Introduction
It is often desirable to visualize student success data with the ability to disaggregate by multiple group variables to highlight equity gaps and disproportionate impact (DI) in an interactive dashboard (e.g., Tableau or Power BI). It is certainly feasible to calculate disproportionate impact on the fly in standard dashboard tools, but doing so:
- increases development time,
- increases the likelihood for error in calculations as the code has to be “re-written” for each dashboard, and
- is more difficult to maintain and support, especially when transitioning projects between analysts.
A suggested workflow is to:
- start with a student-level data set;
- call a single function to pre-calculate success rates and disproportionate impact across all levels of disaggregation, cohorts, and scenarios;
- export the pre-calculated data set;
- import the pre-calculated data set to the dashboard tool of choice for visualization, where every point visualized is a row from the imported data set.
Using this workflow, one could scale up DI calculations and rapidly develop dashboards with the ability to disaggregate and highlight equity gaps / disproportionate impact for many disaggregation variables, many outcomes, and many scenarios / student populations.
The DisImpact package offers the di_iterate
function that allows one to accomplish step 2 in the suggested
workflow.
Load DisImpact and toy data set
First, load the necessary packages.
library(DisImpact)
library(dplyr) # Ease in manipulations with data framesSecond, load a toy data set.
data(student_equity) # provided from DisImpact
dim(student_equity)## [1] 20000 24# head(student_equity)| Ethnicity | Gender | Cohort | Transfer | Cohort_Math | Math | Cohort_English | English | Ed_Goal | College_Status | Student_ID | EthnicityFlag_Asian | EthnicityFlag_Black | EthnicityFlag_Hispanic | EthnicityFlag_NativeAmerican | EthnicityFlag_PacificIslander | EthnicityFlag_White | EthnicityFlag_Carribean | EthnicityFlag_EastAsian | EthnicityFlag_SouthEastAsian | EthnicityFlag_SouthWestAsianNorthAfrican | EthnicityFlag_AANAPI | EthnicityFlag_Unknown | EthnicityFlag_TwoorMoreRaces |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Native American | Female | 2017 | 0 | 2017 | 1 | 2017 | 0 | Deg/Transfer | First-time College | 100001 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| Native American | Female | 2017 | 0 | 2018 | 1 | NA | NA | Deg/Transfer | First-time College | 100002 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| Native American | Female | 2017 | 0 | 2018 | 1 | 2017 | 0 | Deg/Transfer | First-time College | 100003 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| Native American | Male | 2017 | 1 | 2017 | 1 | 2018 | 1 | Other | First-time College | 100004 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| Native American | Male | 2017 | 0 | 2017 | 1 | 2019 | 0 | Deg/Transfer | Other | 100005 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| Native American | Male | 2017 | 1 | 2019 | 1 | 2018 | 1 | Other | First-time College | 100006 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
To get a description of each variable, type
?student_equity in the R console.
Execute di_iterate on a data set
Let’s illustrate the di_iterate function with some key
arguments:
data: a data frame of unitary (student) level or summarized data.success_vars: all outcome variables of interest.group_vars: all variables to disaggregate by (for calculating equity gaps and disproportionate impact).cohort_vars(optional): variables defining cohorts, corresponding to those insuccess_vars.scenario_repeat_by_vars(optional): variables to repeat DI calculations for across all combination of these variables. Use only if the user is interested in performing a DI analysis for variables ingroup_varsfor everyone indata, and separately for each combination of subpopulations specified usingscenario_repeat_by_vars. Each combination of these variables (e.g., full time, first time college students with an ed goal of degree/transfer as one combination) would constitute an iteration / sample for which to calculate disproportionate impact for outcomes listed insuccess_varsand for the disaggregation variables listed ingroup_vars.
To see the details of these and other arguments, type
?di_iterate in the R console.
df_di_summary <- di_iterate(data=student_equity
, success_vars=c('Math', 'English', 'Transfer')
, group_vars=c('Ethnicity', 'Gender')
, cohort_vars=c('Cohort_Math', 'Cohort_English', 'Cohort')
, scenario_repeat_by_vars=c('Ed_Goal', 'College_Status')
)
## df_di_summary <- di_iterate(data=student_equity, success_vars=c('Math', 'English', 'Transfer'), group_vars=c('Ethnicity', 'Gender'), cohort_vars=c('Cohort', 'Cohort', 'Cohort'), scenario_repeat_by_vars=c('Ed_Goal', 'College_Status'))
## df_di_summary <- di_iterate(data=student_equity, success_vars=c('Math', 'English', 'Transfer'), group_vars=c('Ethnicity', 'Gender'), scenario_repeat_by_vars=c('Ed_Goal', 'College_Status'))
## df_di_summary_2 <- di_iterate(data=student_equity, success_vars=c('Math', 'English', 'Transfer'), group_vars=c('Ethnicity', 'Gender'), cohort_vars=c('Cohort_Math', 'Cohort_English', 'Cohort'), scenario_repeat_by_vars=c('Ed_Goal', 'College_Status'), ppg_reference_groups=c('White', 'Male'), di_80_index_reference_groups=c('White', 'Male'))
## df_di_summary <- di_iterate(data=student_equity, success_vars=c('Math', 'English', 'Transfer'), group_vars=c('Ethnicity', 'Gender'), cohort_vars=c('Cohort_Math', 'Cohort_English', 'Cohort'), scenario_repeat_by_vars=c('Ed_Goal', 'College_Status'), ppg_reference_groups=c('all but current'), di_80_index_reference_groups=c('White', 'Male'))Explore resulting summary data set
dim(df_di_summary)## [1] 898 27df_di_summary %>% head %>% as.data.frame # first few rows## Ed_Goal College_Status success_variable cohort_variable cohort
## 1 Deg/Transfer First-time College Math Cohort_Math 2017
## 2 Deg/Transfer First-time College Math Cohort_Math 2017
## 3 Deg/Transfer First-time College Math Cohort_Math 2017
## 4 Deg/Transfer First-time College Math Cohort_Math 2017
## 5 Deg/Transfer First-time College Math Cohort_Math 2017
## 6 Deg/Transfer First-time College Math Cohort_Math 2017
## disaggregation group n success pct ppg_reference
## 1 Ethnicity Asian 776 692 0.8917526 0.8427699
## 2 Ethnicity Black 235 185 0.7872340 0.8427699
## 3 Ethnicity Hispanic 474 347 0.7320675 0.8427699
## 4 Ethnicity Multi-Ethnicity 117 99 0.8461538 0.8427699
## 5 Ethnicity Native American 30 28 0.9333333 0.8427699
## 6 Ethnicity White 823 718 0.8724180 0.8427699
## ppg_reference_group moe pct_lo pct_hi di_indicator_ppg
## 1 overall 0.03517995 0.8565726 0.9269325 0
## 2 overall 0.06392815 0.7233059 0.8511622 0
## 3 overall 0.04501289 0.6870546 0.7770804 1
## 4 overall 0.09060103 0.7555528 0.9367549 0
## 5 overall 0.17892270 0.7544106 1.1122560 0
## 6 overall 0.03416065 0.8382573 0.9065786 0
## success_needed_not_di_ppg success_needed_full_parity_ppg di_prop_index
## 1 0 0 1.0581211
## 2 0 14 0.9341032
## 3 32 53 0.8686446
## 4 0 0 1.0040153
## 5 0 0 1.1074593
## 6 0 0 1.0351794
## di_indicator_prop_index success_needed_not_di_prop_index
## 1 0 0
## 2 0 0
## 3 0 0
## 4 0 0
## 5 0 0
## 6 0 0
## success_needed_full_parity_prop_index di_80_index_reference_group di_80_index
## 1 0 Native American 0.9554492
## 2 15 Native American 0.8434650
## 3 66 Native American 0.7843580
## 4 0 Native American 0.9065934
## 5 0 Native American 1.0000000
## 6 0 Native American 0.9347336
## di_indicator_80_index success_needed_not_di_80_index
## 1 0 0
## 2 0 0
## 3 1 7
## 4 0 0
## 5 0 0
## 6 0 0
## success_needed_full_parity_80_index
## 1 33
## 2 35
## 3 96
## 4 11
## 5 0
## 6 51The variables di_indicator_ppg,
di_indicator_prop_index, and
di_indicator_80_index are DI flags using the three methods.
For additional explanations on other variables/columns in the returned
data set, type ?di_iterate in the R console to bring up the
documentation.
Next, note that the scenario '- All' is included for all
variables passed to scenario_repeat_by_vars by default:
table(df_di_summary$Ed_Goal)##
## - All Deg/Transfer Other
## 300 300 298table(df_di_summary$College_Status)##
## - All First-time College Other
## 300 300 298Also note di_iterate returns non-disaggregated results
by default ('- None' scenario):
table(df_di_summary$disaggregation)##
## - None Ethnicity Gender
## 90 539 269Let’s inspect the rows corresponding to non-disaggregated results.
# No Disaggregation
df_di_summary %>%
filter(Ed_Goal=='- All', College_Status=='- All', disaggregation=='- None') %>%
as.data.frame| Ed_Goal | College_Status | success_variable | cohort_variable | cohort | disaggregation | group | n | success | pct | ppg_reference | ppg_reference_group | moe | pct_lo | pct_hi | di_indicator_ppg | success_needed_not_di_ppg | success_needed_full_parity_ppg | di_prop_index | di_indicator_prop_index | success_needed_not_di_prop_index | success_needed_full_parity_prop_index | di_80_index_reference_group | di_80_index | di_indicator_80_index | success_needed_not_di_80_index | success_needed_full_parity_80_index |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| - All | - All | Math | Cohort_Math | 2017 | - None | - All | 4398 | 3722 | 0.8462938 | 0.8462938 | overall | 0.0300000 | 0.8162938 | 0.8762938 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | - All | 1 | 0 | 0 | 0 |
| - All | - All | Math | Cohort_Math | 2018 | - None | - All | 7295 | 6193 | 0.8489376 | 0.8489376 | overall | 0.0300000 | 0.8189376 | 0.8789376 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | - All | 1 | 0 | 0 | 0 |
| - All | - All | Math | Cohort_Math | 2019 | - None | - All | 4456 | 3807 | 0.8543537 | 0.8543537 | overall | 0.0300000 | 0.8243537 | 0.8843537 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | - All | 1 | 0 | 0 | 0 |
| - All | - All | Math | Cohort_Math | 2020 | - None | - All | 1780 | 1505 | 0.8455056 | 0.8455056 | overall | 0.0300000 | 0.8155056 | 0.8755056 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | - All | 1 | 0 | 0 | 0 |
| - All | - All | English | Cohort_English | 2017 | - None | - All | 5520 | 4183 | 0.7577899 | 0.7577899 | overall | 0.0300000 | 0.7277899 | 0.7877899 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | - All | 1 | 0 | 0 | 0 |
| - All | - All | English | Cohort_English | 2018 | - None | - All | 8543 | 6532 | 0.7646026 | 0.7646026 | overall | 0.0300000 | 0.7346026 | 0.7946026 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | - All | 1 | 0 | 0 | 0 |
| - All | - All | English | Cohort_English | 2019 | - None | - All | 3866 | 2938 | 0.7599586 | 0.7599586 | overall | 0.0300000 | 0.7299586 | 0.7899586 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | - All | 1 | 0 | 0 | 0 |
| - All | - All | English | Cohort_English | 2020 | - None | - All | 913 | 678 | 0.7426068 | 0.7426068 | overall | 0.0324333 | 0.7101735 | 0.7750401 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | - All | 1 | 0 | 0 | 0 |
| - All | - All | Transfer | Cohort | 2017 | - None | - All | 10000 | 5140 | 0.5140000 | 0.5140000 | overall | 0.0300000 | 0.4840000 | 0.5440000 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | - All | 1 | 0 | 0 | 0 |
| - All | - All | Transfer | Cohort | 2018 | - None | - All | 10000 | 5388 | 0.5388000 | 0.5388000 | overall | 0.0300000 | 0.5088000 | 0.5688000 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | - All | 1 | 0 | 0 | 0 |
Visualization (emulating dashboard features)
In this section, we emulate what a dashboard could visualize.
Imagine a dashboard with the following dropdown menus and option values:
- Ed Goal
- ‘- All’
- ‘Degree/Transfer’
- ‘Other’
- College Status
- ‘- All’
- ‘First-time college’
- ‘Other’
- Outcome:
- ‘Transfer’
- ‘Math’
- ‘English’
- Disaggregation:
- ‘- None’
- ‘Ethnicity’
- ‘Gender’
Each combination of this set of dropdown menus could be visualized
using a subset of rows in df_di_summary.
For example, let’s visualize non-disaggregated results for math (the dropdown selections are described at the top of the visualization):
# No Disaggregation
df_di_summary %>%
filter(Ed_Goal=='- All', College_Status=='- All', success_variable=='Math', disaggregation=='- None') %>%
as.data.frame## Ed_Goal College_Status success_variable cohort_variable cohort disaggregation
## 1 - All - All Math Cohort_Math 2017 - None
## 2 - All - All Math Cohort_Math 2018 - None
## 3 - All - All Math Cohort_Math 2019 - None
## 4 - All - All Math Cohort_Math 2020 - None
## group n success pct ppg_reference ppg_reference_group moe pct_lo
## 1 - All 4398 3722 0.8462938 0.8462938 overall 0.03 0.8162938
## 2 - All 7295 6193 0.8489376 0.8489376 overall 0.03 0.8189376
## 3 - All 4456 3807 0.8543537 0.8543537 overall 0.03 0.8243537
## 4 - All 1780 1505 0.8455056 0.8455056 overall 0.03 0.8155056
## pct_hi di_indicator_ppg success_needed_not_di_ppg
## 1 0.8762938 0 0
## 2 0.8789376 0 0
## 3 0.8843537 0 0
## 4 0.8755056 0 0
## success_needed_full_parity_ppg di_prop_index di_indicator_prop_index
## 1 0 1 0
## 2 0 1 0
## 3 0 1 0
## 4 0 1 0
## success_needed_not_di_prop_index success_needed_full_parity_prop_index
## 1 0 0
## 2 0 0
## 3 0 0
## 4 0 0
## di_80_index_reference_group di_80_index di_indicator_80_index
## 1 - All 1 0
## 2 - All 1 0
## 3 - All 1 0
## 4 - All 1 0
## success_needed_not_di_80_index success_needed_full_parity_80_index
## 1 0 0
## 2 0 0
## 3 0 0
## 4 0 0library(ggplot2)
library(forcats)
library(scales)
# No Disaggregation
df_di_summary %>%
filter(Ed_Goal=='- All', College_Status=='- All', success_variable=='Math', disaggregation=='- None') %>%
select(cohort, group, n, pct, di_indicator_ppg, di_indicator_prop_index, di_indicator_80_index) %>%
mutate(group=factor(group) %>% fct_reorder(desc(pct))) %>%
ggplot(data=., mapping=aes(x=factor(cohort), y=pct, group=group, color=group)) +
geom_point() +
geom_line() +
xlab('Cohort') +
ylab('Rate') +
theme_bw() +
scale_color_manual(values=c('#1b9e77'), name='Group') +
# labs(size='Disproportionate Impact') +
scale_y_continuous(labels = percent, limits=c(0, 1)) +
ggtitle('Dashboard drop-down selections:', subtitle=paste0("Ed Goal = '- All' | College Status = '- All' | Outcome = 'Math' | Disaggregation = '- None'"))
In this dashboard, one could choose to disaggregate by ethnicity and
highlight disproportionate impact (for simplicity, let’s use the
percentage point gap method, or the di_indicator_ppg flag
in subsequent visualizations):
# Disaggregation: Ethnicity
df_di_summary %>%
filter(Ed_Goal=='- All', College_Status=='- All', success_variable=='Math', disaggregation=='Ethnicity') %>%
select(cohort, group, n, pct, di_indicator_ppg, di_indicator_prop_index, di_indicator_80_index) %>%
as.data.frame## cohort group n pct di_indicator_ppg
## 1 2017 Asian 1406 0.8968706 0
## 2 2017 Black 421 0.7862233 1
## 3 2017 Hispanic 815 0.7325153 1
## 4 2017 Multi-Ethnicity 211 0.8293839 0
## 5 2017 Native American 45 0.9333333 0
## 6 2017 White 1500 0.8773333 0
## 7 2018 Asian 2212 0.9235986 0
## 8 2018 Black 684 0.7441520 1
## 9 2018 Hispanic 1386 0.7366522 1
## 10 2018 Multi-Ethnicity 369 0.7940379 1
## 11 2018 Native American 68 0.8088235 0
## 12 2018 White 2576 0.8819876 0
## 13 2019 Asian 1429 0.9083275 0
## 14 2019 Black 411 0.7834550 1
## 15 2019 Hispanic 786 0.7404580 1
## 16 2019 Multi-Ethnicity 225 0.8000000 0
## 17 2019 Native American 47 0.8297872 0
## 18 2019 White 1558 0.8896021 0
## 19 2020 Asian 573 0.9301920 0
## 20 2020 Black 180 0.7333333 1
## 21 2020 Hispanic 304 0.7171053 1
## 22 2020 Multi-Ethnicity 99 0.7575758 0
## 23 2020 Native American 14 0.6428571 0
## 24 2020 White 610 0.8819672 0
## di_indicator_prop_index di_indicator_80_index
## 1 0 0
## 2 0 0
## 3 0 1
## 4 0 0
## 5 0 0
## 6 0 0
## 7 0 0
## 8 0 0
## 9 0 1
## 10 0 0
## 11 0 0
## 12 0 0
## 13 0 0
## 14 0 0
## 15 0 0
## 16 0 0
## 17 0 0
## 18 0 0
## 19 0 0
## 20 0 1
## 21 0 1
## 22 0 0
## 23 1 1
## 24 0 0# Disaggregation: Ethnicity
df_di_summary %>%
filter(Ed_Goal=='- All', College_Status=='- All', success_variable=='Math', disaggregation=='Ethnicity') %>%
select(cohort, group, n, pct, di_indicator_ppg, di_indicator_prop_index, di_indicator_80_index) %>%
mutate(group=factor(group) %>% fct_reorder(desc(pct))) %>%
ggplot(data=., mapping=aes(x=factor(cohort), y=pct, group=group, color=group)) +
geom_point(aes(size=factor(di_indicator_ppg, levels=c(0, 1), labels=c('Not DI', 'DI')))) +
geom_line() +
xlab('Cohort') +
ylab('Rate') +
theme_bw() +
scale_color_manual(values=c('#1b9e77', '#d95f02', '#7570b3', '#e7298a', '#66a61e', '#e6ab02'), name='Ethnicity') +
labs(size='Disproportionate Impact') +
scale_y_continuous(labels = percent, limits=c(0, 1)) +
ggtitle('Dashboard drop-down selections:', subtitle=paste0("Ed Goal = '- All' | College Status = '- All' | Outcome = 'Math' | Disaggregation = 'Ethnicity'"))## Warning: Using size for a discrete variable is not advised.
In a dashboard, the user might be interested in focusing on
degree/transfer students. We emulate this by filtering on
Ed_Goal=='Deg/Transer':
# Disaggregation: Ethnicity; Deg/Transfer
df_di_summary %>%
filter(Ed_Goal=='Deg/Transfer', College_Status=='- All', success_variable=='Math', disaggregation=='Ethnicity') %>%
select(cohort, group, n, pct, di_indicator_ppg, di_indicator_prop_index, di_indicator_80_index) %>%
as.data.frame## cohort group n pct di_indicator_ppg
## 1 2017 Asian 975 0.8984615 0
## 2 2017 Black 290 0.7827586 1
## 3 2017 Hispanic 591 0.7292724 1
## 4 2017 Multi-Ethnicity 148 0.8445946 0
## 5 2017 Native American 36 0.9444444 0
## 6 2017 White 1039 0.8748797 0
## 7 2018 Asian 1552 0.9233247 0
## 8 2018 Black 478 0.7322176 1
## 9 2018 Hispanic 988 0.7439271 1
## 10 2018 Multi-Ethnicity 246 0.7886179 0
## 11 2018 Native American 45 0.7555556 0
## 12 2018 White 1829 0.8737015 0
## 13 2019 Asian 972 0.8971193 0
## 14 2019 Black 302 0.7913907 1
## 15 2019 Hispanic 556 0.7607914 1
## 16 2019 Multi-Ethnicity 162 0.8148148 0
## 17 2019 Native American 33 0.8181818 0
## 18 2019 White 1081 0.8843663 0
## 19 2020 Asian 402 0.9203980 0
## 20 2020 Black 127 0.6850394 1
## 21 2020 Hispanic 204 0.7107843 1
## 22 2020 Multi-Ethnicity 69 0.7681159 0
## 23 2020 Native American 8 0.6250000 0
## 24 2020 White 418 0.8851675 0
## di_indicator_prop_index di_indicator_80_index
## 1 0 0
## 2 0 0
## 3 0 1
## 4 0 0
## 5 0 0
## 6 0 0
## 7 0 0
## 8 0 1
## 9 0 0
## 10 0 0
## 11 0 0
## 12 0 0
## 13 0 0
## 14 0 0
## 15 0 0
## 16 0 0
## 17 0 0
## 18 0 0
## 19 0 0
## 20 0 1
## 21 0 1
## 22 0 0
## 23 1 1
## 24 0 0# Disaggregation: Ethnicity; Deg/Transfer
df_di_summary %>%
filter(Ed_Goal=='Deg/Transfer', College_Status=='- All', success_variable=='Math', disaggregation=='Ethnicity') %>%
select(cohort, group, n, pct, di_indicator_ppg, di_indicator_prop_index, di_indicator_80_index) %>%
mutate(group=factor(group) %>% fct_reorder(desc(pct))) %>%
ggplot(data=., mapping=aes(x=factor(cohort), y=pct, group=group, color=group)) +
geom_point(aes(size=factor(di_indicator_ppg, levels=c(0, 1), labels=c('Not DI', 'DI')))) +
geom_line() +
xlab('Cohort') +
ylab('Rate') +
theme_bw() +
scale_color_manual(values=c('#1b9e77', '#d95f02', '#7570b3', '#e7298a', '#66a61e', '#e6ab02'), name='Ethnicity') +
labs(size='Disproportionate Impact') +
scale_y_continuous(labels = percent, limits=c(0, 1)) +
ggtitle('Dashboard drop-down selections:', subtitle=paste0("Ed Goal = 'Deg/Transfer' | College Status = '- All' | Outcome = 'Math' | Disaggregation = 'Ethnicity'"))## Warning: Using size for a discrete variable is not advised.
In a dashboard, the user could switch the outcome to English and disaggregate by Gender:
# Disaggregation: Gender; Deg/Transfer; English
df_di_summary %>%
filter(Ed_Goal=='Deg/Transfer', College_Status=='- All', success_variable=='English', disaggregation=='Gender') %>%
as.data.frame## Ed_Goal College_Status success_variable cohort_variable cohort
## 1 Deg/Transfer - All English Cohort_English 2017
## 2 Deg/Transfer - All English Cohort_English 2017
## 3 Deg/Transfer - All English Cohort_English 2017
## 4 Deg/Transfer - All English Cohort_English 2018
## 5 Deg/Transfer - All English Cohort_English 2018
## 6 Deg/Transfer - All English Cohort_English 2018
## 7 Deg/Transfer - All English Cohort_English 2019
## 8 Deg/Transfer - All English Cohort_English 2019
## 9 Deg/Transfer - All English Cohort_English 2019
## 10 Deg/Transfer - All English Cohort_English 2020
## 11 Deg/Transfer - All English Cohort_English 2020
## 12 Deg/Transfer - All English Cohort_English 2020
## disaggregation group n success pct ppg_reference
## 1 Gender Female 1916 1424 0.7432150 0.7496751
## 2 Gender Male 1863 1411 0.7573806 0.7496751
## 3 Gender Other 68 49 0.7205882 0.7496751
## 4 Gender Female 2833 2151 0.7592658 0.7597185
## 5 Gender Male 3003 2296 0.7645688 0.7597185
## 6 Gender Other 132 87 0.6590909 0.7597185
## 7 Gender Female 1385 1032 0.7451264 0.7577753
## 8 Gender Male 1308 1003 0.7668196 0.7577753
## 9 Gender Other 40 36 0.9000000 0.7577753
## 10 Gender Female 307 213 0.6938111 0.7192429
## 11 Gender Male 315 234 0.7428571 0.7192429
## 12 Gender Other 12 9 0.7500000 0.7192429
## ppg_reference_group moe pct_lo pct_hi di_indicator_ppg
## 1 overall 0.03000000 0.7132150 0.7732150 0
## 2 overall 0.03000000 0.7273806 0.7873806 0
## 3 overall 0.11884246 0.6017458 0.8394307 0
## 4 overall 0.03000000 0.7292658 0.7892658 0
## 5 overall 0.03000000 0.7345688 0.7945688 0
## 6 overall 0.08529805 0.5737929 0.7443890 1
## 7 overall 0.03000000 0.7151264 0.7751264 0
## 8 overall 0.03000000 0.7368196 0.7968196 0
## 9 overall 0.15495161 0.7450484 1.0549516 0
## 10 overall 0.05593155 0.6378795 0.7497426 0
## 11 overall 0.05521674 0.6876404 0.7980739 0
## 12 overall 0.28290163 0.4670984 1.0329016 0
## success_needed_not_di_ppg success_needed_full_parity_ppg di_prop_index
## 1 0 13 0.9913829
## 2 0 0 1.0102784
## 3 0 2 0.9612007
## 4 0 2 0.9994041
## 5 0 0 1.0063843
## 6 3 14 0.8675462
## 7 0 18 0.9833077
## 8 0 0 1.0119352
## 9 0 0 1.1876871
## 10 0 8 0.9646408
## 11 0 0 1.0328321
## 12 0 0 1.0427632
## di_indicator_prop_index success_needed_not_di_prop_index
## 1 0 0
## 2 0 0
## 3 0 0
## 4 0 0
## 5 0 0
## 6 0 0
## 7 0 0
## 8 0 0
## 9 0 0
## 10 0 0
## 11 0 0
## 12 0 0
## success_needed_full_parity_prop_index di_80_index_reference_group
## 1 25 Male
## 2 0 Male
## 3 3 Male
## 4 3 Male
## 5 0 Male
## 6 14 Male
## 7 36 Other
## 8 0 Other
## 9 0 Other
## 10 16 Other
## 11 0 Other
## 12 0 Other
## di_80_index di_indicator_80_index success_needed_not_di_80_index
## 1 0.9812967 0 0
## 2 1.0000000 0 0
## 3 0.9514216 0 0
## 4 0.9930641 0 0
## 5 1.0000000 0 0
## 6 0.8620427 0 0
## 7 0.8279182 0 0
## 8 0.8520217 0 0
## 9 1.0000000 0 0
## 10 0.9250814 0 0
## 11 0.9904762 0 0
## 12 1.0000000 0 0
## success_needed_full_parity_80_index
## 1 28
## 2 0
## 3 3
## 4 16
## 5 0
## 6 14
## 7 215
## 8 175
## 9 0
## 10 18
## 11 3
## 12 0# Disaggregation: Gender; Deg/Transfer; English
df_di_summary %>%
filter(Ed_Goal=='Deg/Transfer', College_Status=='- All', success_variable=='English', disaggregation=='Gender') %>%
select(cohort, group, n, pct, di_indicator_ppg, di_indicator_prop_index, di_indicator_80_index) %>%
mutate(group=factor(group) %>% fct_reorder(desc(pct))) %>%
ggplot(data=., mapping=aes(x=factor(cohort), y=pct, group=group, color=group)) +
geom_point(aes(size=factor(di_indicator_ppg, levels=c(0, 1), labels=c('Not DI', 'DI')))) +
geom_line() +
xlab('Cohort') +
ylab('Rate') +
theme_bw() +
scale_color_manual(values=c('#1b9e77', '#d95f02', '#7570b3', '#e7298a', '#66a61e', '#e6ab02'), name='Gender') +
labs(size='Disproportionate Impact') +
scale_y_continuous(labels = percent, limits=c(0, 1)) +
ggtitle('Dashboard drop-down selections:', subtitle=paste0("Ed Goal = 'Deg/Transfer' | College Status = '- All' | Outcome = 'English' | Disaggregation = 'Gender'"))## Warning: Using size for a discrete variable is not advised.
What is the difference between group_vars and
scenario_repeat_by_vars?
For different classification variables, (e.g., age group, full time
status, and education goal), the user might be confused as to whether to
pass these into the group_vars argument or the
scenario_repeat_by_vars argument. The answer is it depends
on what the user wants to analyze. If we think of a single student
population of interest (e.g., the data set being passed to
di_iterate such as all students enrolled at the
institution), then the user should pass into group_vars all
variables that they are interested in disaggregating on and
performing a DI analysis (e.g., are there disparity among ethnic
student groups? First generation students?). The group_vars
argument is required.
On the other hand, the scenario_repeat_by_vars argument
is optional, and when not specified, the DI analysis is performed on all
outcomes specified in success_vars and all disaggregation
variables specified in group_vars, using all students
passed to data as a single population. The user should only
pass variables into scenario_repeat_by_vars if they want to
split the student population into multiple subpopulations to perform DI
analysis on. For example, if ethnicity, first generation status, and age
group and were specified in group_vars, then the user is
trying to answer the following questions:
- Is there disparity between different ethnic student groups?
- Is there disparity between first generation students vs. non-first generation students?
- Is there disparity between students of different age groups?
If on the other hand, the user passes ethnicity and first generation
status to group_vars, and age group to
scenario_repeat_by_vars, then the user is trying to answer
the following questions:
- Is there disparity between different ethnic student groups?
- Among all students defined by
data? - Among different subpopulations defined by age group? (e.g., among each of these groups: 18-21, 22-25, 26-35, 35-50, 51+)
- Among all students defined by
- Is there disparity between first generation students vs. non-first
generation students?
- Among all students defined by
data? - Among different subpopulations defined by age group? (e.g., among each of these groups: 18-21, 22-25, 26-35, 35-50, 51+)
- Among all students defined by
Understanding the default parameters in di_iterate, and
overriding them
The function di_iterate has been designed to be highly
flexible through the use of function arguments / parameters, with many
defaults:
args(di_iterate)## function (data, success_vars, group_vars, cohort_vars = NULL,
## scenario_repeat_by_vars = NULL, exclude_scenario_df = NULL,
## weight_var = NULL, include_non_disagg_results = TRUE, ppg_reference_groups = "overall",
## min_moe = 0.03, use_prop_in_moe = FALSE, prop_sub_0 = 0.5,
## prop_sub_1 = 0.5, di_prop_index_cutoff = 0.8, di_80_index_cutoff = 0.8,
## di_80_index_reference_groups = "hpg", check_valid_reference = TRUE,
## parallel = FALSE, parallel_n_cores = parallel::detectCores(),
## parallel_split_to_disk = FALSE)
## NULLIn this section, we illustrate how each argument could be used. Type
?di_iterate to read the description of each.
Passing a summarized data set to data and using
weight_var
Instead of passing in a student level data set, the user could also
pass in a summarized data set, which saves space on your disk drive or
in memory when imported into R. When passing a summarized data set, the
user should also specify weight_var to indicate the group
size of each row. Let’s illustrate with an example:
dim(student_equity)## [1] 20000 24## Example summarized data set
student_equity_summ <- student_equity %>%
group_by(Ethnicity, Gender, Cohort, Cohort_Math, Cohort_English, Ed_Goal, College_Status) %>%
summarize(N=n() %>% as.numeric # not needed, for all.equal()
, Math=sum(Math, na.rm=TRUE)
, English=sum(English, na.rm=TRUE)
, Transfer=sum(Transfer, na.rm=TRUE)
) %>%
ungroup## `summarise()` has grouped output by 'Ethnicity', 'Gender', 'Cohort',
## 'Cohort_Math', 'Cohort_English', 'Ed_Goal'. You can override using the
## `.groups` argument.dim(student_equity_summ) # same number of columns, less number of rows## [1] 1402 11student_equity_summ %>% head %>% as.data.frame # first few rows## Ethnicity Gender Cohort Cohort_Math Cohort_English Ed_Goal
## 1 Asian Female 2017 2017 2017 Deg/Transfer
## 2 Asian Female 2017 2017 2017 Deg/Transfer
## 3 Asian Female 2017 2017 2017 Other
## 4 Asian Female 2017 2017 2017 Other
## 5 Asian Female 2017 2017 2018 Deg/Transfer
## 6 Asian Female 2017 2017 2018 Deg/Transfer
## College_Status N Math English Transfer
## 1 First-time College 202 185 178 157
## 2 Other 55 52 50 41
## 3 First-time College 96 87 82 70
## 4 Other 25 23 22 20
## 5 First-time College 104 88 87 71
## 6 Other 31 29 29 26## Run on summarized data set
df_di_summary_2 <- di_iterate(data=student_equity_summ
, success_vars=c('Math', 'English', 'Transfer')
, group_vars=c('Ethnicity', 'Gender')
, cohort_vars=c('Cohort_Math', 'Cohort_English', 'Cohort')
, scenario_repeat_by_vars=c('Ed_Goal', 'College_Status')
, weight_var='N' # SET THIS
)
dim(df_di_summary) ## original results## [1] 898 27dim(df_di_summary_2) # more rows? because of NA cohort from Cohort_English and Cohort_Math## [1] 1075 27dim(df_di_summary_2 %>% filter(!is.na(cohort)))## [1] 898 27## ## if user wants to see the extra rows
## extra_rows <- df_di_summary_2 %>%
## anti_join(df_di_summary %>% select(Ed_Goal, College_Status, success_variable, cohort_variable, cohort, disaggregation, group))
## difference %>% head %>% as.data.frame
all.equal(df_di_summary
, df_di_summary_2 %>% filter(!is.na(cohort))
) # returned results are the same## [1] TRUESuppress non-disaggregated results using
include_non_disagg_results
By default, the non-disaggregated results are also returned. If the
user wants to suppress this, they could set
include_non_disagg_results=FALSE:
df_di_summary_2 <- di_iterate(data=student_equity
, success_vars=c('Math', 'English', 'Transfer')
, group_vars=c('Ethnicity', 'Gender')
, cohort_vars=c('Cohort_Math', 'Cohort_English', 'Cohort')
, scenario_repeat_by_vars=c('Ed_Goal', 'College_Status')
, include_non_disagg_results=FALSE ## SET THIS
)
dim(df_di_summary)## [1] 898 27dim(df_di_summary_2) ## less rows because no longer have disaggregated results## [1] 808 27table(df_di_summary$disaggregation)##
## - None Ethnicity Gender
## 90 539 269table(df_di_summary_2$disaggregation) # No more '- None'##
## Ethnicity Gender
## 539 269PPG reference groups and other parameters
For the percentage point gap (PPG) method, di_iterate
defaults to using the overall success rate as the reference for
comparison (ppg_reference_groups='overall'). The user could
set ppg_reference_groups='hpg' to use the highest
performing group as the comparison group, or
ppg_reference_groups='all but current' for using the
combined success rate of all other groups excluding the group of
interest (e.g., if studying Hispanic students, then the reference group
would be all non-Hispanic students). The latter is sometimes referred to
as “PPG minus 1” or “PPG-1.” The user could also specify specific groups
as reference:
# Highest performing group as reference
df_di_summary_2 <- di_iterate(data=student_equity
, success_vars=c('Math', 'English', 'Transfer')
, group_vars=c('Ethnicity', 'Gender')
, cohort_vars=c('Cohort_Math', 'Cohort_English', 'Cohort')
, scenario_repeat_by_vars=c('Ed_Goal', 'College_Status')
, ppg_reference_groups='hpg' ## SET THIS
)
# Reference: all other groups except group of interest (PPG minus 1)
df_di_summary_2 <- di_iterate(data=student_equity
, success_vars=c('Math', 'English', 'Transfer')
, group_vars=c('Ethnicity', 'Gender')
, cohort_vars=c('Cohort_Math', 'Cohort_English', 'Cohort')
, scenario_repeat_by_vars=c('Ed_Goal', 'College_Status')
, ppg_reference_groups='all but current' ## SET THIS
)
# Reference: custom groups
df_di_summary_2 <- di_iterate(data=student_equity
, success_vars=c('Math', 'English', 'Transfer')
, group_vars=c('Ethnicity', 'Gender')
, cohort_vars=c('Cohort_Math', 'Cohort_English', 'Cohort')
, scenario_repeat_by_vars=c('Ed_Goal', 'College_Status')
, ppg_reference_groups=c('White', 'Male') ## corresponds to each variable in group_vars
)The following arguments apply to the PPG: min_moe,
use_prop_in_moe, prop_sub_0,
prop_sub_1, and use_prop_in_moe. See
?di_ppg for more details.
Proportionality index DI threshold
For the proportionality index (PI) method, DI is determined using
di_prop_index_cutoff=0.8 by default. This could be changed
using the di_prop_index_cutoff argument.
df_di_summary_2 <- di_iterate(data=student_equity
, success_vars=c('Math', 'English', 'Transfer')
, group_vars=c('Ethnicity', 'Gender')
, cohort_vars=c('Cohort_Math', 'Cohort_English', 'Cohort')
, scenario_repeat_by_vars=c('Ed_Goal', 'College_Status')
, di_prop_index_cutoff=0.9 # Easier to declare DI using PI
)80% index reference groups and DI threshold
For the 80% index method, the highest performing group is used as
reference by default (di_80_index_reference_groups='hpg').
Similar to the PPG, the user could specify custom reference groups.
# Custom reference groups
df_di_summary_2 <- di_iterate(data=student_equity
, success_vars=c('Math', 'English', 'Transfer')
, group_vars=c('Ethnicity', 'Gender')
, cohort_vars=c('Cohort_Math', 'Cohort_English', 'Cohort')
, scenario_repeat_by_vars=c('Ed_Goal', 'College_Status')
, di_80_index_reference_groups=c('White', 'Male') ## corresponds to each variable in group_vars
)Besides specifying a specific reference group, the function also
acccepts 'overall' and 'all but current'. The
former uses the overall success rate as reference for comparison. The
latter uses the combined success rate of all other groups as reference
for comparison.
The 80% index uses 80% as the default threshold for declaring DI. The
user could alter this with the di_80_index_cutoff
argument.
df_di_summary_2 <- di_iterate(data=student_equity
, success_vars=c('Math', 'English', 'Transfer')
, group_vars=c('Ethnicity', 'Gender')
, cohort_vars=c('Cohort_Math', 'Cohort_English', 'Cohort')
, scenario_repeat_by_vars=c('Ed_Goal', 'College_Status')
, di_80_index_cutoff=0.5 # Harder to declare DI using 80% index
)Multiple PPG or DI parameter scenarios in results
In a single call of di_iterate, the results of all three
DI methods are returned in one run. If the user is interested in doing
DI calculations using various scenarios of the same method (e.g., using
the overall rate as reference for PPG, and using a pre-specified list of
reference rates), then it is recommended that the user execute
di_iterate multiple times and combining the results
(stacking). If the user chooses to do this, then it is a good idea to
set include_non_disagg_results=FALSE in subsequent
di_iterate runs to not duplicate rows of non-disaggregated
results.
# Multiple group variables and different reference groups
df_di_summary_long <- bind_rows(
di_iterate(data=student_equity
, success_vars=c('Math', 'English', 'Transfer')
, group_vars=c('Ethnicity', 'Gender')
, cohort_vars=c('Cohort_Math', 'Cohort_English', 'Cohort')
, scenario_repeat_by_vars=c('Ed_Goal', 'College_Status')
)
, di_iterate(data=student_equity
, success_vars=c('Math', 'English', 'Transfer')
, group_vars=c('Ethnicity', 'Gender')
, cohort_vars=c('Cohort_Math', 'Cohort_English', 'Cohort')
, scenario_repeat_by_vars=c('Ed_Goal', 'College_Status')
, ppg_reference_groups=c('White', 'Male') ## corresponds to each variable in group_vars
, include_non_disagg_results = FALSE # Already have non-disaggregated results in the first run
)
)
dim(df_di_summary_long)## [1] 1706 27FERPA block / suppression
Since di_iterate disaggregates on many variables and
subpopulations, it is not uncommon the returned results contain rows
summarizing small samples. As is common in education research, care
should be taken to not unintentionally disclose the educational outcomes
of students (results linked to particular students, ie, FERPA
regulation). The user might want to filter out rows with small samples
(e.g., n < 10):
## df_di_summary %>%
## mutate(FERPA_Block=ifelse(n < 10, 1, 0)) %>%
## filter(FERPA_Block == 0)Suppress / disable “Joining, by” messages
The di_iterate function joins various data sets using
dplyr in the course of calculating DI. As such, the
implicit join’s are reported in the R console by various lines starting
with Joining, by =. For runs with many scenarios, this may
be overwhelming. To suppress these messages, the user could wrap / pipe
the di_iterate call with / to the
suppressMessages function:
df_di_summary <- di_iterate(data=student_equity
, success_vars=c('Math', 'English', 'Transfer')
, group_vars=c('Ethnicity', 'Gender')
, cohort_vars=c('Cohort_Math', 'Cohort_English', 'Cohort')
, scenario_repeat_by_vars=c('Ed_Goal', 'College_Status')
) %>%
suppressMessagesParallel execution
When there are many scenarios for which to calculate DI (whenever the
cardinality is high on success_vars,
group_vars, and/or scenario_repeat_by_vars),
the user may benefit from parallel execution (reduce time it takes to
get results). The user could specify parallel=TRUE and the
number of CPU cores using the parallel_n_cores parameter.
The di_iterate function leverages the parallel
package included in base R and executes in parallel the scenarios
generated by scenario_repeat_by_vars.
df_di_summary <- di_iterate(data=student_equity
, success_vars=c('Math', 'English', 'Transfer')
, group_vars=c('Ethnicity', 'Gender')
, cohort_vars=c('Cohort_Math', 'Cohort_English', 'Cohort')
, scenario_repeat_by_vars=c('Ed_Goal', 'College_Status')
, parallel=TRUE
, parallel_n_cores=4
)When the data set specified by data is very large in
size, R or the system could crash in parallel execution since the data
set is copied multiple times (parallel_n_cores times),
using up all of the system’s memory. To benefit from parallel execution
and prevent the likelihood of such a crash, the user could specify
parallel_split_to_disk=TRUE to write intermediate data sets
to disk, and re-importing each data set when necessary, reducing the
need to copy the original data set specified by data
multiple times in memory. This method is more robust, but increases
execution time caused by I/O overhead. Here is a sample scenario for the
user to illustrate on their own system:
# Create a very large student data set
n_college <- 200
student_equity_big <- do.call('rbind', replicate(n_college, student_equity, simplify=FALSE)) # repeat student_equity data set n_college times
student_equity_big$college <- rep(paste0('College ', 1:n_college), each=nrow(student_equity)) # College Name
dim(student_equity_big)## [1] 4000000 25table(student_equity_big$college)##
## College 1 College 10 College 100 College 101 College 102 College 103
## 20000 20000 20000 20000 20000 20000
## College 104 College 105 College 106 College 107 College 108 College 109
## 20000 20000 20000 20000 20000 20000
## College 11 College 110 College 111 College 112 College 113 College 114
## 20000 20000 20000 20000 20000 20000
## College 115 College 116 College 117 College 118 College 119 College 12
## 20000 20000 20000 20000 20000 20000
## College 120 College 121 College 122 College 123 College 124 College 125
## 20000 20000 20000 20000 20000 20000
## College 126 College 127 College 128 College 129 College 13 College 130
## 20000 20000 20000 20000 20000 20000
## College 131 College 132 College 133 College 134 College 135 College 136
## 20000 20000 20000 20000 20000 20000
## College 137 College 138 College 139 College 14 College 140 College 141
## 20000 20000 20000 20000 20000 20000
## College 142 College 143 College 144 College 145 College 146 College 147
## 20000 20000 20000 20000 20000 20000
## College 148 College 149 College 15 College 150 College 151 College 152
## 20000 20000 20000 20000 20000 20000
## College 153 College 154 College 155 College 156 College 157 College 158
## 20000 20000 20000 20000 20000 20000
## College 159 College 16 College 160 College 161 College 162 College 163
## 20000 20000 20000 20000 20000 20000
## College 164 College 165 College 166 College 167 College 168 College 169
## 20000 20000 20000 20000 20000 20000
## College 17 College 170 College 171 College 172 College 173 College 174
## 20000 20000 20000 20000 20000 20000
## College 175 College 176 College 177 College 178 College 179 College 18
## 20000 20000 20000 20000 20000 20000
## College 180 College 181 College 182 College 183 College 184 College 185
## 20000 20000 20000 20000 20000 20000
## College 186 College 187 College 188 College 189 College 19 College 190
## 20000 20000 20000 20000 20000 20000
## College 191 College 192 College 193 College 194 College 195 College 196
## 20000 20000 20000 20000 20000 20000
## College 197 College 198 College 199 College 2 College 20 College 200
## 20000 20000 20000 20000 20000 20000
## College 21 College 22 College 23 College 24 College 25 College 26
## 20000 20000 20000 20000 20000 20000
## College 27 College 28 College 29 College 3 College 30 College 31
## 20000 20000 20000 20000 20000 20000
## College 32 College 33 College 34 College 35 College 36 College 37
## 20000 20000 20000 20000 20000 20000
## College 38 College 39 College 4 College 40 College 41 College 42
## 20000 20000 20000 20000 20000 20000
## College 43 College 44 College 45 College 46 College 47 College 48
## 20000 20000 20000 20000 20000 20000
## College 49 College 5 College 50 College 51 College 52 College 53
## 20000 20000 20000 20000 20000 20000
## College 54 College 55 College 56 College 57 College 58 College 59
## 20000 20000 20000 20000 20000 20000
## College 6 College 60 College 61 College 62 College 63 College 64
## 20000 20000 20000 20000 20000 20000
## College 65 College 66 College 67 College 68 College 69 College 7
## 20000 20000 20000 20000 20000 20000
## College 70 College 71 College 72 College 73 College 74 College 75
## 20000 20000 20000 20000 20000 20000
## College 76 College 77 College 78 College 79 College 8 College 80
## 20000 20000 20000 20000 20000 20000
## College 81 College 82 College 83 College 84 College 85 College 86
## 20000 20000 20000 20000 20000 20000
## College 87 College 88 College 89 College 9 College 90 College 91
## 20000 20000 20000 20000 20000 20000
## College 92 College 93 College 94 College 95 College 96 College 97
## 20000 20000 20000 20000 20000 20000
## College 98 College 99
## 20000 20000# Not run: user test on their own system
# User should try to increase n_college to 800 or another large number if the system has a lot of memory
# User should wrap following call with system.time() to time execution: parallel=FALSE, then parallel=TRUE, then parallel=TRUE and parallel_split_to_disk=TRUE
# Parallel execution + writing to disk
big_di_summary <- di_iterate(data=student_equity_big
, success_vars=c('Math', 'English', 'Transfer')
, group_vars=c('Ethnicity', 'Gender')
, cohort_vars=c('Cohort_Math', 'Cohort_English', 'Cohort')
, scenario_repeat_by_vars=c('Ed_Goal', 'College_Status', 'college') # Add college
, parallel=TRUE
# , parallel_n_cores=4 # when not specified, use the max number of cores
, parallel_split_to_disk=TRUE
)Appendix: R and R Package Versions
This vignette was generated using an R session with the following packages. There may be some discrepancies when the reader replicates the code caused by version mismatch.
sessionInfo()## R version 4.0.2 (2020-06-22)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 19042)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=C
## [2] LC_CTYPE=English_United States.1252
## [3] LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C
## [5] LC_TIME=English_United States.1252
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] forcats_0.5.0 scales_1.1.1 ggplot2_3.3.2 stringr_1.4.0
## [5] knitr_1.39 dplyr_1.0.8 DisImpact_0.0.18
##
## loaded via a namespace (and not attached):
## [1] Rcpp_1.0.8.3 pillar_1.7.0 bslib_0.3.1 compiler_4.0.2
## [5] jquerylib_0.1.4 highr_0.9 prettydoc_0.4.1 tools_4.0.2
## [9] digest_0.6.25 gtable_0.3.0 jsonlite_1.5 evaluate_0.15
## [13] lifecycle_1.0.1 tibble_3.1.6 fstcore_0.9.12 pkgconfig_2.0.3
## [17] rlang_1.0.1 cli_3.2.0 yaml_2.3.5 parallel_4.0.2
## [21] xfun_0.30 fastmap_1.1.0 withr_2.5.0 generics_0.1.2
## [25] vctrs_0.3.8 sass_0.4.1 grid_4.0.2 tidyselect_1.1.2
## [29] glue_1.6.1 R6_2.3.0 fansi_1.0.2 rmarkdown_2.14
## [33] farver_2.0.3 purrr_0.3.4 tidyr_1.2.0 magrittr_2.0.2
## [37] ellipsis_0.3.2 htmltools_0.5.2 fst_0.9.8 colorspace_1.4-1
## [41] labeling_0.3 utf8_1.2.2 stringi_1.4.6 munsell_0.5.0
## [45] crayon_1.5.0