A STEM Professor Like Me: Female Faculty Reduce Gender Gaps among Engineering Students

# Libraries
pacman::p_load(haven, estimatr, extrafont, texreg, janitor, hrbrthemes, xtable, papeR, tidyverse, compareGroups, Hmisc, skimr)

# Student Data
df_stu <- 
  read_dta(here::here("data", "stu_admin_all_latest.dta")) %>%
  left_join(read_dta(here::here("data/reservation_new.dta")), by = "stdid") %>% 
  mutate(
    reservation = dplyr::recode(reservation, "Non-reservation" = 0L, "Reservation" = 1L, .default = NA_integer_),
  )

df <- 
  read_dta(here::here("data", "all_appended.dta")) %>% 
  distinct(stdid, course_name, facid, .keep_all = T) %>% 
  left_join(
    df_stu %>% 
      select(stdid, classid, department_id, reservation, caste, ea_stud_group_criteria, grade),
    by = "stdid"
  ) %>%
  filter(ea_stud_group_criteria == 2, grade == 2) %>%
  left_join(read_dta(here::here("data/fac_covariates.dta")), by = "facid")


# fixing for course cleaning done by sk in sep 2021
df <-
  df %>% 
  left_join(
    read_dta(here::here("data/students_clean.dta")),
    by = c("department_id", "course_name")
  ) %>% 
  mutate(
    course_name = if_else(!is.na(course_clean_sk), course_clean_sk, course_name)
  ) %>%
  distinct(stdid, course_name, facid, .keep_all = T)

# grade data after veda's work
df_grades <-
  read_dta(here::here("data/30jan2022/df_gradefac.dta")) %>% 
  filter(facid != "") %>%
  left_join(df_stu %>% select(stdid, department_id, reservation, caste, b_i_jeemain_score, b_math_g1_score, b_physics_g1_score, b_ses_1, b_ses_2, b_ses_3, b_ses_4, b_ses_5, b_ses_6, b_i_ses_1, b_i_ses_2, b_i_ses_3, b_ct_score, b_ql_score, b_i_enter_engineering_exam, elite, e_talkprof_research, e_workprof_research, you_believe_math = e_belief_1, mathprofs_believe_math = e_belief_2, most_classmates_believe_math = e_belief_3, you_believe_physics = e_belief_4, physprofs_believe_physics = e_belief_5, most_classmates_believe_physics = e_belief_6, b_mathstudy_30, e_mathstudy_30, b_physicsstudy_30, e_physicsstudy_30), by = "stdid") %>%
  left_join(read_dta(here::here("data/controls.dta")), by = "stdid") %>%
  left_join(read_dta(here::here("data/fac_covariates.dta")), by = "facid") %>% 
  arrange(department_id, course_name, course_grade_clean) %>% 
  group_by(department_id, course_name) %>% 
  mutate(
    course_rank = (scale(course_grade_clean) %>% pnorm() * 100) %>% as.vector
  ) %>% 
  ungroup() %>%
  mutate(
    univcode = str_sub(department_id, 1, 5),
    father_college = if_else(father_ed_ind > 3 & !is.na(father_ed_ind), 1L, 0L),
    father_college = if_else(is.na(father_ed_ind), NA_integer_, father_college),
    mother_college = if_else(mother_ed_ind > 3 & !is.na(mother_ed_ind), 1L, 0L),
    mother_college = if_else(is.na(mother_ed_ind), NA_integer_, mother_college),
    female = female %>% as.integer(),
    age = age %>% as.integer(),
  ) %>%
  fastDummies::dummy_cols(select_columns = c("b_i_enter_engineering_exam", "hstype", "area", "father_ed_ind", "mother_ed_ind"), remove_first_dummy = T, ignore_na = F) %>%
  relocate(department_id, course_name, stdid, course_rank) %>% 
  rename(reservation_stu = reservation) %>%
  filter(univcode != "IR036") %>% 
  mutate(
    # student variables
    # miss_age = if_else(is.na(age), 1L, 0L),
    # age = if_else(is.na(age), 0L, age),
    # 
    # miss_reservation_stu = if_else(is.na(reservation_stu), 1L, 0L),
    # reservation_stu = if_else(is.na(reservation_stu), 0L, reservation_stu),
    # 
    # miss_father_college = if_else(is.na(father_college), 1L, 0L),
    # father_college = if_else(is.na(father_college), 0L, father_college),
    # 
    # miss_mother_college = if_else(is.na(mother_college), 1L, 0L),
    # mother_college = if_else(is.na(mother_college), 0L, mother_college),
    # 
    # miss_b_i_jeemain_score = if_else(is.na(b_i_jeemain_score), 1L, 0L),
    # b_i_jeemain_score = if_else(is.na(b_i_jeemain_score), 0, b_i_jeemain_score),
    # 
    # miss_b_math_g1_score = if_else(is.na(b_math_g1_score), 1L, 0L),
    # b_math_g1_score = if_else(is.na(b_math_g1_score), 0, b_math_g1_score),
    # 
    # miss_b_physics_g1_score = if_else(is.na(b_physics_g1_score), 1L, 0L),
    # b_physics_g1_score = if_else(is.na(b_physics_g1_score), 0, b_physics_g1_score),
    # 
    # miss_b_ct_score = if_else(is.na(b_ct_score), 1L, 0L),
    # b_ct_score = if_else(is.na(b_ct_score), 0, b_ct_score),
    # 
    # miss_b_ql_score = if_else(is.na(b_ql_score), 1L, 0L),
    # b_ql_score = if_else(is.na(b_ql_score), 0, b_ql_score),
    # 
    # # faculty variables
    # miss_fac_associate_professor = if_else(is.na(fac_associate_professor), 1L, 0L),
    # fac_associate_professor = if_else(is.na(fac_associate_professor), 0, fac_associate_professor),
    # 
    # miss_fac_professor = if_else(is.na(fac_professor), 1L, 0L),
    # fac_professor = if_else(is.na(fac_professor), 0, fac_professor),
    # 
    # miss_fac_yearsinhighed = if_else(is.na(fac_yearsinhighed), 1L, 0L),
    # fac_yearsinhighed = if_else(is.na(fac_yearsinhighed), 0, fac_yearsinhighed),
    # 
    # miss_fac_highest_degree_phd = if_else(is.na(fac_highest_degree_phd), 1L, 0L),
    # fac_highest_degree_phd = if_else(is.na(fac_highest_degree_phd), 0, fac_highest_degree_phd),
    # 
    # miss_fac_highest_degree_phd_in_prog = if_else(is.na(fac_highest_degree_phd_in_prog), 1L, 0L),
    # fac_highest_degree_phd_in_prog = if_else(is.na(fac_highest_degree_phd_in_prog), 0, fac_highest_degree_phd_in_prog),
    # 
    # miss_fac_degree_college_elite = if_else(is.na(fac_degree_college_elite), 1L, 0L),
    # fac_degree_college_elite = if_else(is.na(fac_degree_college_elite), 0, fac_degree_college_elite),
    # 
    # miss_reservation_fac = if_else(is.na(reservation_fac), 1L, 0L),
    # reservation_fac = if_else(is.na(reservation_fac), 0, reservation_fac)
  ) %>%
  mutate_at(vars(b_ses_1, b_ses_2, b_ses_3, b_ses_4, b_ses_5, b_ses_6, b_i_ses_1, b_i_ses_2, b_i_ses_3), ~ as.integer(.)) %>%
  mutate(
    b_ses_1 = if_else(b_ses_1 == 1L, 1L, 0L) %>% replace_na(0L),
    b_ses_2 = if_else(b_ses_2 == 1L, 1L, 0L) %>% replace_na(0L),
    b_ses_3 = if_else(b_ses_3 == 1L, 1L, 0L) %>% replace_na(0L),
    b_ses_4 = if_else(b_ses_4 == 1L, 1L, 0L) %>% replace_na(0L),
    b_ses_5 = if_else(b_ses_5 == 1L, 1L, 0L) %>% replace_na(0L),
    b_ses_6 = if_else(b_ses_6 == 1L, 1L, 0L) %>% replace_na(0L),
    b_i_ses_1 = if_else(b_i_ses_1 == 1L, 1L, 0L) %>% replace_na(0L),
    b_i_ses_2 = if_else(b_i_ses_2 == 1L, 1L, 0L) %>% replace_na(0L),
    b_i_ses_3 = if_else(b_i_ses_3 == 1L, 1L, 0L) %>% replace_na(0L),
  ) %>%
  mutate(
    old_sib_factor = case_when(
      old_sib == 0 ~ "0",
      old_sib == 1 ~ "1",
      old_sib == 2 ~ "2",
      old_sib == 3 ~ "3",
      old_sib == 4 ~ "4",
      old_sib > 4 ~ "more",
      TRUE ~ NA_character_
    ) %>% as_factor(),
    young_sib_factor = case_when(
      young_sib == 0 ~ "0",
      young_sib == 1 ~ "1",
      young_sib == 2 ~ "2",
      young_sib == 3 ~ "3",
      young_sib == 4 ~ "4",
      young_sib > 4 ~ "more",
      TRUE ~ NA_character_
    ) %>% as_factor(),
    school_years_english_factor = case_when(
      school_years_english == 0 ~ "0",
      school_years_english >= 1 & school_years_english <= 9 ~ "1-9",
      school_years_english >= 10 & school_years_english <= 12 ~ "10-12",
      school_years_english >= 13 & school_years_english <= 16 ~ "13-16",
      TRUE ~ NA_character_
    ) %>% as_factor(),
  ) %>%
  fastDummies::dummy_cols(select_columns = c("old_sib_factor", "young_sib_factor", "school_years_english_factor"), remove_first_dummy = T, ignore_na = F, remove_selected_columns = T) %>%
  mutate_at(vars(b_i_enter_engineering_exam_2, b_i_enter_engineering_exam_3, area_2, area_3, hstype_2, hstype_3, hstype_4, hstype_5, hstype_6, hstype_7, father_ed_ind_2, father_ed_ind_3, father_ed_ind_4, father_ed_ind_5, father_ed_ind_6, father_ed_ind_7, father_ed_ind_8, mother_ed_ind_2, mother_ed_ind_3, mother_ed_ind_4, mother_ed_ind_5, mother_ed_ind_6, mother_ed_ind_7, mother_ed_ind_8), ~ replace_na(., 0L)) %>% 
  mutate_at(vars(contains("_sib_factor_")), ~ replace_na(., 0L)) %>% 
  mutate_at(vars(contains("school_years_english_factor")), ~ replace_na(., 0L))
  

rm(df)

# excluding students facing no gender variation
df_grades_sfix <-
  df_grades %>% 
  left_join(read_dta(here::here("data/cities.dta")) %>% select(stdid, district)) %>%
  mutate(district = str_squish(district) %>% str_to_title()) %>% 
  left_join(read_dta(here::here("data/districts_clean.dta"))) %>%
  arrange(stdid, fac_female) %>% 
  group_by(stdid) %>% 
  mutate(prop_female = mean(fac_female, na.rm = T)) %>% 
  ungroup() %>% 
  relocate(stdid, fac_female, prop_female) %>%
  filter(prop_female > 0, prop_female < 1)

univcodes <- df_grades_sfix %>% count(univcode) %>% pull(univcode)
depids <- df_grades_sfix %>% count(department_id) %>% pull(department_id)
stdids <- df_grades_sfix %>% distinct(stdid) %>% pull(stdid)


# filtering to all faculty surveyed during the endline phase who were also mentioned by students
facdata_mentions <-
  read_dta(here::here("data/all_appended.dta")) %>%
  filter(tag > 1) %>%  # endline only
  left_join(df_stu %>% select(stdid, department_id), by = "stdid") %>%  # get dep_id
  select(facid, department_id) %>% 
  count(facid, department_id) %>% 
  arrange(facid, desc(n)) %>% 
  distinct(facid, .keep_all = T) %>% 
  select(-n) %>% 
  left_join(read_dta(here::here("data/endline_faculty_data_final.dta")), by = "facid")

# fac_stereotype <-
#   read_dta("~/Downloads/faculty_data.dta") %>%
#   select(facid, views_gender_math_core) %>%
#   separate(views_gender_math_core, into = c("math_science_better_start", "math_science_better_after2yrs", "major_better_after2yrs"), sep = "::") %>%
#   mutate_at(vars(contains("better")), ~ str_replace(., ".*&&", "") %>% str_squish() %>% na_if(""))

1 Cronbach alphas

1.1 Confidence

Baseline math confidence:

df_stu %>% 
  select(b_subjective_4, b_subjective_6, b_subjective_7, b_subjective_9) %>% 
  mutate(across(contains("subjective"), ~ as.integer(.))) %>%
  mutate(across(contains("subjective"), ~scale(.)[,1])) %>%
  psych::alpha() %>% 
  pluck("total", "raw_alpha")

## [1] 0.769911

Baseline physics confidence:

df_stu %>% 
  select(b_subjective_14, b_subjective_16, b_subjective_17, b_subjective_19) %>% 
  mutate(across(contains("subjective"), ~ as.integer(.))) %>%
  mutate(across(contains("subjective"), ~scale(.)[,1])) %>%
  psych::alpha() %>% 
  pluck("total", "raw_alpha")

## [1] 0.799303

Endline math confidence:

df_stu %>% 
  select(e_subjective_4, e_subjective_6, e_subjective_7, e_subjective_9) %>% 
  mutate(across(contains("subjective"), ~ as.integer(.))) %>%
  mutate(across(contains("subjective"), ~scale(.)[,1])) %>%
  psych::alpha() %>% 
  pluck("total", "raw_alpha")

## [1] 0.7827924

Endline physics confidence:

df_stu %>% 
  select(e_subjective_14, e_subjective_16, e_subjective_17, e_subjective_19) %>% 
  mutate(across(contains("subjective"), ~ as.integer(.))) %>%
  mutate(across(contains("subjective"), ~scale(.)[,1])) %>%
  psych::alpha() %>% 
  pluck("total", "raw_alpha")

## [1] 0.8005205

1.2 Anxiety

Endline math anxiety:

df_stu %>% 
  select(e_subjective_1, e_subjective_2, e_subjective_3, e_subjective_5, e_subjective_8, e_subjective_10) %>%
  mutate(across(contains("subjective"), ~ as.integer(.))) %>%
  mutate(across(contains("subjective"), ~scale(5 - .)[,1])) %>% 
  psych::alpha() %>% 
  pluck("total", "raw_alpha")

## [1] 0.8190887

Endline physics anxiety:

df_stu %>% 
  select(e_subjective_11, e_subjective_12, e_subjective_13, e_subjective_15, e_subjective_18, e_subjective_20) %>%
  mutate(across(contains("subjective"), ~ as.integer(.))) %>%
  mutate(across(contains("subjective"), ~scale(5 - .)[,1])) %>% 
  psych::alpha() %>% 
  pluck("total", "raw_alpha")

## [1] 0.8239434

Baseline math anxiety:

df_stu %>% 
  select(b_subjective_1, b_subjective_2, b_subjective_3, b_subjective_5, b_subjective_8, b_subjective_10) %>%
  mutate(across(contains("subjective"), ~ as.integer(.))) %>%
  mutate(across(contains("subjective"), ~scale(5 - .)[,1])) %>% 
  psych::alpha() %>% 
  pluck("total", "raw_alpha")

## [1] 0.8072705

Baseline physics anxiety:

df_stu %>% 
  select(b_subjective_11, b_subjective_12, b_subjective_13, b_subjective_15, b_subjective_18, b_subjective_20) %>%
  mutate(across(contains("subjective"), ~ as.integer(.))) %>%
  mutate(across(contains("subjective"), ~scale(5 - .)[,1])) %>% 
  psych::alpha() %>% 
  pluck("total", "raw_alpha")

## [1] 0.8126959

2 Factor scores

# endline math anxiety

df_stu <- 
  df_stu %>%
  mutate(
    e_math_anxiety = select(., e_subjective_1, e_subjective_2, e_subjective_3, e_subjective_5, e_subjective_8, e_subjective_10) %>%
      mutate(across(contains("subjective"), ~ as.integer(.))) %>%
      mutate(across(contains("subjective"), ~scale(5 - .)[,1])) %>%
      psych::principal(nfactors = 1, rotate = "none") %>%
      pluck("scores") %>%
      as.vector()
  )

# endline physics anxiety

df_stu <- 
  df_stu %>%
  mutate(
    e_physics_anxiety = select(., e_subjective_11, e_subjective_12, e_subjective_13, e_subjective_15, e_subjective_18, e_subjective_20) %>%
      mutate(across(contains("subjective"), ~ as.integer(.))) %>%
      mutate(across(contains("subjective"), ~scale(5 - .)[,1])) %>%
      psych::principal(nfactors = 1, rotate = "none") %>%
      pluck("scores") %>%
      as.vector()
  )

# baseline math anxiety

df_stu <- 
  df_stu %>%
  mutate(
    b_math_anxiety = select(., b_subjective_1, b_subjective_2, b_subjective_3, b_subjective_5, b_subjective_8, b_subjective_10) %>%
      mutate(across(contains("subjective"), ~ as.integer(.))) %>%
      mutate(across(contains("subjective"), ~scale(5 - .)[,1])) %>%
      psych::principal(nfactors = 1, rotate = "none") %>%
      pluck("scores") %>%
      as.vector()
  )

# baseline physics anxiety

df_stu <- 
  df_stu %>%
  mutate(
    b_physics_anxiety = select(., b_subjective_11, b_subjective_12, b_subjective_13, b_subjective_15, b_subjective_18, b_subjective_20) %>%
      mutate(across(contains("subjective"), ~ as.integer(.))) %>%
      mutate(across(contains("subjective"), ~scale(5 - .)[,1])) %>%
      psych::principal(nfactors = 1, rotate = "none") %>%
      pluck("scores") %>%
      as.vector()
  )

# baseline math confidence

df_stu <- 
  df_stu %>%
  mutate(
    b_math_confidence = select(., b_subjective_4, b_subjective_6, b_subjective_7, b_subjective_9) %>% 
      mutate(across(contains("subjective"), ~ as.integer(.))) %>%
      mutate(across(contains("subjective"), ~scale(.)[,1])) %>%
      psych::principal(nfactors = 1, rotate = "none") %>%
      pluck("scores") %>%
      as.vector()
  )

# baseline physics confidence

df_stu <- 
  df_stu %>%
  mutate(
    b_physics_confidence = select(., b_subjective_14, b_subjective_16, b_subjective_17, b_subjective_19) %>% 
      mutate(across(contains("subjective"), ~ as.integer(.))) %>%
      mutate(across(contains("subjective"), ~scale(.)[,1])) %>%
      psych::principal(nfactors = 1, rotate = "none") %>%
      pluck("scores") %>%
      as.vector()
  )

# endline math confidence

df_stu <- 
  df_stu %>%
  mutate(
    e_math_confidence = select(., e_subjective_4, e_subjective_6, e_subjective_7, e_subjective_9) %>% 
      mutate(across(contains("subjective"), ~ as.integer(.))) %>%
      mutate(across(contains("subjective"), ~scale(.)[,1])) %>%
      psych::principal(nfactors = 1, rotate = "none") %>%
      pluck("scores") %>%
      as.vector()
  )

# endline physics confidence

df_stu <- 
  df_stu %>%
  mutate(
    e_physics_confidence = select(., e_subjective_14, e_subjective_16, e_subjective_17, e_subjective_19) %>% 
      mutate(across(contains("subjective"), ~ as.integer(.))) %>%
      mutate(across(contains("subjective"), ~scale(.)[,1])) %>%
      psych::principal(nfactors = 1, rotate = "none") %>%
      pluck("scores") %>%
      as.vector()
  )

df_grades_sfix <- 
  df_grades_sfix %>% 
  left_join(
    df_stu %>% 
      select(stdid, e_math_anxiety, e_physics_anxiety, b_math_anxiety, b_physics_anxiety, e_math_confidence, e_physics_confidence, b_math_confidence, b_physics_confidence),
    by = "stdid"
  )

Table 2:

df_temp1 <-
  df_grades_sfix %>%
  filter(subject == "math") %>%
  group_by(stdid, subject, female, reservation_stu, father_college, mother_college, age, department_id, b_math_anxiety, e_math_anxiety, b_math_confidence, e_math_confidence) %>% 
  summarise(
    reservation_fac = mean(reservation_fac, na.rm = T) * 10,
    fac_associate_professor = mean(fac_associate_professor, na.rm = T) * 10,
    fac_professor = mean(fac_professor, na.rm = T) * 10,
    fac_yearsinhighed = mean(fac_yearsinhighed, na.rm = T) * 10,
    fac_highest_degree_phd = mean(fac_highest_degree_phd, na.rm = T) * 10,
    fac_highest_degree_phd_in_prog = mean(fac_highest_degree_phd_in_prog, na.rm = T) * 10,
    fac_degree_college_elite = mean(fac_degree_college_elite, na.rm = T) * 10,
    fac_female = mean(fac_female, na.rm = T) * 10,
    course_rank = mean(course_rank, na.rm = T)
  ) %>% 
  ungroup() %>% 
  mutate(
    b_anxiety = scale(b_math_anxiety) %>% as.vector,
    e_anxiety = scale(e_math_anxiety) %>% as.vector,
    b_confidence = scale(b_math_confidence) %>% as.vector,
    e_confidence = scale(e_math_confidence) %>% as.vector,
    # handle age missingness
    miss_age = if_else(is.na(age), 1L, 0L),
    age = if_else(is.na(age), 0L, age),
    course_rank = scale(course_rank) %>% as.vector,
    female_x_fac_female = female * fac_female
  )

df_temp2 <-
  df_grades_sfix %>%
  filter(subject == "physics") %>%
  group_by(stdid, subject, female, reservation_stu, father_college, mother_college, age, department_id, b_physics_anxiety, e_physics_anxiety, b_physics_confidence, e_physics_confidence) %>% 
  summarise(
    reservation_fac = mean(reservation_fac, na.rm = T) * 10,
    fac_associate_professor = mean(fac_associate_professor, na.rm = T) * 10,
    fac_professor = mean(fac_professor, na.rm = T) * 10,
    fac_yearsinhighed = mean(fac_yearsinhighed, na.rm = T) * 10,
    fac_highest_degree_phd = mean(fac_highest_degree_phd, na.rm = T) * 10,
    fac_highest_degree_phd_in_prog = mean(fac_highest_degree_phd_in_prog, na.rm = T) * 10,
    fac_degree_college_elite = mean(fac_degree_college_elite, na.rm = T) * 10,
    fac_female = mean(fac_female, na.rm = T) * 10,
    course_rank = mean(course_rank, na.rm = T)
  ) %>% 
  ungroup() %>% 
  mutate(
    b_anxiety = scale(b_physics_anxiety) %>% as.vector,
    e_anxiety = scale(e_physics_anxiety) %>% as.vector,
    b_confidence = scale(b_physics_confidence) %>% as.vector,
    e_confidence = scale(e_physics_confidence) %>% as.vector,
    # handle age missingness
    miss_age = if_else(is.na(age), 1L, 0L),
    age = if_else(is.na(age), 0L, age),
    course_rank = scale(course_rank) %>% as.vector,
    female_x_fac_female = female * fac_female
  )


df_temp <-
  bind_rows(df_temp1, df_temp2) %>%
  arrange(stdid, subject) %>% 
  relocate(stdid, subject)

rm(df_temp1, df_temp2)

lm1 <-
  lm_robust(e_confidence ~ female * fac_female + subject + b_confidence + reservation_stu + age + miss_age + father_college + mother_college + fac_associate_professor + fac_professor + fac_yearsinhighed + fac_highest_degree_phd + fac_highest_degree_phd_in_prog + fac_degree_college_elite + reservation_fac, data = df_temp, se_type = "stata", fixed_effects = ~ department_id)

lm2 <-
  lm_robust(e_anxiety ~ female * fac_female + subject + b_anxiety + reservation_stu + age + miss_age + father_college + mother_college + fac_associate_professor + fac_professor + fac_yearsinhighed + fac_highest_degree_phd + fac_highest_degree_phd_in_prog + fac_degree_college_elite + reservation_fac, data = df_temp, se_type = "stata", fixed_effects = ~ department_id)

knitreg(list(lm1, lm2), custom.note = "%stars", stars = c(0.01, 0.05, 0.1), include.ci = F, dcolumn = T, booktabs = T, float.pos = "H", caption = "", digits = 3, include.nclust = F, include.rsquared = F, include.adjrs = F, include.rmse = F, custom.model.names = c("Confidence", "Anxiety"), custom.coef.map = list("female:fac_female" = "Female student x Female faculty share", "fac_female" = "Female faculty share", "female" = "Female student"))

	Confidence	Anxiety
Female student x Female faculty share	-0.011	-0.057***
	(0.015)	(0.015)
Female faculty share	-0.005	0.006
	(0.013)	(0.014)
Female student	0.014	0.062
	(0.064)	(0.068)
Num. obs.	1568	1556
***p < 0.01; **p < 0.05; *p < 0.1

3 Mediation analyses

3.1 Anxiety

All students, female stu x female fac interaction as treatment:

# Step 1: Model M ~ X (mediator model)
model.m <- lm(e_anxiety ~ female_x_fac_female + female + fac_female + reservation_stu + age + miss_age + father_college + mother_college + fac_associate_professor + fac_professor + fac_yearsinhighed + fac_highest_degree_phd + fac_highest_degree_phd_in_prog + fac_degree_college_elite + reservation_fac, data = df_temp %>% drop_na(e_anxiety))

# Step 2: Model Y ~ X + M (outcome model)
model.y <- lm(course_rank ~ female_x_fac_female + e_anxiety + female + fac_female + reservation_stu + age + miss_age + father_college + mother_college + fac_associate_professor + fac_professor + fac_yearsinhighed + fac_highest_degree_phd + fac_highest_degree_phd_in_prog + fac_degree_college_elite + reservation_fac, data = df_temp)

# Step 3: Mediation analysis
results <- mediation::mediate(model.m, model.y, 
                   treat = "female_x_fac_female", 
                   mediator = "e_anxiety",
                   boot = TRUE, 
                   sims = 1000)

summary(results)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                  Estimate 95% CI Lower 95% CI Upper p-value    
## ACME            0.0119667    0.0056353    0.0186000  <2e-16 ***
## ADE            -0.0380642   -0.0693565   -0.0027793   0.038 *  
## Total Effect   -0.0260975   -0.0587958    0.0090127   0.140    
## Prop. Mediated -0.4585366   -3.4086674    3.6496338   0.140    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 1729 
## 
## 
## Simulations: 1000

plot(results)

Female students only:

# Step 1: Model M ~ X (mediator model)
model.m <- lm(e_anxiety ~ fac_female + reservation_stu + age + miss_age + father_college + mother_college + fac_associate_professor + fac_professor + fac_yearsinhighed + fac_highest_degree_phd + fac_highest_degree_phd_in_prog + fac_degree_college_elite + reservation_fac, data = df_temp %>% filter(female == 1) %>% drop_na(e_anxiety))

# Step 2: Model Y ~ X + M (outcome model)
model.y <- lm(course_rank ~ fac_female + e_anxiety + reservation_stu + age + miss_age + father_college + mother_college + fac_associate_professor + fac_professor + fac_yearsinhighed + fac_highest_degree_phd + fac_highest_degree_phd_in_prog + fac_degree_college_elite + reservation_fac, data = df_temp %>% filter(female == 1))

# Step 3: Mediation analysis
results <- mediation::mediate(model.m, model.y, 
                   treat = "fac_female", 
                   mediator = "e_anxiety",
                   boot = TRUE, 
                   sims = 1000)

summary(results)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                   Estimate 95% CI Lower 95% CI Upper p-value   
## ACME             0.0110069    0.0028527    0.0202437   0.010 **
## ADE             -0.0186328   -0.0524821    0.0126291   0.232   
## Total Effect    -0.0076259   -0.0416317    0.0261877   0.622   
## Prop. Mediated  -1.4433456  -11.3378671    8.0638307   0.628   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 562 
## 
## 
## Simulations: 1000

plot(results)

Male students only:

# Step 1: Model M ~ X (mediator model)
model.m <- lm(e_anxiety ~ fac_female + reservation_stu + age + miss_age + father_college + mother_college + fac_associate_professor + fac_professor + fac_yearsinhighed + fac_highest_degree_phd + fac_highest_degree_phd_in_prog + fac_degree_college_elite + reservation_fac, data = df_temp %>% filter(female == 0) %>% drop_na(e_anxiety))

# Step 2: Model Y ~ X + M (outcome model)
model.y <- lm(course_rank ~ fac_female + e_anxiety + reservation_stu + age + miss_age + father_college + mother_college + fac_associate_professor + fac_professor + fac_yearsinhighed + fac_highest_degree_phd + fac_highest_degree_phd_in_prog + fac_degree_college_elite + reservation_fac, data = df_temp %>% filter(female == 0))

# Step 3: Mediation analysis
results <- mediation::mediate(model.m, model.y, 
                   treat = "fac_female", 
                   mediator = "e_anxiety",
                   boot = TRUE, 
                   sims = 1000)

summary(results)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                   Estimate 95% CI Lower 95% CI Upper p-value  
## ACME           -0.00366624  -0.00779264   0.00011921   0.054 .
## ADE             0.00036366  -0.01832029   0.02022600   0.992  
## Total Effect   -0.00330257  -0.02215784   0.01716742   0.732  
## Prop. Mediated  1.11011536  -7.59067974   4.79610806   0.714  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 1167 
## 
## 
## Simulations: 1000

plot(results)

3.2 Confidence

All students, female stu x female fac interaction as treatment:

# Step 1: Model M ~ X (mediator model)
model.m <- lm(e_confidence ~ female_x_fac_female + female + fac_female + reservation_stu + age + miss_age + father_college + mother_college + fac_associate_professor + fac_professor + fac_yearsinhighed + fac_highest_degree_phd + fac_highest_degree_phd_in_prog + fac_degree_college_elite + reservation_fac, data = df_temp %>% drop_na(e_confidence))

# Step 2: Model Y ~ X + M (outcome model)
model.y <- lm(course_rank ~ female_x_fac_female + e_confidence + female + fac_female + reservation_stu + age + miss_age + father_college + mother_college + fac_associate_professor + fac_professor + fac_yearsinhighed + fac_highest_degree_phd + fac_highest_degree_phd_in_prog + fac_degree_college_elite + reservation_fac, data = df_temp)

# Step 3: Mediation analysis
results <- mediation::mediate(model.m, model.y, 
                   treat = "female_x_fac_female", 
                   mediator = "e_confidence",
                   boot = TRUE, 
                   sims = 1000)

summary(results)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                   Estimate 95% CI Lower 95% CI Upper p-value  
## ACME            0.00433474  -0.00045205   0.01014912   0.076 .
## ADE            -0.03054338  -0.06291720   0.00143577   0.060 .
## Total Effect   -0.02620863  -0.05923856   0.00592994   0.116  
## Prop. Mediated -0.16539376  -2.04360994   1.08352045   0.188  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 1735 
## 
## 
## Simulations: 1000

plot(results)

Female students only:

# Step 1: Model M ~ X (mediator model)
model.m <- lm(e_confidence ~ fac_female + reservation_stu + age + miss_age + father_college + mother_college + fac_associate_professor + fac_professor + fac_yearsinhighed + fac_highest_degree_phd + fac_highest_degree_phd_in_prog + fac_degree_college_elite + reservation_fac, data = df_temp %>% filter(female == 1) %>% drop_na(e_confidence))

# Step 2: Model Y ~ X + M (outcome model)
model.y <- lm(course_rank ~ fac_female + e_confidence + reservation_stu + age + miss_age + father_college + mother_college + fac_associate_professor + fac_professor + fac_yearsinhighed + fac_highest_degree_phd + fac_highest_degree_phd_in_prog + fac_degree_college_elite + reservation_fac, data = df_temp %>% filter(female == 1))

# Step 3: Mediation analysis
results <- mediation::mediate(model.m, model.y, 
                   treat = "fac_female", 
                   mediator = "e_confidence",
                   boot = TRUE, 
                   sims = 1000)

summary(results)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                  Estimate 95% CI Lower 95% CI Upper p-value
## ACME            0.0041146   -0.0039791    0.0126946   0.298
## ADE            -0.0122971   -0.0443945    0.0174192   0.436
## Total Effect   -0.0081825   -0.0420999    0.0225491   0.630
## Prop. Mediated -0.5028480   -4.2266439    3.2607702   0.848
## 
## Sample Size Used: 560 
## 
## 
## Simulations: 1000

plot(results)

Male students only:

# Step 1: Model M ~ X (mediator model)
model.m <- lm(e_confidence ~ fac_female + reservation_stu + age + miss_age + father_college + mother_college + fac_associate_professor + fac_professor + fac_yearsinhighed + fac_highest_degree_phd + fac_highest_degree_phd_in_prog + fac_degree_college_elite + reservation_fac, data = df_temp %>% filter(female == 0) %>% drop_na(e_confidence))

# Step 2: Model Y ~ X + M (outcome model)
model.y <- lm(course_rank ~ fac_female + e_confidence + reservation_stu + age + miss_age + father_college + mother_college + fac_associate_professor + fac_professor + fac_yearsinhighed + fac_highest_degree_phd + fac_highest_degree_phd_in_prog + fac_degree_college_elite + reservation_fac, data = df_temp %>% filter(female == 0))

# Step 3: Mediation analysis
results <- mediation::mediate(model.m, model.y, 
                   treat = "fac_female", 
                   mediator = "e_confidence",
                   boot = TRUE, 
                   sims = 1000)

summary(results)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                   Estimate 95% CI Lower 95% CI Upper p-value
## ACME           -0.00099019  -0.00406790   0.00169239   0.462
## ADE            -0.00175747  -0.02145989   0.01779428   0.920
## Total Effect   -0.00274767  -0.02218984   0.01742164   0.836
## Prop. Mediated  0.36037635  -2.10213813   3.23889059   0.918
## 
## Sample Size Used: 1175 
## 
## 
## Simulations: 1000

plot(results)