data_s1)
boot_s1 = BootstrapAPCEipw(data_s1, rep = 10)
data_s1w0 = subset(synth, synth$Sex==1&synth$White==0,select=-c(Sex,White,SexWhite))
freq_s1w0 = CalAPCEipw(data_s1w0)
boot_s1w0 = BootstrapAPCEipw(data_s1w0, rep = 10)
data_s1w1 = subset(synth, synth$Sex==1&synth$White==1,select=-c(Sex,White,SexWhite))
freq_s1w1 = CalAPCEipw(data_s1w1)
boot_s1w1 = BootstrapAPCEipw(data_s1w1, rep = 10)

freq_apce_summary <- APCEsummaryipw(freq_apce, freq_s0, freq_s1, freq_s1w0, freq_s1w1,
                                    boot_apce, boot_s0, boot_s1, boot_s1w0, boot_s1w0)
PlotAPCE(freq_apce_summary, y.max = 0.25, decision.labels = c("signature","small cash",
         "middle cash","large cash"), shape.values = c(16, 17, 15, 18), 
         col.values = c("blue", "black", "red", "brown", "purple"), label = FALSE)

Bootstrap for estimating variance of APCE

Description

Estimate variance of APCE for frequentist analysis using bootstrap. See S7 for more details.

Usage

BootstrapAPCEipw(data, rep = 1000)
BootstrapAPCEipw(data, rep = 1000)

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.
`rep`	Size of bootstrap

Value

An object of class list with the following elements:

`P.D1.boot`	An array with dimension rep by (k+1) by (k+2) for quantity P(D(1)=d\| R=r), dimension 1 is rep (size of bootstrap), dimension 2 is (k+1) values of D from 0 to k, dimension 3 is (k+2) values of R from 0 to k+1.
`P.D0.boot`	An array with dimension rep by (k+1) by (k+2) for quantity P(D(0)=d\| R=r).
`APCE.boot`	An array with dimension rep by (k+1) by (k+2) for quantity P(D(1)=d\| R=r)-P(D(0)=d\| R=r).
`P.R.boot`	An array with dimension rep by (k+2) for quantity P(R=r) for r from 0 to (k+1).
`alpha.boot`	An array with estimated alpha for each bootstrap.
`delta.boot`	An array with estimated delta for each bootstrap.

Examples

data(synth)
set.seed(123)
boot_apce = BootstrapAPCEipw(synth, rep = 100)


data(synth)
set.seed(123)
boot_apce = BootstrapAPCEipw(synth, rep = 100)

Bootstrap for estimating variance of APCE with random effects

Description

Estimate variance of APCE for frequentist analysis with random effects using bootstrap. See S7 for more details.

Usage

BootstrapAPCEipwRE(data, rep = 1000, formula, CourtEvent_HearingDate, nAGQ = 1)
BootstrapAPCEipwRE(data, rep = 1000, formula, CourtEvent_HearingDate, nAGQ = 1)

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.
`rep`	Size of bootstrap
`formula`	A formula of the model to fit.
`CourtEvent_HearingDate`	The court event hearing date.
`nAGQ`	Integer scalar - the number of points per axis for evaluating the adaptive Gauss-Hermite approximation to the log-likelihood. Defaults to 1, corresponding to the Laplace approximation.

Value

An object of class list with the following elements:

`P.D1.boot`	An array with dimension rep by (k+1) by (k+2) for quantity P(D(1)=d\| R=r), dimension 1 is rep (size of bootstrap), dimension 2 is (k+1) values of D from 0 to k, dimension 3 is (k+2) values of R from 0 to k+1.
`P.D0.boot`	An array with dimension rep by (k+1) by (k+2) for quantity P(D(0)=d\| R=r).
`APCE.boot`	An array with dimension rep by (k+1) by (k+2) for quantity P(D(1)=d\| R=r)-P(D(0)=d\| R=r).
`P.R.boot`	An array with dimension rep by (k+2) for quantity P(R=r) for r from 0 to (k+1).

Examples


data(synth)
data(hearingdate_synth)
synth$CourtEvent_HearingDate = hearingdate_synth
set.seed(123)
boot_apce_re = BootstrapAPCEipwRE(synth, rep = 10, formula = "Y ~ Sex + White + Age + 
                                  CurrentViolentOffense + PendingChargeAtTimeOfOffense + 
                                  PriorMisdemeanorConviction + PriorFelonyConviction + 
                                  PriorViolentConviction + (1|CourtEvent_HearingDate) + D", 
                                  CourtEvent_HearingDate = hearingdate_synth)


data(synth)
data(hearingdate_synth)
synth$CourtEvent_HearingDate = hearingdate_synth
set.seed(123)
boot_apce_re = BootstrapAPCEipwRE(synth, rep = 10, formula = "Y ~ Sex + White + Age + 
                                  CurrentViolentOffense + PendingChargeAtTimeOfOffense + 
                                  PriorMisdemeanorConviction + PriorFelonyConviction + 
                                  PriorViolentConviction + (1|CourtEvent_HearingDate) + D", 
                                  CourtEvent_HearingDate = hearingdate_synth)

Bootstrap for estimating variance of APCE with random effects

Description

Estimate variance of APCE for frequentist analysis with random effects using bootstrap. See S7 for more details.

Usage

BootstrapAPCEipwREparallel(data, rep = 1000, formula, nAGQ = 1, size = 5)
BootstrapAPCEipwREparallel(data, rep = 1000, formula, nAGQ = 1, size = 5)

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.
`rep`	Size of bootstrap
`formula`	A formula of the model to fit.
`nAGQ`	Integer scalar - the number of points per axis for evaluating the adaptive Gauss-Hermite approximation to the log-likelihood. Defaults to 1, corresponding to the Laplace approximation.
`size`	The number of parallel computing. The default is `5`.

Value

An object of class list with the following elements:

`P.D1.boot`	An array with dimension rep by (k+1) by (k+2) for quantity P(D(1)=d\| R=r), dimension 1 is rep (size of bootstrap), dimension 2 is (k+1) values of D from 0 to k, dimension 3 is (k+2) values of R from 0 to k+1.
`P.D0.boot`	An array with dimension rep by (k+1) by (k+2) for quantity P(D(0)=d\| R=r).
`APCE.boot`	An array with dimension rep by (k+1) by (k+2) for quantity P(D(1)=d\| R=r)-P(D(0)=d\| R=r).
`P.R.boot`	An array with dimension rep by (k+2) for quantity P(R=r) for r from 0 to (k+1).

Examples


data(synth)
data(hearingdate_synth)
synth$CourtEvent_HearingDate = hearingdate_synth
set.seed(123)
boot_apce_re = BootstrapAPCEipwREparallel(synth, rep = 10, 
                                          formula = "Y ~ Sex + White + Age + 
                                          CurrentViolentOffense + PendingChargeAtTimeOfOffense + 
                                          PriorMisdemeanorConviction + PriorFelonyConviction + 
                                          PriorViolentConviction + (1|CourtEvent_HearingDate) + 
                                          D", size = 1) # adjust the size


data(synth)
data(hearingdate_synth)
synth$CourtEvent_HearingDate = hearingdate_synth
set.seed(123)
boot_apce_re = BootstrapAPCEipwREparallel(synth, rep = 10, 
                                          formula = "Y ~ Sex + White + Age + 
                                          CurrentViolentOffense + PendingChargeAtTimeOfOffense + 
                                          PriorMisdemeanorConviction + PriorFelonyConviction + 
                                          PriorViolentConviction + (1|CourtEvent_HearingDate) + 
                                          D", size = 1) # adjust the size

Calculate APCE

Description

Calculate average principal causal effects (APCE) with ordinal decision. See Section 3.4 for more details.

Usage

CalAPCE(
  data,
  mcmc.re,
  subgroup,
  name.group = c("overall", "Sex0", "Sex1", "Sex1 White0", "Sex1 White1"),
  rho = 0,
  burnin = 0,
  out.length = 500,
  c0 = 0,
  c1 = 0,
  ZX = NULL,
  save.individual.optimal.decision = FALSE,
  parallel = FALSE,
  optimal.decision.only = FALSE,
  dmf = NULL,
  fair.dmf.only = FALSE
)
CalAPCE(
  data,
  mcmc.re,
  subgroup,
  name.group = c("overall", "Sex0", "Sex1", "Sex1 White0", "Sex1 White1"),
  rho = 0,
  burnin = 0,
  out.length = 500,
  c0 = 0,
  c1 = 0,
  ZX = NULL,
  save.individual.optimal.decision = FALSE,
  parallel = FALSE,
  optimal.decision.only = FALSE,
  dmf = NULL,
  fair.dmf.only = 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.
`subgroup`	A list of numeric vectors for the index of each of the five subgroups.
`name.group`	A list of character vectors for the label of five subgroups.
`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`.
`c0`	The cost of an outcome. See Section 3.7 for more details. The default is `0`.
`c1`	The cost of an unnecessarily harsh decision. See Section 3.7 for more details. The default is `0`.
`ZX`	The data matrix for interaction terms. The default is the interaction between Z and all of the pre-treatment covariates (X).
`save.individual.optimal.decision`	A logical argument specified to save individual optimal decision rules. The default is `FALSE`.
`parallel`	A logical argument specifying whether parallel computing is conducted. Do not change this argument manually.
`optimal.decision.only`	A logical argument specified to compute only the optimal decision rule. The default is `FALSE`.
`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).
`fair.dmf.only`	A logical argument specified to compute only the fairness of given DMF recommendations. The default is `FALSE`. Not used in the analysis for the JRSSA paper.

Value

An object of class list with the following elements:

`P.D1.mcmc`	An array with dimension n.mcmc by 5 by (k+1) by (k+2) for quantity P(D(1)=d\| R=r), dimension 1 is each posterior sample; dimension 2 is subgroup, dimension 3 is (k+1) values of D from 0 to k, dimension 4 is (k+2) values of R from 0 to k+1.
`P.D0.mcmc`	An array with dimension n.mcmc by 5 by (k+1) by (k+2) for quantity P(D(0)=d\| R=r).
`APCE.mcmc`	An array with dimension n.mcmc by 5 by (k+1) by (k+2) for quantity P(D(1)=d\| R=r)-P(D(0)=d\| R=r).
`P.R.mcmc`	An array with dimension n.mcmc by 5 by (k+2) for quantity P(R=r) for r from 0 to (k+1).
`Optimal.Z.mcmc`	An array with dimension n.mcmc by 5 for the proportion of the cases where treatment (PSA provided) is optimal.
`Optimal.D.mcmc`	An array with dimension n.mcmc by 5 by (k+1) for the proportion of optimal decision rule (average over observations). If `save.individual.optimal.decision = TRUE`, the dimension would be n by (k+1) (average over mcmc samples).
`P.DMF.mcmc`	An array with dimension n.mcmc by 5 by (k+1) by (k+2) for the proportion of binary DMF recommendations. Not used in the analysis for the JRSSA paper.
`Utility.g_d.mcmc`	Included if `save.individual.optimal.decision = TRUE`. An array with dimension n for the individual utility of judge's decisions.
`Utility.g_dmf.mcmc`	Included if `save.individual.optimal.decision = TRUE`. An array with dimension n for the individual utility of DMF recommendation.
`Utility.diff.control.mcmc`	Included if `save.individual.optimal.decision = TRUE`. An array with dimension n.mcmc for estimated difference in utility between judge's decisions and DMF recommendation among control group.
`Utility.diff.treated.mcmc`	Included if `save.individual.optimal.decision = TRUE`. An array with dimension n.mcmc for estimated difference in utility between judge's decisions and DMF recommendation among treated group.

Examples

data(synth)
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 2)
subgroup_synth = list(1:nrow(synth),which(synth$Sex==0),which(synth$Sex==1),
                      which(synth$Sex==1&synth$White==0),which(synth$Sex==1&synth$White==1))
sample_apce = CalAPCE(data = synth, mcmc.re = sample_mcmc, subgroup = subgroup_synth)

data(synth)
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 2)
subgroup_synth = list(1:nrow(synth),which(synth$Sex==0),which(synth$Sex==1),
                      which(synth$Sex==1&synth$White==0),which(synth$Sex==1&synth$White==1))
sample_apce = CalAPCE(data = synth, mcmc.re = sample_mcmc, subgroup = subgroup_synth)

Compute APCE using frequentist analysis

Description

Estimate propensity score and use Hajek estimator to compute APCE. See S7 for more details.

Usage

CalAPCEipw(data)
CalAPCEipw(data)

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.

Value

An object of class list with the following elements:

`P.D1`	An array with dimension (k+1) by (k+2) for quantity P(D(1)=d\| R=r), dimension 1 is (k+1) values of D from 0 to k, dimension 2 is (k+2) values of R from 0 to k+1.
`P.D0`	An array with dimension (k+1) by (k+2) for quantity P(D(0)=d\| R=r).
`APCE`	An array with dimension (k+1) by (k+2) for quantity P(D(1)=d\| R=r)-P(D(0)=d\| R=r).
`P.R`	An array with dimension (k+2) for quantity P(R=r) for r from 0 to (k+1).
`alpha`	An array with estimated alpha.
`delta`	An array with estimated delta.

Examples

data(synth)
freq_apce = CalAPCEipw(synth)

data(synth)
freq_apce = CalAPCEipw(synth)

Compute APCE using frequentist analysis with random effects

Description

Estimate propensity score and use Hajek estimator to compute APCE. See S7 for more details.

Usage

CalAPCEipwRE(data, formula, nAGQ = 1)
CalAPCEipwRE(data, formula, nAGQ = 1)

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.
`formula`	A formula of the model to fit.
`nAGQ`	Integer scalar - the number of points per axis for evaluating the adaptive Gauss-Hermite approximation to the log-likelihood. Defaults to 1, corresponding to the Laplace approximation.

Value

An object of class list with the following elements:

`P.D1`	An array with dimension (k+1) by (k+2) for quantity P(D(1)=d\| R=r), dimension 1 is (k+1) values of D from 0 to k, dimension 2 is (k+2) values of R from 0 to k+1.
`P.D0`	An array with dimension (k+1) by (k+2) for quantity P(D(0)=d\| R=r).
`APCE`	An array with dimension (k+1) by (k+2) for quantity P(D(1)=d\| R=r)-P(D(0)=d\| R=r).
`P.R`	An array with dimension (k+2) for quantity P(R=r) for r from 0 to (k+1).
`alpha`	An array with estimated alpha.
`delta`	An array with estimated delta.

Examples

data(synth)
data(hearingdate_synth)
synth$CourtEvent_HearingDate = hearingdate_synth
freq_apce_re = CalAPCEipwRE(synth, formula = "Y ~ Sex + White + Age + 
                            CurrentViolentOffense + PendingChargeAtTimeOfOffense + 
                            PriorMisdemeanorConviction + PriorFelonyConviction + 
                            PriorViolentConviction + (1|CourtEvent_HearingDate) + D")

data(synth)
data(hearingdate_synth)
synth$CourtEvent_HearingDate = hearingdate_synth
freq_apce_re = CalAPCEipwRE(synth, formula = "Y ~ Sex + White + Age + 
                            CurrentViolentOffense + PendingChargeAtTimeOfOffense + 
                            PriorMisdemeanorConviction + PriorFelonyConviction + 
                            PriorViolentConviction + (1|CourtEvent_HearingDate) + D")

Calculate APCE using parallel computing

Description

Calculate average principal causal effects (APCE) with ordinal decision using parallel computing. See Section 3.4 for more details.

Usage

CalAPCEparallel(
  data,
  mcmc.re,
  subgroup,
  name.group = c("overall", "Sex0", "Sex1", "Sex1 White0", "Sex1 White1"),
  rho = 0,
  burnin = 0,
  out.length = 500,
  c0 = 0,
  c1 = 0,
  ZX = NULL,
  save.individual.optimal.decision = FALSE,
  optimal.decision.only = FALSE,
  dmf = NULL,
  fair.dmf.only = FALSE,
  size = 5
)
CalAPCEparallel(
  data,
  mcmc.re,
  subgroup,
  name.group = c("overall", "Sex0", "Sex1", "Sex1 White0", "Sex1 White1"),
  rho = 0,
  burnin = 0,
  out.length = 500,
  c0 = 0,
  c1 = 0,
  ZX = NULL,
  save.individual.optimal.decision = FALSE,
  optimal.decision.only = FALSE,
  dmf = NULL,
  fair.dmf.only = FALSE,
  size = 5
)

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.
`subgroup`	A list of numeric vectors for the index of each of the five subgroups.
`name.group`	A list of character vectors for the label of five subgroups.
`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`.
`c0`	The cost of an outcome. See Section 3.7 for more details. The default is `0`.
`c1`	The cost of an unnecessarily harsh decision. See Section 3.7 for more details. The default is `0`.
`ZX`	The data matrix for interaction terms. The default is the interaction between Z and all of the pre-treatment covariates (X).
`save.individual.optimal.decision`	A logical argument specified to save individual optimal decision rules. The default is `FALSE`.
`optimal.decision.only`	A logical argument specified to compute only the optimal decision rule. The default is `FALSE`.
`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).
`fair.dmf.only`	A logical argument specified to compute only the fairness of given DMF recommendations. The default is `FALSE`. Not used in the analysis for the JRSSA paper.
`size`	The number of parallel computing. The default is `5`.

Value

An object of class list with the following elements:

`P.D1.mcmc`	An array with dimension n.mcmc by 5 by (k+1) by (k+2) for quantity P(D(1)=d\| R=r), dimension 1 is each posterior sample; dimension 2 is subgroup, dimension 3 is (k+1) values of D from 0 to k, dimension 4 is (k+2) values of R from 0 to k+1.
`P.D0.mcmc`	An array with dimension n.mcmc by 5 by (k+1) by (k+2) for quantity P(D(0)=d\| R=r).
`APCE.mcmc`	An array with dimension n.mcmc by 5 by (k+1) by (k+2) for quantity P(D(1)=d\| R=r)-P(D(0)=d\| R=r).
`P.R.mcmc`	An array with dimension n.mcmc by 5 by (k+2) for quantity P(R=r) for r from 0 to (k+1).
`Optimal.Z.mcmc`	An array with dimension n.mcmc by 5 for the proportion of the cases where treatment (PSA provided) is optimal.
`Optimal.D.mcmc`	An array with dimension n.mcmc by 5 by (k+1) for the proportion of optimal decision rule.
`P.DMF.mcmc`	An array with dimension n.mcmc by 5 by (k+1) by (k+2) for the proportion of binary DMF recommendations. Not used in the analysis for the JRSSA paper.
`Utility.g_d.mcmc`	Included if `save.individual.optimal.decision = TRUE`. An array with dimension n for the individual utility of judge's decisions.
`Utility.g_dmf.mcmc`	Included if `save.individual.optimal.decision = TRUE`. An array with dimension n for the individual utility of DMF recommendation.
`Utility.diff.control.mcmc`	Included if `save.individual.optimal.decision = TRUE`. An array with dimension n.mcmc for estimated difference in utility between judge's decisions and DMF recommendation among control group.
`Utility.diff.treated.mcmc`	Included if `save.individual.optimal.decision = TRUE`. An array with dimension n.mcmc for estimated difference in utility between judge's decisions and DMF recommendation among treated group.

Examples


data(synth)
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 10)
subgroup_synth = list(1:nrow(synth),which(synth$Sex==0),which(synth$Sex==1),
                      which(synth$Sex==1&synth$White==0),which(synth$Sex==1&synth$White==1))
sample_apce = CalAPCEparallel(data = synth, mcmc.re = sample_mcmc, 
                              subgroup = subgroup_synth, 
                              size = 1) # adjust the size


data(synth)
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 10)
subgroup_synth = list(1:nrow(synth),which(synth$Sex==0),which(synth$Sex==1),
                      which(synth$Sex==1&synth$White==0),which(synth$Sex==1&synth$White==1))
sample_apce = CalAPCEparallel(data = synth, mcmc.re = sample_mcmc, 
                              subgroup = subgroup_synth, 
                              size = 1) # adjust the size

Calculate the delta given the principal stratum

Description

Calculate the maximal deviation of decisions probability among the distributions for different groups (delta) given the principal stratum (R).

Usage

CalDelta(r, k, pd0, pd1, attr)
CalDelta(r, k, pd0, pd1, attr)

Arguments

`r`	The given principal stratum.
`k`	The maximum decision (e.g., largest bail amount).
`pd0`	P.D0.mcmc array generated from `CalAPCE` or `CalAPCEparallel`.
`pd1`	P.D1.mcmc array generated from `CalAPCE` or `CalAPCEparallel`.
`attr`	The index of subgroups (within the output of CalAPCE/CalAPCEparallel) that corresponds to the protected attributes.

Value

A data.frame of the delta.

Examples


data(synth)
subgroup_synth = list(1:nrow(synth), which(synth$Sex==0), which(synth$Sex==1), 
                      which(synth$Sex==1&synth$White==0), which(synth$Sex==1&synth$White==1))
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 10)
sample_apce = CalAPCE(data = synth, mcmc.re = sample_mcmc, subgroup = subgroup_synth, 
                      burnin = 0)
CalDelta(0, 3, sample_apce[["P.D0.mcmc"]], sample_apce[["P.D1.mcmc"]], c(2,3))


data(synth)
subgroup_synth = list(1:nrow(synth), which(synth$Sex==0), which(synth$Sex==1), 
                      which(synth$Sex==1&synth$White==0), which(synth$Sex==1&synth$White==1))
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 10)
sample_apce = CalAPCE(data = synth, mcmc.re = sample_mcmc, subgroup = subgroup_synth, 
                      burnin = 0)
CalDelta(0, 3, sample_apce[["P.D0.mcmc"]], sample_apce[["P.D1.mcmc"]], c(2,3))

Calculate diff-in-means estimates

Description

Calculate average causal effect based on diff-in-means estimator.

Usage

CalDIM(data)
CalDIM(data)

Arguments

data

A data.frame of which columns includes a binary treatment (Z), an ordinal decision (D), and an outcome variable (Y).

Value

A data.frame of diff-in-means estimates effect for each value of D and Y.

Examples

data(synth)
CalDIM(synth)

data(synth)
CalDIM(synth)

Calculate diff-in-means estimates

Description

Calculate average causal effect based on diff-in-means estimator.

Usage

CalDIMsubgroup(
  data,
  subgroup,
  name.group = c("Overall", "Female", "Male", "Non-white\nMale", "White\nMale")
)
CalDIMsubgroup(
  data,
  subgroup,
  name.group = c("Overall", "Female", "Male", "Non-white\nMale", "White\nMale")
)

Arguments

`data`	A `data.frame` of which columns includes a binary treatment (Z), an ordinal decision (D), and an outcome variable (Y).
`subgroup`	A list of numeric vectors for the index of each of the five subgroups.
`name.group`	A character vector including the labels of five subgroups.

Value

A data.frame of diff-in-means estimates for each value of D and Y for each subgroup.

Examples

data(synth)
subgroup_synth = list(1:nrow(synth),which(synth$Sex==0),which(synth$Sex==1),
                      which(synth$Sex==1&synth$White==0),which(synth$Sex==1&synth$White==1))
CalDIMsubgroup(synth, subgroup = subgroup_synth)

data(synth)
subgroup_synth = list(1:nrow(synth),which(synth$Sex==0),which(synth$Sex==1),
                      which(synth$Sex==1&synth$White==0),which(synth$Sex==1&synth$White==1))
CalDIMsubgroup(synth, subgroup = subgroup_synth)

Calculate the principal fairness

Description

See Section 3.6 for more details.

Usage

CalFairness(apce, attr = c(2, 3))
CalFairness(apce, attr = c(2, 3))

Arguments

`apce`	The list generated from `CalAPCE` or `CalAPCEparallel`.
`attr`	The index of subgroups (within the output of CalAPCE/CalAPCEparallel) that corresponds to the protected attributes.

Value

A data.frame of the delta.

Examples


data(synth)
subgroup_synth = list(1:nrow(synth), which(synth$Sex==0), which(synth$Sex==1), 
                      which(synth$Sex==1&synth$White==0), which(synth$Sex==1&synth$White==1))
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 10)
sample_apce = CalAPCE(data = synth, mcmc.re = sample_mcmc, subgroup = subgroup_synth, 
                      burnin = 0)
CalFairness(sample_apce)


data(synth)
subgroup_synth = list(1:nrow(synth), which(synth$Sex==0), which(synth$Sex==1), 
                      which(synth$Sex==1&synth$White==0), which(synth$Sex==1&synth$White==1))
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 10)
sample_apce = CalAPCE(data = synth, mcmc.re = sample_mcmc, subgroup = subgroup_synth, 
                      burnin = 0)
CalFairness(sample_apce)

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
)
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


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

Calculate the proportion of principal strata (R)

Description

Calculate the proportion of each principal stratum (R).

Usage

CalPS(
  p.r.mcmc,
  name.group = c("Overall", "Female", "Male", "Non-white\nMale", "White\nMale")
)
CalPS(
  p.r.mcmc,
  name.group = c("Overall", "Female", "Male", "Non-white\nMale", "White\nMale")
)

Arguments

`p.r.mcmc`	P.R.mcmc array generated from `CalAPCE` or `CalAPCEparallel`.
`name.group`	A character vector including the labels of five subgroups.

Value

A data.frame of the proportion of each principal stratum.

Examples


data(synth)
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 10)
subgroup_synth = list(1:nrow(synth),which(synth$Sex==0),which(synth$Sex==1),
                      which(synth$Sex==1&synth$White==0),which(synth$Sex==1&synth$White==1))
sample_apce = CalAPCE(data = synth, mcmc.re = sample_mcmc, 
                      subgroup = subgroup_synth)
CalPS(sample_apce[["P.R.mcmc"]])


data(synth)
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 10)
subgroup_synth = list(1:nrow(synth),which(synth$Sex==0),which(synth$Sex==1),
                      which(synth$Sex==1&synth$White==0),which(synth$Sex==1&synth$White==1))
sample_apce = CalAPCE(data = synth, mcmc.re = sample_mcmc, 
                      subgroup = subgroup_synth)
CalPS(sample_apce[["P.R.mcmc"]])

Interim Dane data with failure to appear (FTA) as an outcome

Description

An interim dataset containing pre-treatment covariates, a binary treatment (Z), an ordinal decision (D), and an outcome variable (Y). The data used for the paper, and made available here, are interim, based on only half of the observations in the study and (for those observations) only half of the study follow-up period. We use them only to illustrate methods, not to draw substantive conclusions.

Usage

FTAdata
FTAdata

Format

A data frame with 1891 rows and 19 variables:

Z: binary treatment
D: ordinal decision
Y: outcome
Sex: male or female
White: white or non-white
SexWhite: the interaction between gender and race
Age: age
PendingChargeAtTimeOfOffense: binary variable for pending charge (felony, misdemeanor, or both) at the time of offense
NCorNonViolentMisdemeanorCharge: binary variable for current non-violent felony charge
ViolentMisdemeanorCharge: binary variable for current violent misdemeanor charge
ViolentFelonyCharge: binary variable for current violent felony charge
NonViolentFelonyCharge: binary variable for current non-violent felony charge
PriorMisdemeanorConviction: binary variable for prior conviction of misdemeanor
PriorFelonyConviction: binary variable for prior conviction of felony
PriorViolentConviction: four-level ordinal variable for prior violent conviction
PriorSentenceToIncarceration: binary variable for prior sentence to incarceration
PriorFTAInPastTwoYears: three-level ordinal variable for FTAs from past two years
PriorFTAOlderThanTwoYears: binary variable for FTAs from over two years ago
Staff_ReleaseRecommendation: four-level ordinal variable for the DMF recommendation

Pulling ggplot legend

Description

Pulling ggplot legend

Usage

g_legend(p)
g_legend(p)

Arguments

`p`	A `ggplot` of which legend should be pulled.

Value

A ggplot legend.

Interim court event hearing date

Description

An Interim Dane court event hearing date of Dane data in factor format. The data used for the paper, and made available here, are interim, based on only half of the observations in the study and (for those observations) only half of the study follow-up period. We use them only to illustrate methods, not to draw substantive conclusions.

Usage

HearingDate
HearingDate

Format

A date variable in factor format.

Synthetic court event hearing date

Description

A synthetic court event hearing date

Usage

hearingdate_synth
hearingdate_synth

Format

A date variable.

Interim Dane data with new criminal activity (NCA) as an outcome

Description

Usage

NCAdata
NCAdata

Format

A data frame with 1891 rows and 19 variables:

Z: binary treatment
D: ordinal decision
Y: outcome
Sex: male or female
White: white or non-white
SexWhite: the interaction between gender and race
Age: age
PendingChargeAtTimeOfOffense: binary variable for pending charge (felony, misdemeanor, or both) at the time of offense
NCorNonViolentMisdemeanorCharge: binary variable for current non-violent felony charge
ViolentMisdemeanorCharge: binary variable for current violent misdemeanor charge
ViolentFelonyCharge: binary variable for current violent felony charge
NonViolentFelonyCharge: binary variable for current non-violent felony charge
PriorMisdemeanorConviction: binary variable for prior conviction of misdemeanor
PriorFelonyConviction: binary variable for prior conviction of felony
PriorViolentConviction: four-level ordinal variable for prior violent conviction
PriorSentenceToIncarceration: binary variable for prior sentence to incarceration
PriorFTAInPastTwoYears: three-level ordinal variable for FTAs from past two years
PriorFTAOlderThanTwoYears: binary variable for FTAs from over two years ago
Staff_ReleaseRecommendation: four-level ordinal variable for the DMF recommendation

Interim Dane data with new violent criminal activity (NVCA) as an outcome

Description

Usage

NVCAdata
NVCAdata

Format

A data frame with 1891 rows and 19 variables:

Z: binary treatment
D: ordinal decision
Y: outcome
Sex: male or female
White: white or non-white
SexWhite: the interaction between gender and race
Age: age
PendingChargeAtTimeOfOffense: binary variable for pending charge (felony, misdemeanor, or both) at the time of offense
NCorNonViolentMisdemeanorCharge: binary variable for current non-violent felony charge
ViolentMisdemeanorCharge: binary variable for current violent misdemeanor charge
ViolentFelonyCharge: binary variable for current violent felony charge
NonViolentFelonyCharge: binary variable for current non-violent felony charge
PriorMisdemeanorConviction: binary variable for prior conviction of misdemeanor
PriorFelonyConviction: binary variable for prior conviction of felony
PriorViolentConviction: four-level ordinal variable for prior violent conviction
PriorSentenceToIncarceration: binary variable for prior sentence to incarceration
PriorFTAInPastTwoYears: three-level ordinal variable for FTAs from past two years
PriorFTAOlderThanTwoYears: binary variable for FTAs from over two years ago
Staff_ReleaseRecommendation: four-level ordinal variable for the DMF recommendation

Plot APCE

Description

See Figure 4 for example.

Usage

PlotAPCE(
  res,
  y.max = 0.1,
  decision.labels = c("signature bond", "small cash bond", "large cash bond"),
  shape.values = c(16, 17, 15),
  col.values = c("blue", "black", "red", "brown"),
  label = TRUE,
  r.labels = c("safe", "easily\npreventable", "prevent-\nable", "risky\n"),
  label.position = c("top", "top", "top", "top"),
  top.margin = 0.01,
  bottom.margin = 0.01,
  name.group = c("Overall", "Female", "Male", "Non-white\nMale", "White\nMale"),
  label.size = 4
)
PlotAPCE(
  res,
  y.max = 0.1,
  decision.labels = c("signature bond", "small cash bond", "large cash bond"),
  shape.values = c(16, 17, 15),
  col.values = c("blue", "black", "red", "brown"),
  label = TRUE,
  r.labels = c("safe", "easily\npreventable", "prevent-\nable", "risky\n"),
  label.position = c("top", "top", "top", "top"),
  top.margin = 0.01,
  bottom.margin = 0.01,
  name.group = c("Overall", "Female", "Male", "Non-white\nMale", "White\nMale"),
  label.size = 4
)

Arguments

`res`	A `data.frame` generated with `APCEsummary()`.
`y.max`	Maximum value of y-axis.
`decision.labels`	Labels of decisions (D).
`shape.values`	Shape of point for each decisions.
`col.values`	Color of point for each principal stratum.
`label`	A logical argument whether to specify label of each principal stratum. The default is `TRUE`.
`r.labels`	Label of each principal stratum.
`label.position`	The position of labels.
`top.margin`	Top margin of labels.
`bottom.margin`	Bottom margin of labels.
`name.group`	A character vector including the labels of five subgroups.
`label.size`	Size of label.

Value

A ggplot.

Examples


data(synth)
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 10)
subgroup_synth = list(1:nrow(synth),which(synth$Sex==0),which(synth$Sex==1),
                      which(synth$Sex==1&synth$White==0),which(synth$Sex==1&synth$White==1))
sample_apce = CalAPCE(data = synth, mcmc.re = sample_mcmc, 
                      subgroup = subgroup_synth)
sample_apce_summary = APCEsummary(sample_apce[["APCE.mcmc"]])
PlotAPCE(sample_apce_summary, y.max = 0.25, decision.labels = c("signature","small cash",
         "middle cash","large cash"), shape.values = c(16, 17, 15, 18), 
         col.values = c("blue", "black", "red", "brown", "purple"), label = FALSE)


data(synth)
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 10)
subgroup_synth = list(1:nrow(synth),which(synth$Sex==0),which(synth$Sex==1),
                      which(synth$Sex==1&synth$White==0),which(synth$Sex==1&synth$White==1))
sample_apce = CalAPCE(data = synth, mcmc.re = sample_mcmc, 
                      subgroup = subgroup_synth)
sample_apce_summary = APCEsummary(sample_apce[["APCE.mcmc"]])
PlotAPCE(sample_apce_summary, y.max = 0.25, decision.labels = c("signature","small cash",
         "middle cash","large cash"), shape.values = c(16, 17, 15, 18), 
         col.values = c("blue", "black", "red", "brown", "purple"), label = FALSE)

Plot diff-in-means estimates

Description

See Figure 2 for example.

Usage

PlotDIMdecisions(
  res,
  y.max = 0.2,
  decision.labels = c("signature bond   ", "small cash bond   ", "large cash bond"),
  col.values = c("grey60", "grey30", "grey6"),
  shape.values = c(16, 17, 15)
)
PlotDIMdecisions(
  res,
  y.max = 0.2,
  decision.labels = c("signature bond   ", "small cash bond   ", "large cash bond"),
  col.values = c("grey60", "grey30", "grey6"),
  shape.values = c(16, 17, 15)
)

Arguments

`res`	A `data.frame` generated with `CalDIMsubgroup`.
`y.max`	Maximum value of y-axis.
`decision.labels`	Labels of decisions (D).
`col.values`	Color of point for each decisions.
`shape.values`	Shape of point for each decisions.

Value

A ggplot.

Examples

data(synth)
subgroup_synth = list(1:nrow(synth),which(synth$Sex==0),which(synth$Sex==1),
                      which(synth$Sex==1&synth$White==0),which(synth$Sex==1&synth$White==1))
res_dec = CalDIMsubgroup(synth, subgroup = subgroup_synth)
PlotDIMdecisions(res_dec, decision.labels = c("signature","small cash","middle cash","large cash"),
                 col.values = c("grey60", "grey30", "grey6", "grey1"), 
                 shape.values = c(16, 17, 15, 18))

data(synth)
subgroup_synth = list(1:nrow(synth),which(synth$Sex==0),which(synth$Sex==1),
                      which(synth$Sex==1&synth$White==0),which(synth$Sex==1&synth$White==1))
res_dec = CalDIMsubgroup(synth, subgroup = subgroup_synth)
PlotDIMdecisions(res_dec, decision.labels = c("signature","small cash","middle cash","large cash"),
                 col.values = c("grey60", "grey30", "grey6", "grey1"), 
                 shape.values = c(16, 17, 15, 18))

Plot diff-in-means estimates

Description

See Figure 2 for example.

Usage

PlotDIMoutcomes(
  res.fta,
  res.nca,
  res.nvca,
  label.position = c("top", "top", "top"),
  top.margin = 0.01,
  bottom.margin = 0.01,
  y.max = 0.2,
  label.size = 7,
  name.group = c("Overall", "Female", "Male", "Non-white\nMale", "White\nMale")
)
PlotDIMoutcomes(
  res.fta,
  res.nca,
  res.nvca,
  label.position = c("top", "top", "top"),
  top.margin = 0.01,
  bottom.margin = 0.01,
  y.max = 0.2,
  label.size = 7,
  name.group = c("Overall", "Female", "Male", "Non-white\nMale", "White\nMale")
)

Arguments

`res.fta`	A `data.frame` generated with `CalDIMsubgroup` with Y = FTA.
`res.nca`	A `data.frame` generated with `CalDIMsubgroup` with Y = NCA.
`res.nvca`	A `data.frame` generated with `CalDIMsubgroup` with Y = NVCA.
`label.position`	The position of labels.
`top.margin`	Top margin of labels.
`bottom.margin`	Bottom margin of labels.
`y.max`	Maximum value of y-axis.
`label.size`	Size of label.
`name.group`	A character vector including the labels of five subgroups.

Value

A ggplot.

Examples

data(synth)
subgroup_synth = list(1:nrow(synth),which(synth$Sex==0),which(synth$Sex==1),
                      which(synth$Sex==1&synth$White==0),which(synth$Sex==1&synth$White==1))
synth_fta <- synth_nca <- synth_nvca <- synth
set.seed(123)
synth_fta$Y <- sample(0:1, 1000, replace = TRUE)
synth_nca$Y <- sample(0:1, 1000, replace = TRUE)
synth_nvca$Y <- sample(0:1, 1000, replace = TRUE)
res_fta = CalDIMsubgroup(synth_fta, subgroup = subgroup_synth)
res_nca = CalDIMsubgroup(synth_nca, subgroup = subgroup_synth)
res_nvca = CalDIMsubgroup(synth_nvca, subgroup = subgroup_synth)
PlotDIMoutcomes(res_fta, res_nca, res_nvca)

data(synth)
subgroup_synth = list(1:nrow(synth),which(synth$Sex==0),which(synth$Sex==1),
                      which(synth$Sex==1&synth$White==0),which(synth$Sex==1&synth$White==1))
synth_fta <- synth_nca <- synth_nvca <- synth
set.seed(123)
synth_fta$Y <- sample(0:1, 1000, replace = TRUE)
synth_nca$Y <- sample(0:1, 1000, replace = TRUE)
synth_nvca$Y <- sample(0:1, 1000, replace = TRUE)
res_fta = CalDIMsubgroup(synth_fta, subgroup = subgroup_synth)
res_nca = CalDIMsubgroup(synth_nca, subgroup = subgroup_synth)
res_nvca = CalDIMsubgroup(synth_nvca, subgroup = subgroup_synth)
PlotDIMoutcomes(res_fta, res_nca, res_nvca)

Plot the principal fairness

Description

See Figure 5 for example.

Usage

PlotFairness(
  res,
  top.margin = 0.01,
  y.max = 0.2,
  y.min = -0.1,
  r.labels = c("Safe", "Easily\nPreventable", "Preventable", "Risky"),
  label = TRUE
)
PlotFairness(
  res,
  top.margin = 0.01,
  y.max = 0.2,
  y.min = -0.1,
  r.labels = c("Safe", "Easily\nPreventable", "Preventable", "Risky"),
  label = TRUE
)

Arguments

`res`	The data frame generated from `CalFairness`.
`top.margin`	The index of subgroups (within the output of CalAPCE/CalAPCEparallel) that corresponds to the protected attributes.
`y.max`	Maximum value of y-axis.
`y.min`	Minimum value of y-axis.
`r.labels`	Label of each principal stratum.
`label`	A logical argument whether to specify label.

Value

A data.frame of the delta.

Examples


data(synth)
subgroup_synth = list(1:nrow(synth), which(synth$Sex==0), which(synth$Sex==1), 
                      which(synth$Sex==1&synth$White==0), which(synth$Sex==1&synth$White==1))
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 10)
sample_apce = CalAPCE(data = synth, mcmc.re = sample_mcmc, subgroup = subgroup_synth, 
                      burnin = 0)
sample_fair = CalFairness(sample_apce)
PlotFairness(sample_fair, y.max = 0.4, y.min = -0.4, r.labels = c("Safe", "Preventable 1", 
             "Preventable 2", "Preventable 3", "Risky"))


data(synth)
subgroup_synth = list(1:nrow(synth), which(synth$Sex==0), which(synth$Sex==1), 
                      which(synth$Sex==1&synth$White==0), which(synth$Sex==1&synth$White==1))
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 10)
sample_apce = CalAPCE(data = synth, mcmc.re = sample_mcmc, subgroup = subgroup_synth, 
                      burnin = 0)
sample_fair = CalFairness(sample_apce)
PlotFairness(sample_fair, y.max = 0.4, y.min = -0.4, r.labels = c("Safe", "Preventable 1", 
             "Preventable 2", "Preventable 3", "Risky"))

Plot optimal decision

Description

See Figure 6 for example.

Usage

PlotOptimalDecision(res, colname.d, idx = NULL)
PlotOptimalDecision(res, colname.d, idx = NULL)

Arguments

`res`	The data frame generated from `CalOptimalDecision`.
`colname.d`	The column name of decision to be plotted.
`idx`	The row index of observations to be included. The default is all the observations from the data.

Value

A ggplot.

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
sample_optd$cash = sample_optd$d1 + sample_optd$d2 + sample_optd$d3
PlotOptimalDecision(sample_optd, "cash")


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
sample_optd$cash = sample_optd$d1 + sample_optd$d2 + sample_optd$d3
PlotOptimalDecision(sample_optd, "cash")

Plot the proportion of principal strata (R)

Description

See Figure 3 for example.

Usage

PlotPS(
  res,
  y.min = 0,
  y.max = 0.75,
  col.values = c("blue", "black", "red", "brown"),
  label = TRUE,
  r.labels = c("safe", " easily             \n preventable    ",
    "\n          preventable\n", "  risky"),
  label.position = c("top", "top", "top", "bottom"),
  top.margin = 0.02,
  bottom.margin = 0.02,
  label.size = 6.5
)
PlotPS(
  res,
  y.min = 0,
  y.max = 0.75,
  col.values = c("blue", "black", "red", "brown"),
  label = TRUE,
  r.labels = c("safe", " easily             \n preventable    ",
    "\n          preventable\n", "  risky"),
  label.position = c("top", "top", "top", "bottom"),
  top.margin = 0.02,
  bottom.margin = 0.02,
  label.size = 6.5
)

Arguments

`res`	A `data.frame` generated with `CalPS`.
`y.min`	Minimum value of y-axis.
`y.max`	Maximum value of y-axis.
`col.values`	Color of point for each principal stratum.
`label`	A logical argument whether to specify label of each principal stratum. The default is `TRUE`.
`r.labels`	Label of each principal stratum.
`label.position`	The position of labels.
`top.margin`	Top margin of labels.
`bottom.margin`	Bottom margin of labels.
`label.size`	Size of label.

Value

A ggplot.

Examples


data(synth)
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 10)
subgroup_synth = list(1:nrow(synth),which(synth$Sex==0),which(synth$Sex==1),
                      which(synth$Sex==1&synth$White==0),which(synth$Sex==1&synth$White==1))
sample_apce = CalAPCE(data = synth, mcmc.re = sample_mcmc, 
                      subgroup = subgroup_synth)
sample_ps = CalPS(sample_apce[["P.R.mcmc"]])
PlotPS(sample_ps, col.values = c("blue", "black", "red", "brown", "purple"), label = FALSE)


data(synth)
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 10)
subgroup_synth = list(1:nrow(synth),which(synth$Sex==0),which(synth$Sex==1),
                      which(synth$Sex==1&synth$White==0),which(synth$Sex==1&synth$White==1))
sample_apce = CalAPCE(data = synth, mcmc.re = sample_mcmc, 
                      subgroup = subgroup_synth)
sample_ps = CalPS(sample_apce[["P.R.mcmc"]])
PlotPS(sample_ps, col.values = c("blue", "black", "red", "brown", "purple"), label = FALSE)

Plot conditional randomization test

Description

See Figure S8 for example.

Usage

PlotSpilloverCRT(res)
PlotSpilloverCRT(res)

Arguments

res

A list generated with SpilloverCRT.

Value

A ggplot

Examples


data(synth)
data(hearingdate_synth)
crt <- SpilloverCRT(D = synth$D, Z = synth$Z, CourtEvent_HearingDate = hearingdate_synth)
PlotSpilloverCRT(crt)


data(synth)
data(hearingdate_synth)
crt <- SpilloverCRT(D = synth$D, Z = synth$Z, CourtEvent_HearingDate = hearingdate_synth)
PlotSpilloverCRT(crt)

Plot power analysis of conditional randomization test

Description

See Figure S9 for example.

Usage

PlotSpilloverCRTpower(res)
PlotSpilloverCRTpower(res)

Arguments

res

A data.frame generated with SpilloverCRTpower.

Value

A ggplot

Examples


data(synth)
data(hearingdate_synth)
crt_power <- SpilloverCRTpower(D = synth$D, Z = synth$Z, 
                               CourtEvent_HearingDate = hearingdate_synth,
                               size = 1) # adjust the size
PlotSpilloverCRTpower(crt_power)


data(synth)
data(hearingdate_synth)
crt_power <- SpilloverCRTpower(D = synth$D, Z = synth$Z, 
                               CourtEvent_HearingDate = hearingdate_synth,
                               size = 1) # adjust the size
PlotSpilloverCRTpower(crt_power)

Stacked barplot for the distribution of the decision given psa

Description

See Figure 1 for example.

Usage

PlotStackedBar(
  data,
  fta.label = "FTAScore",
  nca.label = "NCAScore",
  nvca.label = "NVCAFlag",
  d.colors = c("grey60", "grey30", "grey10"),
  d.labels = c("signature bond", "small cash bond", "large cash bond"),
  legend.position = "none"
)
PlotStackedBar(
  data,
  fta.label = "FTAScore",
  nca.label = "NCAScore",
  nvca.label = "NVCAFlag",
  d.colors = c("grey60", "grey30", "grey10"),
  d.labels = c("signature bond", "small cash bond", "large cash bond"),
  legend.position = "none"
)

Arguments

`data`	A `data.frame` of which columns includes an ordinal decision (D), and psa variables (fta, nca, and nvca).
`fta.label`	Column name of fta score in the data. The default is `"FTAScore"`.
`nca.label`	Column name of nca score in the data. The default is `"NCAScore"`.
`nvca.label`	Column name of nvca score in the data. The default is `"NVCAFlag"`.
`d.colors`	The color of each decision.
`d.labels`	The label of each decision.
`legend.position`	The position of legend. The default is `"none"`.

Value

A list of three ggplots.

Examples

data(psa_synth)
# Control group (PSA not provided)
PlotStackedBar(psa_synth[psa_synth$Z == 0, ], d.colors = c("grey80", "grey60", 
               "grey30", "grey10"), d.labels = c("signature","small",
               "middle","large"))
# Treated group (PSA provided)
PlotStackedBar(psa_synth[psa_synth$Z == 0, ], d.colors = c("grey80", "grey60", 
               "grey30", "grey10"), d.labels = c("signature","small",
               "middle","large"))

data(psa_synth)
# Control group (PSA not provided)
PlotStackedBar(psa_synth[psa_synth$Z == 0, ], d.colors = c("grey80", "grey60", 
               "grey30", "grey10"), d.labels = c("signature","small",
               "middle","large"))
# Treated group (PSA provided)
PlotStackedBar(psa_synth[psa_synth$Z == 0, ], d.colors = c("grey80", "grey60", 
               "grey30", "grey10"), d.labels = c("signature","small",
               "middle","large"))

Stacked barplot for the distribution of the decision given DMF recommendation

Description

See Figure 1 for example.

Usage

PlotStackedBarDMF(
  data,
  dmf.label = "dmf",
  dmf.category = NULL,
  d.colors = c("grey60", "grey30", "grey10"),
  d.labels = c("signature bond", "small cash bond", "large cash bond"),
  legend.position = "none"
)
PlotStackedBarDMF(
  data,
  dmf.label = "dmf",
  dmf.category = NULL,
  d.colors = c("grey60", "grey30", "grey10"),
  d.labels = c("signature bond", "small cash bond", "large cash bond"),
  legend.position = "none"
)

Arguments

`data`	A `data.frame` of which columns includes a binary treatment (Z; PSA provision), an ordinal decision (D), and DMF recommendation.
`dmf.label`	Column name of DMF recommendation in the data. The default is `"dmf"`.
`dmf.category`	The name of each category of DMF recommendation.
`d.colors`	The color of each decision.
`d.labels`	The label of each decision.
`legend.position`	The position of legend. The default is `"none"`.

Value

A list of three ggplots.

Examples

data(psa_synth)
PlotStackedBarDMF(psa_synth, dmf.label = "DMF", d.colors = c("grey80", 
                  "grey60", "grey30", "grey10"), d.labels = c("signature",
                  "small","middle","large"))

data(psa_synth)
PlotStackedBarDMF(psa_synth, dmf.label = "DMF", d.colors = c("grey80", 
                  "grey60", "grey30", "grey10"), d.labels = c("signature",
                  "small","middle","large"))

Plot utility difference

Description

See Figure 7 for example.

Usage

PlotUtilityDiff(res, idx = NULL)
PlotUtilityDiff(res, idx = NULL)

Arguments

`res`	The data frame generated from `CalUtilityDiff`.
`idx`	The row index of observations to be included. The default is all the observations from the data.

Value

A ggplot.

Examples


data(synth)
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 10)
synth_dmf = sample(0:1, nrow(synth), replace = TRUE) # random dmf recommendation
sample_utility = CalOptimalDecision(data = synth, mcmc.re = sample_mcmc, 
                                    c0.ls = seq(0,5,1), c1.ls = seq(0,5,1), 
                                    dmf = synth_dmf, size = 1) # adjust the size
PlotUtilityDiff(sample_utility)


data(synth)
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 10)
synth_dmf = sample(0:1, nrow(synth), replace = TRUE) # random dmf recommendation
sample_utility = CalOptimalDecision(data = synth, mcmc.re = sample_mcmc, 
                                    c0.ls = seq(0,5,1), c1.ls = seq(0,5,1), 
                                    dmf = synth_dmf, size = 1) # adjust the size
PlotUtilityDiff(sample_utility)

Plot utility difference with 95% confidence interval

Description

See Figure S17 for example.

Usage

PlotUtilityDiffCI(res)
PlotUtilityDiffCI(res)

Arguments

res

The second data frame (res.mcmc) generated from CalUtilityDiff(include.utility.diff.mcmc = TRUE).

Value

A ggplot.

Examples


data(synth)
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 10)
synth_dmf = sample(0:1, nrow(synth), replace = TRUE) # random dmf recommendation
sample_utility = CalOptimalDecision(data = synth, mcmc.re = sample_mcmc, 
                                    c0.ls = seq(0,5,1), c1.ls = seq(0,5,1), 
                                    dmf = synth_dmf, size = 1, # adjust the size
                                    include.utility.diff.mcmc = TRUE)
PlotUtilityDiffCI(sample_utility$res.mcmc)


data(synth)
sample_mcmc = AiEvalmcmc(data = synth, n.mcmc = 10)
synth_dmf = sample(0:1, nrow(synth), replace = TRUE) # random dmf recommendation
sample_utility = CalOptimalDecision(data = synth, mcmc.re = sample_mcmc, 
                                    c0.ls = seq(0,5,1), c1.ls = seq(0,5,1), 
                                    dmf = synth_dmf, size = 1, # adjust the size
                                    include.utility.diff.mcmc = TRUE)
PlotUtilityDiffCI(sample_utility$res.mcmc)

Synthetic PSA data

Description

A synthetic dataset containing a binary treatment (Z), ordinal decision (D), three PSA variables (FTAScore, NCAScore, and NVCAFlag), and DMF recommendation.

Usage

psa_synth
psa_synth

Format

A data frame with 1000 rows and 4 variables:

Z: binary treatment
D: ordinal decision
FTAScore: FTA score
NCAScore: NCA score
NVCAFlag: NVCA flag
DMF: DMF recommendation

Interim Dane PSA data

Description

An interim dataset containing a binary treatment (Z), ordinal decision (D), three PSA variables (FTAScore, NCAScore, and NVCAFlag), DMF recommendation, and two pre-treatment covariates (binary indicator for gender; binary indicator for race). The data used for the paper, and made available here, are interim, based on only half of the observations in the study and (for those observations) only half of the study follow-up period. We use them only to illustrate methods, not to draw substantive conclusions.

Usage

PSAdata
PSAdata

Format

A data frame with 1891 rows and 7 variables:

Z: binary treatment
D: ordinal decision
FTAScore: FTA score
NCAScore: NCA score
NVCAFlag: NVCA flag
DMF: DMF recommendation
Sex: male or female
White: white or non-white

Conduct conditional randomization test

Description

See S3.1 for more details.

Usage

SpilloverCRT(D, Z, CourtEvent_HearingDate, n = 100, seed.number = 12345)
SpilloverCRT(D, Z, CourtEvent_HearingDate, n = 100, seed.number = 12345)

Arguments

`D`	A numeric vector of judge's decision.
`Z`	A numeric vector of treatment variable.
`CourtEvent_HearingDate`	The court event hearing date.
`n`	Number of permutations.
`seed.number`	An integer for random number generator.

Value

A list of the observed and permuted test statistics and its p-value.

Examples


data(synth)
data(hearingdate_synth)
crt <- SpilloverCRT(D = synth$D, Z = synth$Z, CourtEvent_HearingDate = hearingdate_synth)


data(synth)
data(hearingdate_synth)
crt <- SpilloverCRT(D = synth$D, Z = synth$Z, CourtEvent_HearingDate = hearingdate_synth)

Conduct power analysis of conditional randomization test

Description

See S3.2 for more details.

Usage

SpilloverCRTpower(
  D,
  Z,
  CourtEvent_HearingDate,
  n = 4,
  m = 4,
  size = 2,
  cand_omegaZtilde = seq(-1.5, 1.5, by = 0.5)
)
SpilloverCRTpower(
  D,
  Z,
  CourtEvent_HearingDate,
  n = 4,
  m = 4,
  size = 2,
  cand_omegaZtilde = seq(-1.5, 1.5, by = 0.5)
)

Arguments

`D`	A numeric vector of judge's decision.
`Z`	A numeric vector of treatment variable.
`CourtEvent_HearingDate`	The court event hearing date.
`n`	Number of permutations.
`m`	Number of permutations.
`size`	The number of parallel computing. The default is `2`.
`cand_omegaZtilde`	Candidate values

Value

A data.frame of the result of power analysis.

Examples


data(synth)
data(hearingdate_synth)
crt_power <- SpilloverCRTpower(D = synth$D, Z = synth$Z, 
                               CourtEvent_HearingDate = hearingdate_synth,
                               size = 1) # adjust the size


data(synth)
data(hearingdate_synth)
crt_power <- SpilloverCRTpower(D = synth$D, Z = synth$Z, 
                               CourtEvent_HearingDate = hearingdate_synth,
                               size = 1) # adjust the size

Synthetic data

Description

A synthetic dataset containing pre-treatment covariates, a binary treatment (Z), an ordinal decision (D), and an outcome variable (Y).

Usage

synth
synth

Format

A data frame with 1000 rows and 11 variables:

Z: binary treatment
D: ordinal decision
Y: outcome
Sex: male or female
White: white or non-white
Age: age
CurrentViolentOffense: binary variable for current violent offense
PendingChargeAtTimeOfOffense: binary variable for pending charge (felony, misdemeanor, or both) at the time of offense
PriorMisdemeanorConviction: binary variable for prior conviction of misdemeanor
PriorFelonyConviction: binary variable for prior conviction of felony
PriorViolentConviction: four-level ordinal variable for prior violent conviction

Test monotonicity

Description

Test monotonicity using frequentist analysis

Usage

TestMonotonicity(data)
TestMonotonicity(data)

Arguments

data

Value

Message indicating whether the monotonicity assumption holds.

Examples

data(synth)
TestMonotonicity(synth)

data(synth)
TestMonotonicity(synth)

Test monotonicity with random effects

Description

Test monotonicity using frequentist analysis with random effects for the hearing date of the case.

Usage

TestMonotonicityRE(data, formula)
TestMonotonicityRE(data, formula)

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.
`formula`	A formula of the model to fit.

Value

Message indicating whether the monotonicity assumption holds.

Examples

data(synth)
data(hearingdate_synth)
synth$CourtEvent_HearingDate = hearingdate_synth
TestMonotonicityRE(synth, formula = "Y ~ Sex + White + Age + 
                   CurrentViolentOffense + PendingChargeAtTimeOfOffense + 
                   PriorMisdemeanorConviction + PriorFelonyConviction + 
                   PriorViolentConviction + (1|CourtEvent_HearingDate) + D")

data(synth)
data(hearingdate_synth)
synth$CourtEvent_HearingDate = hearingdate_synth
TestMonotonicityRE(synth, formula = "Y ~ Sex + White + Age + 
                   CurrentViolentOffense + PendingChargeAtTimeOfOffense + 
                   PriorMisdemeanorConviction + PriorFelonyConviction + 
                   PriorViolentConviction + (1|CourtEvent_HearingDate) + D")

Package 'aihuman'

Help Index

Experimental Evaluation of Algorithm-Assisted Human Decision-Making

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Package Content

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Gibbs sampler for the main analysis

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Summary of APCE

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Summary of APCE for frequentist analysis

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Bootstrap for estimating variance of APCE

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Bootstrap for estimating variance of APCE with random effects

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Bootstrap for estimating variance of APCE with random effects

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Calculate APCE

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Compute APCE using frequentist analysis

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Compute APCE using frequentist analysis with random effects

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Calculate APCE using parallel computing

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Calculate the delta given the principal stratum

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Calculate diff-in-means estimates

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Calculate diff-in-means estimates