+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Mind the gender gap: COVID-19 lockdown effects on gender differences in research
+Iñaki Úcar, Margarita Torre, Antonio Elías Fernández
+ +
+
+Functions
get_file <- function(x) {
+ dir.create("data", showWarnings=FALSE)
+ file <- file.path("data", x)
+ if (!file.exists(file)) download.file(
+ paste0("https://zenodo.org/record/5142676/files/", x, "?download=1"), file)
+ file
+}
+
+mutate_cond <- function(.data, condition, ..., envir = parent.frame()) {
+ require(dplyr)
+
+ condition <- eval(substitute(condition), .data, envir)
+ .data[condition, ] <- mutate(.data[condition, ], ...)
+ .data
+}
+
+get_main <- function(repo, data, n=100) {
+ require(dplyr)
+
+ subcat <- data %>%
+ filter(repository %in% repo) %>%
+ group_by(subcategory) %>%
+ summarise(weight = n(), .groups="drop") %>%
+ arrange(desc(weight)) %>%
+ pull(subcategory)
+
+ data %>%
+ filter(repository %in% repo) %>%
+ group_by(id) %>%
+ summarise(main = subcat[subcat %in% subcategory][1], .groups="drop") %>%
+ group_by(main) %>%
+ summarise(N = n(), .groups="drop") %>%
+ arrange(desc(N)) %>%
+ filter(N >= n) %>%
+ pull(main)
+}
+
+# performance
+model_performance <- function(m) {
+ require(ggplot2)
+
+ # obs. vs fitted
+ df <- data.frame(fitted=fitted(m), response=model.response(model.frame(m)))
+ ggplot(df) + aes(fitted, response) +
+ geom_point(alpha=0.3) + geom_abline() + geom_smooth(method="lm") +
+ ggpmisc::stat_poly_eq(formula=y~x, parse=TRUE)
+}
+
+1 Data preparation
+
+
+1.1 Cleaning and filtering
+library(dplyr)
+
+articles <- readr::read_csv(get_file("categories.csv")) %>%
+ left_join(readr::read_csv(get_file("articles.csv")), by="id") %>%
+ rename(subcategory = subcategory_name) %>%
+ select(id, repository, category, subcategory, date) %>%
+ distinct() %>%
+ collect() %>%
+
+ # define main categories for repo != arXiv
+ mutate_cond(subcategory %in% c("Epidemiology", "Clinical Trials"), repository = "medrxiv") %>%
+ mutate_cond(repository == "medrxiv", category = "Health Sciences") %>%
+ mutate_cond(repository == "biorxiv", category = "Biology") %>%
+ mutate_cond(repository == "psyarxiv", category = "Psychology") %>%
+ mutate_cond(repository == "socarxiv", category = "Social Sciences")
+
+articles %>%
+ group_by(repository, category) %>%
+ summarise(subcategories=length(unique(subcategory)), n=n())
+
+
+articles <- articles %>%
+ # mark lockdown period & move time reference to 0
+ mutate(year = lubridate::year(date), month = lubridate::month(date)) %>%
+ mutate(lockdown = year == 2020 & month > 2) %>%
+ mutate(yearmon = (year - min(year)) + (month - 1) / 12) %>%
+
+ # adjustments to Biology and Economics
+ mutate_cond(category == "Quantitative Biology", category = "Biology") %>%
+ mutate_cond(category == "Quantitative Finance", category = "Economics") %>%
+
+ # adjustments to socarxiv
+ filter(subcategory != "Social and Behavioral Sciences") %>%
+ mutate_cond(repository == "socarxiv" & subcategory %in% c(
+ "Science and Technology Studies",
+ "Environmental Studies",
+ "International and Area Studies",
+ "Leisure Studies",
+ "Organization Development",
+ "Leadership Studies"
+ ), subcategory = "Other Social and Behavioral Sciences") %>%
+ mutate_cond(repository == "socarxiv" & subcategory %in% c(
+ "Library and Information Science",
+ "Linguistics"
+ ), subcategory = "Arts and Humanities") %>%
+ mutate_cond(repository == "socarxiv" & subcategory %in% c(
+ "Urban Studies and Planning",
+ "Social Statistics"
+ ), subcategory = "Sociology") %>%
+ mutate_cond(repository == "socarxiv" & subcategory %in% c(
+ "Social Work",
+ "Legal Studies"
+ ), subcategory = "Law") %>%
+ mutate_cond(repository == "socarxiv" & subcategory %in% c(
+ "Public Affairs, Public Policy and Public Administration"
+ ), subcategory = "Political Science") %>%
+ mutate_cond(repository == "socarxiv" & subcategory %in% c(
+ "Agricultural and Resource Economics"
+ ), subcategory = "Economics") %>%
+ mutate_cond(id %in% filter(
+ ., repository == "socarxiv" & subcategory == "Psychology")$id,
+ category = "Psychology") %>%
+ filter(subcategory != "Psychology") %>%
+ na.omit() %>%
+ distinct() %>%
+
+ # get just main categories with more than 100 papers for socarxiv & psyarxiv
+ filter((!repository %in% c("socarxiv", "psyarxiv")) | subcategory %in% unlist(
+ lapply(c("socarxiv", "psyarxiv"), get_main, .)))
+
+articles %>%
+ group_by(category) %>%
+ summarise(subcategories=length(unique(subcategory)), n=n())
+
+
+text <- readr::read_csv(get_file("text.csv")) %>%
+ select(id, title) %>%
+ collect() %>%
+ mutate(covidpaper = grepl("covid-19", title, ignore.case=TRUE) |
+ grepl("sars-cov-2", title, ignore.case=TRUE) |
+ grepl("coronavirus", title, ignore.case=TRUE))authors <- readr::read_csv(get_file("authors.csv")) %>%
+ distinct() %>%
+ collect() %>%
+ mutate(across(probability, as.numeric)) %>%
+ mutate(across(alphabetical_ordered, as.logical)) %>%
+ mutate_cond(is.na(alphabetical_ordered), alphabetical_ordered=TRUE)
+
+1.2 Feature engineering
+merge_info <- function(.data) .data %>%
+ left_join(articles, by="id") %>%
+ left_join(text[, c("id", "covidpaper")], by="id") %>%
+ distinct() %>%
+ na.omit() %>%
+ mutate_cond(year < 2020, covidpaper = FALSE) %>%
+ group_by(subcategory) %>%
+ filter(min(year) < 2020) %>%
+ ungroup()
+
+# features all
+df.id <- authors %>%
+ filter(probability >= 0.95 & count >= 10) %>%
+ group_by(id) %>%
+ summarise(n_male = sum(gender == "male", na.rm=TRUE),
+ n_female = sum(gender == "female", na.rm=TRUE),
+ n_na = sum(is.na(gender)),
+ total = n_male + n_female, .groups="drop") %>%
+ merge_info() %>%
+ # remove papers with more than 25% of authors with missing gender
+ filter(n_na < 0.25 * (n_na + n_male + n_female)) %>%
+ # remove observations with less than 30 people per month
+ group_by(repository, category, subcategory, covidpaper, lockdown, yearmon) %>%
+ filter(sum(total) > 30) %>%
+ ungroup()
+df.all <- df.id %>%
+ group_by(repository, category, subcategory, covidpaper, lockdown, yearmon) %>%
+ summarise(p_male = sum(n_male) / sum(total),
+ total = sum(total), .groups="drop")
+
+# features first
+df.first <- authors %>%
+ filter(probability >= 0.95 & count >= 10) %>%
+ filter(!alphabetical_ordered & rank == "first") %>%
+ merge_info() %>%
+ group_by(repository, category, subcategory, covidpaper, lockdown, yearmon) %>%
+ summarise(n_male = sum(gender == "male", na.rm=TRUE),
+ n_female = sum(gender == "female", na.rm=TRUE),
+ total = n_male + n_female,
+ p_male = n_male / total, .groups="drop")
+
+# features last
+df.last <- authors %>%
+ filter(probability >= 0.95 & count >= 10) %>%
+ filter(!alphabetical_ordered & rank == "last") %>%
+ merge_info() %>%
+ group_by(repository, category, subcategory, covidpaper, lockdown, yearmon) %>%
+ summarise(n_male = sum(gender == "male", na.rm=TRUE),
+ n_female = sum(gender == "female", na.rm=TRUE),
+ total = n_male + n_female,
+ p_male = n_male / total, .groups="drop")
+
+# features single
+df.single <- authors %>%
+ filter(probability >= 0.95 & count >= 10) %>%
+ filter(rank == "single") %>%
+ merge_info() %>%
+ group_by(repository, category, subcategory, covidpaper, lockdown, yearmon) %>%
+ summarise(n_male = sum(gender == "male", na.rm=TRUE),
+ n_female = sum(gender == "female", na.rm=TRUE),
+ total = n_male + n_female,
+ p_male = n_male / total, .groups="drop")
+
+2 Descriptive
+
+
+2.1 Number of papers per month
+library(ggplot2)
+theme_set(theme_bw())
+
+df.plot.papers <- count(df.id, yearmon, category)
+df.plot.papers.all <- df.plot.papers %>%
+ group_by(yearmon) %>%
+ summarise(n = sum(n), .groups="drop") %>%
+ mutate(category="(all)")
+
+ggplot(df.plot.papers) +
+ aes(yearmon+2017, n) + facet_wrap(~category, scales="free_y") +
+ geom_col(data=df.plot.papers.all) +
+ geom_smooth(data=df.plot.papers.all) +
+ geom_col() + geom_smooth() +
+ zoo::scale_x_yearmon(format="%Y") +
+ labs(y="Number of papers per month", x=NULL)## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
+## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
+
+2.2 Number of authors per month
+df.plot.authors <- df.id %>%
+ group_by(yearmon, category) %>%
+ summarise(n = sum(total), .groups="drop")
+df.plot.authors.all <- df.plot.authors %>%
+ group_by(yearmon) %>%
+ summarise(n = sum(n), .groups="drop") %>%
+ mutate(category="(all)")
+
+ggplot(df.plot.authors) +
+ aes(yearmon+2017, n) + facet_wrap(~category, scales="free_y") +
+ geom_col(data=df.plot.authors.all) +
+ geom_smooth(data=df.plot.authors.all) +
+ geom_col() + geom_smooth() +
+ zoo::scale_x_yearmon(format="%Y") +
+ labs(y="Number of authors per month", x=NULL)## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
+## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
+
+2.3 Proportion of males per month
+df.plot.p_male <- df.id %>%
+ group_by(yearmon, category) %>%
+ summarise(p_male = sum(n_male) / sum(total), .groups="drop")
+df.plot.p_male.all <- df.id %>%
+ group_by(yearmon) %>%
+ summarise(p_male = sum(n_male) / sum(total), .groups="drop") %>%
+ mutate(category="(all)")
+
+ggplot(df.plot.p_male) +
+ aes(yearmon+2017, p_male) + facet_wrap(~category) +
+ geom_point(data=df.plot.p_male.all) +
+ geom_smooth(method="gam", data=df.plot.p_male.all) +
+ geom_point() + geom_smooth(method="gam") +
+ zoo::scale_x_yearmon(format="%Y") +
+ labs(y="Proportion of male authors", x=NULL)## `geom_smooth()` using formula 'y ~ s(x, bs = "cs")'
+## `geom_smooth()` using formula 'y ~ s(x, bs = "cs")'
+
+
+
+
+3 Modelling
+
+
+3.1 Simple model
+model.glm <- p_male ~ yearmon + lockdown + covidpaper
+fit.glm <- glm(model.glm, df.all, family=binomial, weights=total)
+summary(fit.glm)##
+## Call:
+## glm(formula = model.glm, family = binomial, data = df.all, weights = total)
+##
+## Deviance Residuals:
+## Min 1Q Median 3Q Max
+## -26.0616 -1.3754 0.9651 2.5727 16.1094
+##
+## Coefficients:
+## Estimate Std. Error z value Pr(>|z|)
+## (Intercept) 1.826402 0.006090 299.901 <2e-16 ***
+## yearmon -0.104284 0.003042 -34.283 <2e-16 ***
+## lockdownTRUE 0.071570 0.007224 9.908 <2e-16 ***
+## covidpaperTRUE -0.613698 0.019441 -31.568 <2e-16 ***
+## ---
+## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+##
+## (Dispersion parameter for binomial family taken to be 1)
+##
+## Null deviance: 64761 on 3367 degrees of freedom
+## Residual deviance: 62173 on 3364 degrees of freedom
+## AIC: 79001
+##
+## Number of Fisher Scoring iterations: 4model_performance(fit.glm)## `geom_smooth()` using formula 'y ~ x'
performance::check_model(fit.glm)## Loading required namespace: qqplotr
+
+3.2 Hierarchical model
+library(lme4)## Loading required package: Matrixmodel <- p_male ~ yearmon + lockdown + covidpaper + (1 | category/subcategory)
+fit.all <- glmer(model, df.all, family=binomial, weights=total)
+summary(fit.all)## Generalized linear mixed model fit by maximum likelihood (Laplace
+## Approximation) [glmerMod]
+## Family: binomial ( logit )
+## Formula: p_male ~ yearmon + lockdown + covidpaper + (1 | category/subcategory)
+## Data: df.all
+## Weights: total
+##
+## AIC BIC logLik deviance df.resid
+## 22667.8 22704.5 -11327.9 22655.8 3362
+##
+## Scaled residuals:
+## Min 1Q Median 3Q Max
+## -6.8130 -0.7773 0.0898 0.8462 6.2945
+##
+## Random effects:
+## Groups Name Variance Std.Dev.
+## subcategory:category (Intercept) 0.0852 0.2919
+## category (Intercept) 0.3838 0.6196
+## Number of obs: 3368, groups: subcategory:category, 192; category, 10
+##
+## Fixed effects:
+## Estimate Std. Error z value Pr(>|z|)
+## (Intercept) 1.595286 0.199014 8.016 1.09e-15 ***
+## yearmon -0.049239 0.003202 -15.378 < 2e-16 ***
+## lockdownTRUE 0.030571 0.007491 4.081 4.48e-05 ***
+## covidpaperTRUE 0.076362 0.021791 3.504 0.000458 ***
+## ---
+## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+##
+## Correlation of Fixed Effects:
+## (Intr) yearmn lcTRUE
+## yearmon -0.030
+## lockdwnTRUE 0.011 -0.629
+## covdpprTRUE -0.005 -0.001 -0.143model_performance(fit.all)## `geom_smooth()` using formula 'y ~ x'
performance::check_model(fit.all)## Warning in sqrt(crit * n_params * (1 - .hat)/.hat): NaNs produced## Warning in sqrt(cook.levels[.level] * n_params * (1 - .hat80)/.hat80): NaNs
+## produced
+
+## Warning in sqrt(cook.levels[.level] * n_params * (1 - .hat80)/.hat80): NaNs
+## produced
df.re.category <- sjPlot::get_model_data(fit.all, "re")[[2]] %>%
+ mutate(group = ifelse(conf.low < 1 & conf.high > 1, NA, group)) %>%
+ mutate(term = forcats::fct_reorder(term, estimate))
+
+ggplot(df.re.category) +
+ aes(estimate, term, xmin=conf.low, xmax=conf.high, color=group) +
+ geom_vline(xintercept=1, color="black", linetype="dashed") +
+ geom_errorbarh(height=0, size=1) + geom_point(size=2) +
+ scale_x_log10(breaks=c(0.2, 0.5, 1, 2, 5)) +
+ scale_color_manual(
+ breaks=c("pos", "neg"), values=c("blue", "red"),
+ na.value=grDevices::adjustcolor("grey50", 0.5)) +
+ labs(y=NULL, x="Odds ratio", title="Random effect: category") +
+ theme(legend.position="none")
df.re.subcategory <- sjPlot::get_model_data(fit.all, "re")[[1]] %>%
+ mutate(group = ifelse(conf.low < 1 & conf.high > 1, NA, group)) %>%
+ mutate(facet = sapply(strsplit(as.character(term), ":"), tail, 1)) %>%
+ mutate(term = forcats::fct_reorder(term, estimate))
+
+ggplot(df.re.subcategory) +
+ aes(estimate, term, xmin=conf.low, xmax=conf.high, color=group) +
+ facet_grid("facet", scales="free_y", space="free_y") +
+ geom_vline(xintercept=1, color="black", linetype="dashed") +
+ geom_errorbarh(height=0, size=1) + geom_point(size=2) +
+ scale_x_log10(breaks=c(0.2, 0.5, 1, 2, 5)) +
+ scale_color_manual(
+ breaks=c("pos", "neg"), values=c("blue", "red"),
+ na.value=grDevices::adjustcolor("grey50", 0.5)) +
+ labs(y=NULL, x="Odds ratio", title="Random effect: subcategory") +
+ theme(legend.position="none")
+
+
+
+3.3 All together
+fit <- list(
+ glm = fit.glm,
+ all = fit.all,
+ first = glmer(model, df.first, family=binomial, weights=total),
+ last = glmer(model, df.last, family=binomial, weights=total),
+ single = glmer(model, df.single, family=binomial, weights=total)
+)
+
+df.terms <- lapply(fit, sjPlot::get_model_data, "est") %>%
+ bind_rows(.id="fit") %>%
+ mutate(type = ifelse(fit=="glm", "GLM", "GLMM")) %>%
+ mutate(fit = ifelse(fit=="glm", "all", fit)) %>%
+ mutate(fit = forcats::fct_inorder(fit)) %>%
+ mutate(type = ifelse(p.value >= 0.05, NA, type))
+
+levels(df.terms$term) <- c("COVID paper", "lockdown", "year")stargazer::stargazer(fit, type="html")| + | +|||||
| + | ++Dependent variable: + | +||||
| + | ++ | +||||
| + | ++p_male + | +||||
| + | ++logistic + | ++generalized linear + | +|||
| + | ++ + | ++mixed-effects + | +|||
| + | ++(1) + | ++(2) + | ++(3) + | ++(4) + | ++(5) + | +
| + | +|||||
| +yearmon + | ++-0.104*** + | ++-0.049*** + | ++-0.044*** + | ++-0.059*** + | ++-0.029 + | +
| + | ++(0.003) + | ++(0.003) + | ++(0.009) + | ++(0.009) + | ++(0.018) + | +
| + | ++ | ++ | ++ | ++ | ++ | +
| +lockdown + | ++0.072*** + | ++0.031*** + | ++0.035* + | ++0.008 + | ++0.136*** + | +
| + | ++(0.007) + | ++(0.007) + | ++(0.020) + | ++(0.021) + | ++(0.052) + | +
| + | ++ | ++ | ++ | ++ | ++ | +
| +covidpaper + | ++-0.614*** + | ++0.076*** + | ++0.399*** + | ++0.129** + | ++0.715** + | +
| + | ++(0.019) + | ++(0.022) + | ++(0.064) + | ++(0.065) + | ++(0.298) + | +
| + | ++ | ++ | ++ | ++ | ++ | +
| +Constant + | ++1.826*** + | ++1.595*** + | ++1.520*** + | ++1.819*** + | ++2.480*** + | +
| + | ++(0.006) + | ++(0.199) + | ++(0.195) + | ++(0.173) + | ++(0.169) + | +
| + | ++ | ++ | ++ | ++ | ++ | +
| + | +|||||
| +Observations + | ++3,368 + | ++3,368 + | ++3,996 + | ++4,027 + | ++3,517 + | +
| +Log Likelihood + | ++-39,496.310 + | ++-11,327.900 + | ++-7,182.127 + | ++-6,955.634 + | ++-3,788.911 + | +
| +Akaike Inf. Crit. + | ++79,000.620 + | ++22,667.800 + | ++14,376.250 + | ++13,923.270 + | ++7,589.823 + | +
| +Bayesian Inf. Crit. + | ++ | ++22,704.540 + | ++14,414.010 + | ++13,961.070 + | ++7,626.815 + | +
| + | +|||||
| +Note: + | ++p<0.1; p<0.05; p<0.01 + | +||||
ggplot(df.terms) +
+ aes(estimate, term, xmin=conf.low, xmax=conf.high, color=type) +
+ facet_grid("fit", scales="free_y", space="free_y") +
+ geom_vline(xintercept=1, color="black", linetype="dashed") +
+ geom_errorbarh(height=0, size=1) + geom_point(size=2) +
+ ggrepel::geom_text_repel(
+ aes(label=p.label), nudge_y=0.3, nudge_x=0.01, segment.size=0, show.legend=FALSE) +
+ scale_x_log10(breaks=c(0.2, 0.5, 1, 2, 5)) +
+ scale_color_manual(
+ breaks=c("GLM", "GLMM"), values=c("red", "black"),
+ na.value=grDevices::adjustcolor("grey50", 0.5)) +
+ labs(y=NULL, x="Odds ratio", color="Model") +
+ theme(legend.position=c(.99, .99), legend.justification=c(1, 1)) +
+ theme(legend.background=element_rect(fill="#ffffff88"))
