results.Rmd

---
title: "The Limits of Human Predictions of Recidivism"
author:
- Zhiyuan "Jerry" Lin, Jongbin Jung, Sharad Goel, Jennifer Skeem
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, warning = FALSE, fig.align="center")
setwd("src")
library(tidyverse)
library(kableExtra)
source("consts.R")
theme_set(theme_bw())
```

This is an R Markdown recreating the plots and tables in the paper.

```{r read}
paper_results <- read_rds(PAPER_RESULTS_RDS)
```


## Dataset Summary
```{r, echo=FALSE, fig.width = 8, fig.height = 3}
paper_results$t$data_summary_table %>% 
  mutate(baserate = paste0(round(100 * baserate), "%")) %>% 
  kable() %>%
  kable_styling()
```

__Table 1__: 
Characteristics of the four datasets we considered (Note: "BR"" is "base rate").

<br/><br/>

## Figures
```{r, echo=FALSE, fig.width = 8, fig.height = 3}
paper_results$p$p_acc_perf
```

__Figure 2__: Classification accuracy of: 
(1) human predictions,
with and without immediate feedback;
(2) a logistic regression model
that we trained using the same information provided to study participants;
and (3) the existing tools, COMPAS or LSI-R.
For participants in the feedback condition,
only the last 10 responses for each participant were used,
to account for the effects of learning.
Error bars represent 95% confidence intervals,
and are typically smaller than the height of the red square for the logistic regression models.
    

<br/><br/><br/><br/>
```{r, echo=FALSE, fig.width = 5.5, fig.height = 3}
paper_results$p$p_short_v_long
```

__Figure 3__: Ranking accuracy (AUC) of: 
(1) human predictions without feedback;
(2) logistic regression models that use the same information provided to study participants;
and (3) the existing LSI-R tools.
Error bars indicate 95% confidence intervals.

<br/><br/><br/><br/>
```{r, echo=FALSE, fig.width = 8, fig.height = 5}
paper_results$p$p_recall
```

__Figure 4__: Proportion of people who recidivated that were identified when ranking by the
risk assessments of humans in the no-feedback condition, a logistic regression model,
and existing tools (COMPAS or LSI-R).
For each value $p$ on the horizontal axis,
the vertical axis shows the proportion of all recidivists
that are included among the $p$-percent of the population deemed riskiest.
Human performance was generally comparable to algorithmic tools in the ”streamlined“ condition
(top panels), but algorithmic tools outperformed humans when more information was made
available (”enriched“ condition, in the bottom panels).


<br/><br/><br/><br/>
```{r, echo=FALSE, fig.width = 8, fig.height = 3}
paper_results$p$p_auc_perf
```

__Figure A1__:
Ranking performance (AUC) of:
(1) human predictions without feedback;
(2) logistic regression models
that use the same information provided to study participants;
and (3) the existing tools, COMPAS or LSI-R.
Error bars indicate 95% confidence intervals.

<br/><br/><br/><br/>
```{r, echo=FALSE, fig.width = 5, fig.height = 3}
paper_results$p$p_t_dist
```

__Figure A2__:
Distribution of the $t$-statistic for the difference in accuracy between humans
and existing tools (COMPAS or LSI-R) across all 645 participants.
The vertical dashed line is at $t=2$.
None of the participants outperformed the 
existing tools by a statistically significant margin.


<br/><br/><br/><br/>
```{r, echo=FALSE, fig.width = 10, fig.height = 4}
paper_results$p$p_acc_overtime
```

__Figure A3__:
Average classification accuracy over time with feedback, for a sliding window of 10 questions, where the window ID indicates the last question of that window.
Humans recalibrated as a result of feedback, and we accordingly observed increasing accuracy. 
The largest improvements occurred for groups with low base rates.
Grey bands indicate 95% confidence intervals.

<br/><br/><br/><br/>
```{r, echo=FALSE, fig.width = 9, fig.height = 5}
paper_results$p$p_calib
```

__Figure A4__:
Calibration plot for human responses.
Lines show a logistic regression of participants' estimated probabilities against the
actual outcomes, and indicate that human predictions suffered from poor calibration.
In the feedback conditions, we restricted to the final 10 responses to adjust for learning gains.
In a re-analysis of Dressel and Farid's data, Bansak likewise found evidence of poor calibration in human predictions of recidivism.


<br/><br/>

## Tables
```{r, echo=FALSE}
paper_results$t$acc_hvm_perf_table_nofb %>%
  mutate(features = factor(features, levels=c('short', 'long'), 
                           labels=c("streamlined", "enriched"))) %>% 
  mutate_all(~cell_spec(.x, "html", bold = grepl("\\\\textbf", .x))) %>%
  mutate_all(~str_remove_all(.x, "\\\\textbf\\{|\\}")) %>% 
  kable(format = "html", escape = F) %>%
  kable_styling()
```

__Table A1__:
Difference in 
classification accuracy (in percentage points) between
humans without feedback and:
(1) existing tools (COMPAS or LSI-R);
and (2)
our own logistic regression models.
In all cases, the algorithms 
outperformed the study participants
by a statistically significant margin, 
with the standard error of estimates in parentheses.

<br/><br/><br/><br/>
```{r, echo=FALSE}
paper_results$t$acc_hvm_perf_table_fb %>%
  mutate(features = factor(features, levels=c('short', 'long'), 
                           labels=c("streamlined", "enriched"))) %>% 
  mutate_all(~cell_spec(.x, "html", bold = grepl("\\\\textbf", .x))) %>%
  mutate_all(~str_remove_all(.x, "\\\\textbf\\{|\\}")) %>% 
  kable(format = "html", escape = F) %>%
  kable_styling()
```

__Table A2__:
Difference in classification accuracy (in percentage points) between
humans with feedback and:
(1) existing tools (COMPAS or LSI-R);
and (2)
our own logistic regression models.
The algorithms outperformed humans in 
all cases,
with bolded entries indicating
statistically significant gaps
and standard errors in parentheses.


<br/><br/><br/><br/>
```{r, echo=FALSE}
paper_results$t$acc_hvh_perf_table %>%
  mutate(features = factor(features, levels=c('short', 'long'), 
                           labels=c("streamlined", "enriched"))) %>% 
  mutate_all(~cell_spec(.x, "html", bold = grepl("\\\\textbf", .x))) %>%
  mutate_all(~str_remove_all(.x, "\\\\textbf\\{|\\}")) %>% 
  kable(format = "html", escape = F) %>%
  kable_styling()
```

__Table A3__:
Difference in classification accuracy (in percentage points) between participants who did and did not receive feedback.
In all cases, feedback improved accuracy, with statistically significant differences indicated in bold.

<br/><br/><br/><br/>
```{r, echo=FALSE}
paper_results$t$auc_hvm_perf_table_nofb %>%
  mutate(features = factor(features, levels=c('short', 'long'), 
                           labels=c("streamlined", "enriched"))) %>% 
  mutate_all(~cell_spec(.x, "html", bold = grepl("\\\\textbf", .x))) %>%
  mutate_all(~str_remove_all(.x, "\\\\textbf\\{|\\}")) %>% 
  kable(format = "html", escape = F) %>%
  kable_styling()
```

__Table A4__:
Difference in ranking accuracy (AUC) between
humans without feedback and:
(1) existing tools (COMPAS or LSI-R);
and (2)
our own logisitic regression models.
The algorithms outperformed humans in 
nearly every case,
with bolded entries indicating
statistically significant gaps
and standard errors in parentheses.



<br/><br/><br/><br/>
```{r, echo=FALSE}
paper_results$t$short_long_perf_table %>%
  mutate_all(~cell_spec(.x, "html", bold = grepl("\\\\textbf", .x))) %>%
  mutate_all(~str_remove_all(.x, "\\\\textbf\\{|\\}")) %>% 
  kable(format = "html", escape = F) %>%
  kable_styling()
```

__Table A5__:
Difference in performance
(as measured by classification accuracy and AUC)
between the 
streamlined and the enriched conditions, 
for both humans without feedback and our logistic regression models.
Positive values indicate better performance in the enriched condition, with standard errors in parentheses and statistically significant differences in bold.
For ranking accuracy (AUC), our models improved by a statistically significant margin in both datasets 
when provided with enriched information, but the study participants did not.


<br/><br/><br/><br/>
```{r, echo=FALSE}
paper_results$t$recall_at50_table %>%
  arrange(features, expName) %>% 
  mutate_all(~cell_spec(.x, "html", bold = grepl("\\\\textbf", .x))) %>%
  mutate_all(~str_remove_all(.x, "\\\\textbf\\{|\\}")) %>% 
  kable(format = "html", escape = F) %>%
  kable_styling()
```

__Table A6__:
Difference in recall-at-50% (in percentage points) between humans without feedback and:
(1) existing tools (COMPAS or LSI-R);
and (2) our own logistic regression models.
Recall-at-50% is the proportion of recidivists in the dataset that are contained in a list of the 50% of individuals deemed riskiest by a particular method.
The algorithms outperformed humans in all cases, with bolded entries indicating statistically significant gaps.