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 (eg, Tableau or Power BI). It is certainly feasible to calculate disproportionate impact on the fly in standard dashboard tools, but doing so:

1. increases development time,
2. increases the likelihood for error in calculations as the code has to be “re-written” for each dashboard, and
3. is more difficult to maintain and support, especially when transitioning projects between analysts.

A suggested workflow is to:

1. start with a student-level data set;
2. call a single function to pre-calculate success rates and disproportionate impact across all levels of disaggregation, cohorts, and scenarios;
3. export the pre-calculated data set;
4. 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 frames

Second, load a toy data set.

data(student_equity) # provided from DisImpact
dim(student_equity)

## [1] 20000    11

# head(student_equity)

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 in success_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 in group_vars for everyone in data, and separately for each combination of subpopulations specified using scenario_repeat_by_vars. Each combination of these variables (eg, 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 in success_vars and for the disaggregation variables listed in group_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')
                            )

## Joining, by = c("Ed_Goal", "College_Status")
## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = "College_Status"

## Joining, by = c("Ed_Goal", "College_Status")
## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = "College_Status"

## Joining, by = "Ed_Goal"
## Joining, by = "Ed_Goal"

## 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  21

df_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 800     698 0.8725000     0.8150224
## 2      Ethnicity           Black 260     199 0.7653846     0.8150224
## 3      Ethnicity        Hispanic 549     390 0.7103825     0.8150224
## 4      Ethnicity Multi-Ethnicity 136     108 0.7941176     0.8150224
## 5      Ethnicity Native American  28      22 0.7857143     0.8150224
## 6      Ethnicity           White 903     764 0.8460687     0.8150224
##   ppg_reference_group        moe    pct_lo    pct_hi di_indicator_ppg
## 1             overall 0.03464823 0.8378518 0.9071482                0
## 2             overall 0.06077702 0.7046076 0.8261616                0
## 3             overall 0.04182538 0.6685571 0.7522079                1
## 4             overall 0.08403431 0.7100833 0.8781520                0
## 5             overall 0.18520259 0.6005117 0.9709169                0
## 6             overall 0.03261236 0.8134563 0.8786810                0
##   di_prop_index di_indicator_prop_index di_80_index_reference_group
## 1     1.0705227                       0                       Asian
## 2     0.9390964                       0                       Asian
## 3     0.8716110                       0                       Asian
## 4     0.9743507                       0                       Asian
## 5     0.9640401                       0                       Asian
## 6     1.0380925                       0                       Asian
##   di_80_index di_indicator_80_index
## 1   1.0000000                     0
## 2   0.8772317                     0
## 3   0.8141920                     0
## 4   0.9101635                     0
## 5   0.9005321                     0
## 6   0.9697062                     0

The variables di_indicator_ppg, di_indicator_prop_index, and di_indicator_80_index are DI flags using the three methods.

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          298

table(df_di_summary$College_Status)

## 
##              - All First-time College              Other 
##                300                300                298

Also note di_iterate returns non-disaggregated results by default ('- None' scenario):

table(df_di_summary$disaggregation)

## 
##    - None Ethnicity    Gender 
##        90       539       269

Let'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

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
## 1   - All          - All             Math     Cohort_Math   2017
## 2   - All          - All             Math     Cohort_Math   2018
## 3   - All          - All             Math     Cohort_Math   2019
## 4   - All          - All             Math     Cohort_Math   2020
##   disaggregation group    n success       pct ppg_reference
## 1         - None - All 4691    3828 0.8160307     0.8160307
## 2         - None - All 7416    6108 0.8236246     0.8236246
## 3         - None - All 4622    3772 0.8160969     0.8160969
## 4         - None - All 1855    1573 0.8479784     0.8479784
##   ppg_reference_group  moe    pct_lo    pct_hi di_indicator_ppg
## 1             overall 0.03 0.7860307 0.8460307                0
## 2             overall 0.03 0.7936246 0.8536246                0
## 3             overall 0.03 0.7860969 0.8460969                0
## 4             overall 0.03 0.8179784 0.8779784                0
##   di_prop_index di_indicator_prop_index di_80_index_reference_group
## 1             1                       0                       - All
## 2             1                       0                       - All
## 3             1                       0                       - All
## 4             1                       0                       - All
##   di_80_index di_indicator_80_index
## 1           1                     0
## 2           1                     0
## 3           1                     0
## 4           1                     0

{width=100%}

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 1456 0.8804945                0
## 2    2017           Black  452 0.7190265                1
## 3    2017        Hispanic  901 0.6947836                1
## 4    2017 Multi-Ethnicity  245 0.8204082                0
## 5    2017 Native American   46 0.8260870                0
## 6    2017           White 1591 0.8522942                0
## 7    2018           Asian 2251 0.9009329                0
## 8    2018           Black  736 0.7160326                1
## 9    2018        Hispanic 1404 0.6972934                1
## 10   2018 Multi-Ethnicity  379 0.8179420                0
## 11   2018 Native American   77 0.7792208                0
## 12   2018           White 2569 0.8579214                0
## 13   2019           Asian 1450 0.8862069                0
## 14   2019           Black  435 0.7195402                1
## 15   2019        Hispanic  866 0.6755196                1
## 16   2019 Multi-Ethnicity  227 0.8193833                0
## 17   2019 Native American   41 0.8048780                0
## 18   2019           White 1603 0.8546475                0
## 19   2020           Asian  582 0.9278351                0
## 20   2020           Black  171 0.7543860                1
## 21   2020        Hispanic  345 0.6956522                1
## 22   2020 Multi-Ethnicity   81 0.8395062                0
## 23   2020 Native American   17 0.8235294                0
## 24   2020           White  659 0.8831563                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                     1
## 10                       0                     0
## 11                       0                     0
## 12                       0                     0
## 13                       0                     0
## 14                       0                     0
## 15                       0                     1
## 16                       0                     0
## 17                       0                     0
## 18                       0                     0
## 19                       0                     0
## 20                       0                     0
## 21                       0                     1
## 22                       0                     0
## 23                       0                     0
## 24                       0                     0

{width=100%}

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 1000 0.8820000                0
## 2    2017           Black  320 0.7500000                1
## 3    2017        Hispanic  665 0.7037594                1
## 4    2017 Multi-Ethnicity  164 0.8109756                0
## 5    2017 Native American   32 0.8125000                0
## 6    2017           White 1108 0.8546931                0
## 7    2018           Asian 1564 0.8951407                0
## 8    2018           Black  515 0.6990291                1
## 9    2018        Hispanic  989 0.6966633                1
## 10   2018 Multi-Ethnicity  262 0.8511450                0
## 11   2018 Native American   62 0.7741935                0
## 12   2018           White 1763 0.8536585                0
## 13   2019           Asian 1019 0.8802748                0
## 14   2019           Black  310 0.6838710                1
## 15   2019        Hispanic  602 0.6843854                1
## 16   2019 Multi-Ethnicity  166 0.8012048                0
## 17   2019 Native American   26 0.7692308                0
## 18   2019           White 1160 0.8465517                0
## 19   2020           Asian  408 0.9117647                0
## 20   2020           Black  122 0.7459016                1
## 21   2020        Hispanic  244 0.7172131                1
## 22   2020 Multi-Ethnicity   57 0.8245614                0
## 23   2020 Native American    9 0.6666667                0
## 24   2020           White  458 0.8711790                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                     1
## 10                       0                     0
## 11                       0                     0
## 12                       0                     0
## 13                       0                     0
## 14                       0                     1
## 15                       0                     1
## 16                       0                     0
## 17                       0                     0
## 18                       0                     0
## 19                       0                     0
## 20                       0                     0
## 21                       0                     1
## 22                       0                     0
## 23                       1                     1
## 24                       0                     0

{width=100%}

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
##    di_prop_index di_indicator_prop_index di_80_index_reference_group
## 1      0.9913829                       0                        Male
## 2      1.0102784                       0                        Male
## 3      0.9612007                       0                        Male
## 4      0.9994041                       0                        Male
## 5      1.0063843                       0                        Male
## 6      0.8675462                       0                        Male
## 7      0.9833077                       0                       Other
## 8      1.0119352                       0                       Other
## 9      1.1876871                       0                       Other
## 10     0.9646408                       0                       Other
## 11     1.0328321                       0                       Other
## 12     1.0427632                       0                       Other
##    di_80_index di_indicator_80_index
## 1    0.9812967                     0
## 2    1.0000000                     0
## 3    0.9514216                     0
## 4    0.9930641                     0
## 5    1.0000000                     0
## 6    0.8620427                     0
## 7    0.8279182                     0
## 8    0.8520217                     0
## 9    1.0000000                     0
## 10   0.9250814                     0
## 11   0.9904762                     0
## 12   1.0000000                     0

{width=100%}

What is the difference between group_vars and scenario_repeat_by_vars?

For different classification variables, (eg, 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 (eg, 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 (eg, 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:

1. Is there disparity between different ethnic student groups?
2. Is there disparity between first generation students vs. non-first generation students?
3. 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:

1. Is there disparity between different ethnic student groups? a. Among all students defined by data? b. Among different subpopulations defined by age group? (eg, among each of these groups: 18-21, 22-25, 26-35, 35-50, 51+)
2. Is there disparity between first generation students vs. non-first generation students? a. Among all students defined by data? b. Among different subpopulations defined by age group? (eg, among each of these groups: 18-21, 22-25, 26-35, 35-50, 51+)

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) 
## NULL

In 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    11

## 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

dim(student_equity_summ) # same number of columns, less number of rows

## [1] 1392   11

student_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 218  196     185      162
## 2              Other  60   55      50       40
## 3 First-time College  99   87      86       74
## 4              Other  22   20      18       16
## 5 First-time College 136  118     113       94
## 6              Other  37   34      35       28

## 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
                            )

## Joining, by = c("Ed_Goal", "College_Status")
## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = "College_Status"

## Joining, by = c("Ed_Goal", "College_Status")
## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = "College_Status"

## Joining, by = "Ed_Goal"
## Joining, by = "Ed_Goal"

dim(df_di_summary)  ## original results

## [1] 898  21

dim(df_di_summary_2) # more rows?  because of NA cohort from Cohort_English and Cohort_Math

## [1] 1075   21

dim(df_di_summary_2 %>% filter(!is.na(cohort)))

## [1] 898  21

## ## 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] TRUE

Suppress 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
                            )

## Joining, by = c("Ed_Goal", "College_Status")
## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = "College_Status"

## Joining, by = c("Ed_Goal", "College_Status")
## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = "College_Status"

## Joining, by = "Ed_Goal"
## Joining, by = "Ed_Goal"

dim(df_di_summary)

## [1] 898  21

dim(df_di_summary_2) ## less rows because no longer have disaggregated results

## [1] 808  21

table(df_di_summary$disaggregation)

## 
##    - None Ethnicity    Gender 
##        90       539       269

table(df_di_summary_2$disaggregation) # No more '- None'

## 
## Ethnicity    Gender 
##       539       269

PPG 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' for using 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 (eg, if studying Hispanic students, then the reference group would be all non-Hispanic students). The latter is sometimes referred to as “PPG minus 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
                              )

## Joining, by = c("Ed_Goal", "College_Status")
## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = "College_Status"

## Joining, by = c("Ed_Goal", "College_Status")
## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = "College_Status"

## Joining, by = "Ed_Goal"
## Joining, by = "Ed_Goal"

# 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
                              )

## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = "College_Status"

## Joining, by = c("Ed_Goal", "College_Status")
## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = "College_Status"

## Joining, by = "Ed_Goal"
## Joining, by = "Ed_Goal"

# 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
                              )

## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = "College_Status"

## Joining, by = c("Ed_Goal", "College_Status")
## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = "College_Status"

## Joining, by = "Ed_Goal"
## Joining, by = "Ed_Goal"

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
                              )

## Joining, by = c("Ed_Goal", "College_Status")
## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = "College_Status"

## Joining, by = c("Ed_Goal", "College_Status")
## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = "College_Status"

## Joining, by = "Ed_Goal"
## Joining, by = "Ed_Goal"

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=NA). Similar to the PPG, the user could specify custom reference groups.

# Custom referene 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
                              )

## Joining, by = c("Ed_Goal", "College_Status")
## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = "College_Status"

## Joining, by = c("Ed_Goal", "College_Status")
## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = "College_Status"

## Joining, by = "Ed_Goal"
## Joining, by = "Ed_Goal"

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
                              )

## Joining, by = c("Ed_Goal", "College_Status")
## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = "College_Status"

## Joining, by = c("Ed_Goal", "College_Status")
## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = "College_Status"

## Joining, by = "Ed_Goal"
## Joining, by = "Ed_Goal"

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 (eg, 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
             )
)

## Joining, by = c("Ed_Goal", "College_Status")
## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = "College_Status"

## Joining, by = c("Ed_Goal", "College_Status")
## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = "College_Status"

## Joining, by = "Ed_Goal"
## Joining, by = "Ed_Goal"

## Joining, by = c("Ed_Goal", "College_Status")
## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = "College_Status"

## Joining, by = c("Ed_Goal", "College_Status")
## Joining, by = c("Ed_Goal", "College_Status")

## Joining, by = "College_Status"

## Joining, by = "Ed_Goal"
## Joining, by = "Ed_Goal"

dim(df_di_summary_long)

## [1] 1706   21

FERPA 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 (eg, n < 10):

## df_di_summary %>%
##   mutate(FERPA_Block=ifelse(n < 10, 1, 0)) %>%
##   filter(FERPA_Block == 0)