Bradford's Law and Autoethnography Journal Articles

This is simply an exercise to demonstrate Bradford's law, which has been used as a collection development tool for librarians, as a method to analyze scholarly communication patterns by those who study information science and sociology of science, and as a way to identify, in literature searches, the most relevant bibliographic material on a given topic.

The test subject is 'authoethnography.' Authoethnography makes an interesting test subject because it's a relatively new kind of research design. Plus, I'm also using this exercise to work out some of the programming needed in R to do later bibliometric projects.

Data collection

I downloaded data from the Scopus bibliographic database on March 17, 2013 and saved the data as a comma separated value file called 'autoEthnoScopus.csv'.

The Scopus query used to retrieve the data was:

TITLE-ABS-KEY(“autoethnography”) AND (EXCLUDE(PUBYEAR, 2013)) AND (LIMIT-TO(DOCTYPE, “ar”))

The query specifies a search for the term “autoethnography” in title, abstract, or keywords. I excluded the 2013 publication year (current year) and limited publication type to journal articles. The publication range for the articles in the data set is 1993 to 2012. Although the data is most likely fairly comprehensive, this is not meant to be a rigorous or thorough analysis.

Importing and setting up the data

First, let me note that I'm using R Studio (http://rstudio.org) as my IDE to the R programming language (http://www.r-project.org), the knitr (http://CRAN.R-project.org/package=knitr) package to produce markdown output, and the ggplot2 (http://ggplot2.org/) package to plot the data.

I begin by importing the CSV file I downloaded from Scopus:

autoEthnoScopus <- read.csv("~/Dropbox/workspace/playing/autoethnographic/autoEthnoScopus.csv", 
    header = TRUE)

In order to do the analysis, the data has to be properly set up. To do this, I create a table from the imported CSV file and save it to an object called x. The table contains a column with the title of the journal and another column with the number (or frequency) of articles in each journal. It's nicer to work with data frames, so I convert and save x as one.

# Create table of journal titles
x <- table(autoEthnoScopus$Source.title)

# Convert to data frame
x <- data.frame(x)

The data frame is ordered alphabetically by the first letter of the journal. I want the data frame sorted by descending order of article frequency per journal, so that the journal with the most articles is listed first, and so forth. In the code that follows, I do this and save the new ordering as a data frame called x.ordered.

Next I generate three new variables: the cumulative frequency of the articles, the cumulative percentage of the articles, and the Bradford zones of the articles. I assign a Bradford zone by cumulative percentage. The zones indicate the core and scatter of the distribution; that is, the journals representing the core of the subject and the journals representing the scatter. Normally, the zones are divided by equal number of articles, but since the data set is fairly small, this would mean one of the journals would be simultaneously assigned to zones 1 and 2. So to prevent overlap, zoning by cumulative percentage is helpful. Each zone contains about 33% of the articles.

Lastly, I factorize the zones. Here I'm simply correcting the data type of the Bradford zone variable as stored in R. Then I assign descriptive names to two of the variables and create a final variable that ranks the journals. The highest rank goes to the most productive journal for the topic, and for ties I'm assigning the average (mean). There are a lot of ties in this data set.

# Order data frame by frequency and save to new data frame, with
# descending order on x$Freq (negative sign)
x.ordered <- x[order(-x$Freq), ]

# Compute cumulative frequency of articles
x.ordered$cumFreq <- cumsum(x.ordered$Freq)

# Compute cumulative percentage of articles
x.ordered$cumPerc <- round(cumsum(x.ordered$Freq)/sum(x.ordered$Freq) * 100, 
    2)

# Add bradford zones, separate by percentages rather than by article
# counts
x.ordered$bfZone <- ifelse((x.ordered$cumPerc <= 33), 3, 0)
x.ordered$bfZone <- ifelse((x.ordered$cumPerc > 33) & (x.ordered$cumPerc <= 
    67), 2, 3)
x.ordered$bfZone[1:2] <- 1

# Factorize and label zones
x.ordered$bfZone <- factor(x.ordered$bfZone, labels = c("1", "2", "3"))

# Assign new names to variables
names(x.ordered)[1] <- "Journals"
names(x.ordered)[2] <- "Articles"

# Rank the journals by number of articles, assign average value for ties,
# and reverse order to match high to low no. of articles
x.ordered$jRank <- rank(-x.ordered$Articles, ties.method = "average")

The result is a data frame with 199 cases (or journals) and six variables. Here are the ten journals that have published the most autoethnography articles, according to Scopus, and within the time frame (see the Appendix for the complete listing). As you can see, the journal Qualitative Inquiry has published the most, this is followed by Cultural Studies - Critical Methodologies, and so forth.

library(xtable)
print(xtable(head(x.ordered, n = 10)), type = "html", include.rownames = FALSE)

Quick descriptives

We may want to keep in mind the number of journals and the number of articles in the data set:

length(x.ordered$Journals)

## [1] 199

sum(x.ordered$Articles)

## [1] 504

And a histogram illustrates the publication time span, per Scopus, and helpfully shows that most articles were written after 2005:

library("ggplot2")
p <- qplot(Year, data = autoEthnoScopus, geom = "histogram", binwidth = 1)
p + xlab("Publication Year") + ylab("Article Frequency")

Because of the rapid increase in 2005 publications, and the apparent trend afterwards, it may be interesting to trace what happened around the middle of the last decade that might have led to a surge in autoethnography publications.

Bradford zone statistics

The Bradford zones identify the core and scatter of a distribution of articles on a specific topic. There are traditionally three zones. The first zone will include the core journals, the second zone will include a greater number of journals, and the last zone an even greater number, all the while holding the number of articles fairly constant across all three zones. Here I hold the cumulative percentage constant, which does pretty much the same work.

First, we compute the statistics for Zones 1, 2, and 3, and then summarize in a table:

Zone 1

# count of journals in Zone 1
length(x.ordered$Journals[x.ordered$bfZone == 1])

## [1] 2

# number of articles in Zone 1
sum(x.ordered$Articles[x.ordered$bfZone == 1])

## [1] 167

# percentage of articles in Zone 1
round(sum(x.ordered$Articles[x.ordered$bfZone == 1])/sum(x.ordered$Articles), 
    4) * 100

## [1] 33.13

Zone 2

# count of journals in Zone 2
length(x.ordered$Articles[x.ordered$bfZone == 2])

## [1] 43

# numer of articles in Zone 2
sum(x.ordered$Articles[x.ordered$bfZone == 2])

## [1] 170

# percentage of articles in Zone 2
round(sum(x.ordered$Articles[x.ordered$bfZone == 2])/sum(x.ordered$Articles), 
    4) * 100

## [1] 33.73

Zone 3

# count of journals in Zone 3
length(x.ordered$Journals[x.ordered$bfZone == 3])

## [1] 154

# number of articles in Zone 3
sum(x.ordered$Articles[x.ordered$bfZone == 3])

## [1] 167

# percentage of articles in Zone 3
round(sum(x.ordered$Articles[x.ordered$bfZone == 3])/sum(x.ordered$Articles), 
    4) * 100

## [1] 33.13

Bradford zone Summary

Bradford distribution plots

A Bradford plot takes the log of the journal rank on the x-axis and the cumulative number of articles on the y-axis (Brookes, 1969). Because of the relatively small data set and the rather large number of rank ties, it's not surprising that the plot line is staggered. If and when more journals begin publishing more autoethnographic studies, it's likely that, over time, the plot line will be more continuous. However, with only two journals in the core zone and with the rather large count of journals that have only published one or two autoethnographic articles, the staggered plot makes sense.

p <- qplot(log(jRank), cumFreq, data = x.ordered, geom = c("line", "point"), 
    colour = factor(bfZone))
p + xlab("Journal Rank (log)") + ylab("Cumulative Number of Articles") + labs(colour = "Bradford Zones")

However, the plot can be displayed with a loess line. This is the kind of line I'd expect to see if there were thousands of autoethnographic articles.

# Note: I'm suppressing some warnings due to the small data set.
p <- qplot(log(jRank), cumFreq, data = x.ordered, geom = ("smooth"))
p + xlab("Journal Rank (log)") + ylab("Cumulative Number of Articles")

Conclusion

My intention with this post was twofold: to demonstrate Bradford's law and to work out some R code that I can later use in a more thorough bibliometric study.

Authoethnography represents an interesting test subject because it's such a new kind of research, at least in practice. At some point I'd like to do a more thorough analysis. Is this the birth of something that will become much bigger? Will its growth stabilize in the near future? Will the core zone grow? Do the journals that currently represent the core zone for authoethnography also represent core zones for other topics or research designs? So on.

References

Brookes, B. C. (1969). Bradford's Law and the bibliography of science. Nature, 224(5223), 953-956. doi: 10.1038/224953a0

Appendix

# The complete data frame
print(xtable(x.ordered), type = "html", include.rownames = FALSE)