The motivation for a study of MARC fields in bibliographic records stems from the desire to understand the kinds of information that are available to build more informative displays into online library catalog interfaces. The deficiencies of online catalogs have been well documented. In separate studies, Calhoun and Markey pointed out how online catalogs have been slow to implement features that would greatly increase their utility, such as advanced retrieval techniques for subject searching, the inclusion of tables of contents, expanding the use of full-text searching, and leveraging classifications schemes as finding aids.² Certainly libraries faced many impediments in producing advanced catalogs, including financial limitations and the reliance on integrated library system vendors who were unable or unwilling to produce these additional functionalities.

Online catalogs have largely lacked the ability to identify and display relationships between different works and between representations of the same work.³ Many different kinds of bibliographic relationships exist between library resources. Tillett identified seven types of relationships: equivalence, derivative, descriptive, whole-part, accompanying, sequential or chronological, and shared characteristic.⁴ Smiraglia created a taxonomy that expanded on Tillett’s derivative relationship and included seven categories: simultaneous derivations, successive derivations, translations, amplifications, extractions, adaptations, and performances.⁵ Bibliographic relationships between library resources are common. Smiraglia and Leazer found that approximately 30 percent of bibliographic works in the OCLC’s WorldCat have associated derivative works.⁶ These relationships are manifested in a number of ways in MARC records, including through uniform titles, series statements, and added entries.⁷ Despite this, most conventional library catalogs provide little in the way of collocation based on bibliographic relationships. Integrating these relationships into catalog displays would provide users with a significantly more powerful way to navigate through library resources.⁸

FRBR is the most visible effort to give bibliographic relationships a more central role in modeling the bibliographic universe. FRBR describes a conceptual model that identifies four main bibliographic entities: works, expressions, manifestations, and items. The first three entities are abstract concepts while the fourth entity, the item, represents the physical resource that exists on a library shelf. The FRBR model has been criticized for having a lack of conceptual clarity in the distinctions between the abstract work, expression, and manifestation entities, and for glossing over important differences between books and nonbook materials.⁹ Despite these criticisms, the next generation cataloging code, Resource Description and Access (RDA), is integrating the FRBR entity-relationship model into the arrangement and implementation of the new cataloging rules.¹⁰

This study uses power law functions to characterize the patterns of MARC field use in bibliographic records. A power law function is a mathematical expression that describes an inverse exponential relationship between two phenomena. Power laws are commonly illustrated through the “80/20 rule” of wealth and power, that is, 80 percent of the world’s resources are held by 20 percent of the world’s countries, or by the “long-tail” phenomena of marketing and consumption, where very few music or book titles sell a large number of copies and a great many titles sell very few copies.¹¹ Power law functions have been used extensively in the library and information science literature. A study in 1995 showed that the individuals behind two of the classic bibliometric power laws, George Kingsley Zipf and Alfred J. Lotka, were at that time among the most cited people in the history of the discipline.¹²

Zipf’s and Lotka’s power laws provide similar formulations for different kinds of bibliometric phenomena.¹³ Zipf derived his law from a study of word counts in a selection of English language texts. He showed an inverse relationship between the number of times a word is used and its use rank with the set of all words used. So, if the most frequently used word was used one hundred times, the second most frequently used word was used roughly fifty times (one-half as many), the third most frequently used word was used roughly thirty-three times (one-third as many), and so on down the word list. Lotka, on the other hand, derived his law from a study of the publication productivity of individual authors within a corpus of chemistry and physics journals. Lotka found an inverse-square relationship between the number of publications by each author and the number of authors with a given number of publications. In other words, if one hundred authors produced one published paper, the number of authors that produced two published papers was roughly twenty-five (one-fourth as many), the number of authors who produced three published papers was roughly eleven (one-ninth as many), and so on. The authorship and publication patterns of many disciplines, including the library and information sciences, have been shown to follow power law distributions.¹⁴

Zipfian and Lotkan distributions have been observed in a number of other library and information science settings. Power laws have been used to describe the forms of names on bibliographic records, the frequency of name headings in the library catalog, library resource circulation patterns, and the use of descriptor term co-occurrences in a bibliographic hypertext system.¹⁵ In 1990, Blair proposed that Zipf’s distribution of word use might be used as an indicator of indexing effectiveness.¹⁶ He suggested that the distribution of index term use should match distribution of word usage in documents. According to Blair, a match in term usage distributions would indicate that the indexers and users were using language in a similar fashion and thus bring the conceptions of document representation between the two groups closer together.

The scope of power law functions extend beyond the study of word counts and author productivity, however; power law relationships can be used to describe many natural and human phenomena, such as the size of cities, earthquakes, and forest fires. Newman described a number of theories proposed to explain the existence of power law forms in such a wide variety of phenomena.¹⁷ One of the most important physical mechanisms Newman identified as explaining the occurrence of power laws is the Yule process, better known as the “rich get richer” phenomena. The Yule process is named for the developer of the first mathematical description of this process, G. Udny Yule. The description of the Yule process for the population size of cities, which follows a power law distribution, is that new instances, in this case new people moving to a city, occur in proportion to the number of people already living in each city. In other words, large cities are much more likely to add new members than small cities or towns, leading to the situation that currently exists where there are very few cities with a very large population and a large number of cities with a small population. Similarly for book sales figures, book titles that have already sold large numbers of copies are much more likely to sell more copies, while titles with lower sales figures are less likely to sell additional copies. Newman described how it has been shown mathematically that this “rich get richer” process leads to power law distributions.

The present study extends the application of power law functions to a new area: the distribution of MARC fields in catalog records. The author was only able to find one work that explored the distribution of field use in MARC records. Markey and Calhoun studied the prevalence of fields that provided “subject-rich” words, which they define as words that would be useful when performing subject searches in online catalogs.¹⁸ They found that less than 5 percent of bibliographic records they studied contained the MARC 505 (Formatted Contents Note) and 520 (Summary, etc.) notes fields. No other work on this topic was found. The next sections describe the method used to sample and analyze bibliographic records from the LC website and outline the major results. This is followed by a discussion of the methods used to collect a smaller targeted sample of records for the two case study works, Lord of the Flies and Republic.

The author observed 144 MARC fields in the 1,500 record sample, and the incidence rates ranged widely for different fields. Each field was incident in an average of 190 records. The median incidence rate, however, was far lower, at 14 records per field. The difference in the mean and median values indicates a large skew in the field incidence rate. Four fields were incident in all 1,500 records in the sample, and the minimum number of incidences was one record. Nineteen fields were only observed in a single record. Figure 2 shows a rank–frequency plot of the field incidence. In this figure, the y-axis shows the number of incident records that contained at least one instance of a given field, with the x-axis showing the rank in order of frequency of incidence. The vast majority of fields were incident in only a small number of records, but a small number of fields appear in nearly all of the sampled records. Appendix A lists the 23 most incident fields. All other fields were incident in less than 20 percent of the sampled records. The curve in figure 2 shows the obvious shape of a power law distribution, with the notable exception of the ten top ranked fields, which, as appendix A shows, were all incident in greater than 99 percent of the sampled records.

The next step was to test how the Zipf distribution fits the distribution of MARC fields in bibliographic records. The equation for Zipf’s law is f = c/r^a, where f is the frequency of incidence, r is the rank, c is a constant, and following Zipf’s original formulation, a = 1.²⁰Figure 3 shows the same data with the ten highest ranked fields that were incident in 99 percent or more of the sampled records collapsed into a single entry with an assigned frequency of 100 percent. The two lines represent Zipf functions with c = 30 (solid line) and c = 45 (dotted line). The best fitting value lies somewhere between these two values. As this figure shows, the Zipf functions appear to provide a good model for the field incidence rates when the highest ranked fields are collapsed into a single entry.

But is this collapsing necessary? Can the incidence data be modeled even with the inclusion of the top ranked fields? The next step was to see if the Lotka function fit the data better than the Zipf function. Egghe provides a method for fitting Lotka functions to informetric data.²¹ The formula for the Lotka function is similar to the Zipf function, y = c/xⁿ, where y = the number of records in which a field is incident, x = the rank in order of incidence rate, and c is a constant, as is n, which may or may not equal one. Following Egghe, the values of c and n can be found in the following manner:

c = y(1) = the number of incident records for the top ranked field = 1,500. And n = (2*A-T)/(A-T), where A = 27,310 = the total number of incident records (sum of the third column in appendix A), and T = 144 = the number of unique MARC fields observed. Thus, n = 2.005301.

Plugging these values into the Lotka function and plotting it alongside the data created figure 4. In this figure, the line represents the function y = 1500/x^2.005301. As this figure shows, this function fits the data very well. Thus the Lotka function appears to give a good model for the incidence rates of MARC fields in the LC bibliographic records.

As explained above, incidence rates measure how many records contained a given field at least once, and occurrence rates measure how often each field is used in a given record. Many fields occurred more than once in an individual MARC record. Counting all occurrences of individual fields, the mean number of occurrences per field was 206 with a median of 14 occurrences (compare with the incidence mean of 190 and median of 14). The maximum number of occurrences of a single field was 1,817 for the 650 field, and the minimum number of occurrences was 1 for 19 different fields.

The total number of field occurrences across all records does not tell a great deal about the use of individual fields, however, as the incidence rate has a large effect on the occurrence rate. Thus the occurrence rates for each field were normalized by dividing them by their incidence rate. Appendix B shows the 20 highest ranked MARC fields in order of their normalized occurrence rates. The last column shows the total number of times individual fields occurred. The 880 field (Alternate Graphic Representation) had the highest normalized occurrence rate, an average of 4 per each incident record.

The average normalized occurrence rate for the observed fields was 1.10 field occurrences per record, and this rate again showed the power law shape. A Zipfian distribution line showed the best fit to the normalized occurrence rate, as illustrated in figure 5. In this plot, the equation for the solid line is f = 1+ 1/(20*r), and the equation for the dotted line is f = 1+ 1/(30*r). Thus c is approximately equal to 1/20 or 1/30.

The case study results generally followed the results of the random sample analysis. For the Lord of the Flies records pulled from the RLIN union catalog, there was an average of 19 fields per record (maximum = 53 fields, minimum = 8 fields), with a standard deviation of 8.8. For the Republic records pulled from the UCLA catalog, there was an average of 22.5 fields per record (maximum = 46 fields, minimum = 12 fields), with a standard deviation of 5.3. The two works exhibited 87 different fields. Appendix C shows the fields that appeared in more than 20 percent for the records of each work. For the Lord of the Flies records, 34 percent of the incident fields (23 of 68) had incidence rates greater than 20 percent, and similarly, for the Republic records, 39 percent of the incident fields (24 of 62) had incidence rate greater than 20 percent. These results echo what was found in the random sample discussed above, though the incidence rates of some fields varied between the two works and the random sample.

Fitting Lotka functions to the MARC data from these works was not as successful as for the random sample. Applying Egghe’s method, one can try to fit Lotka functions for each work.²² For the Lord of the Flies data, c = 98 (the number of incident records for the top ranked field), A = 1,499 (total number of incident fields), T = 68 (number of unique MARC fields), giving n = 2.047519. For the Republic data, c = 100, A = 1,918, and T = 62, giving n = 2.033405.

Figures 6 and 7 show rank-frequency plots of the MARC incidence data for both works. Figure 6 displays the Lord of the Flies data, with a line representing the Lotka function y = 98/x^2.047519. Figure 7 displays the Republic data, with a line representing the function Lotka function y = 100/x^2.033405.

The power law curves in these figures generally follow the trends of the data, though not as well as the data from the random sample of LC records. This is likely because of the smaller number of records sampled as well as the differences in cataloging practice that generated the records. For example, the most obvious difference between the two case studies is that only 6 fields were present in more than 95 percent of the Lord of the Flies records, but 11 fields were present in the Republic records at that rate. Looking more closely at appendix C, 3 of the fields found in 100 percent of the Republic records are processing fields that were either for local UCLA use (000 and 910) or were not included in the RLIN catalog (005). The presence of additional processing fields in the Lord of the Flies records would more closely align the results of the two case studies.

Moving now to the observed power law relationships themselves, one may ask why these relationships were observed. Can these power law relationships in MARC field use by catalogers be accounted for in some way? Earlier, the “rich get richer” process was discussed as one possible mechanism that can lead to the observation of power law relationships in a wide variety of settings.²⁵ This “rich get richer” process is likely an important mechanism in relation to the findings of this study. The most widely used fields follow long established cataloging traditions. Charles Ammi Cutter, in his well-known 1904 work Rules for a Dictionary Catalog, describes the objects of the catalog as the following:

1. To enable a person to find a book of which either
   • A. The author is known.
   • B. The title is known.
   • C. The subject is known.
2. To show what the library has
   • A. By a given author.
   • B. On a given subject.
   • C. In a given kind of literature.
3. To assist in the choice of a book
   • A. As to its edition (bibliographically).
   • B. As to its character (literary or topical).²⁶

To achieve these objectives, Cutter proposed the following means:

1. Author-entry with the necessary references (for A and D).
2. Title-entry or title-reference (for B).
3. Subject-entry, cross-references, and classed subject-table (for C and E).
4. Form-entry and language-entry (for F).
5. Giving edition and imprint with notes when necessary (for G).
6. Notes (for H).²⁷

Cutter’s catalog objectives and means for achieving them identified the kinds of information most useful to achieving what in his view were the objectives of the catalog. Cutter was highly influential to the subsequent development of cataloging practice, particularly to the code-developing work of Seymour Lubetzky, and his catalog objectives (and corresponding means to achieve them) were ultimately encoded into the Anglo-American Cataloguing Rules.²⁸

Looking back at appendix A, one sees a close correspondence between the MARC fields with the highest incidence rates from the random sample of LC records and Cutter’s list of means for achieving his catalog objectives. The 100 field (74 percent incidence) meets means 1, the 245 field (99.9 percent incidence) meets means 2, the 050 and 650 fields (99 percent and 66 percent incidence respectively) meet means 3, the 008 field (100 percent incidence) meets the language-entry aspect of means 4, and the 260 and 300 fields (both 99.7 percent incidence) meet means 4 and 5 on Cutter’s list. Thus, in a “rich get richer” manner, certain kinds of information were identified to be important by scholars such as Cutter, and over time the practice of including these particular kinds of information became “richer” through wider incorporation into cataloging practices and cataloging code.

The relation of cataloging code to the power law distribution of MARC fields is another important implication of this study. It may seem tautological to say that there are important relations between the distributions observed in this study and the Anglo-American Cataloging Rules, given that a large portion of the records included in this study were cataloged to either the first or second edition of the Anglo-American Cataloguing Rules, but with the pending release of the RDA next generation cataloging rules, probing these relations may shed light on potential issues in converting to the new rules.²⁹ The Anglo-American Cataloguing Rules, 2nd edition (AACR2) is organized in such a way that the fields found to be most prevalent in MARC records are given prime importance. AACR2 is broken into two main sections: Part 1 provides the rules for describing library resources, and Part 2 provides the rules for creating headings, uniform titles, and references. Focusing on Part 1, the first chapter of AACR2 gives the general rules for description and is followed by eleven chapters that enumerate sets of rules for dealing with particular kinds of resources, such as books, pamphlets, and printed sheets (chapter 2); cartographic materials (chapter 3); and manuscripts (chapter 4). Each chapter contains section headings for the following description areas: title and statement of responsibility, edition, material specific details, publication and distribution, physical description, series, note, and standard number. These main headings encompass the nonprocessing fields that in this study had the highest incidence rates in catalog records (illustrated in appendix A), as well as fields that were less prevalent, such as the edition statement, material specific details, and series statement. The rules specific to the lesser used fields are found by looking further into the chapters for each particular material type. The material-specific chapters in AACR2 emphasize certain description areas in greater or lesser detail depending on the needs of each type of material. For example, the physical description area in chapter 5, “Music,” has six subsections under the physical description area, whereas chapter 6, “Sound Recordings,” has nineteen subsections under the physical description area.

The organization of the rules in RDA is notably different.³⁰ RDA’s main organizational scheme draws on the conceptual models found in the FRBR and Functional Requirements for Authority Data (FRAD) reports.³¹ RDA is broken into ten sections. Each section contains between one and five chapters devoted to recording information about particular entities in the FRBR and FRAD models. For example, the first four sections are “Recording Attributes of Manifestation and Item,” “Recording Attributes of Work and Expression,” “Recording Attributes of Person, Family, and Corporate Body,” and “Recording Attributes of Concept, Object, Event, and Place.” Subsequent chapters specify rules for recording information about relationships between entities. Looking closer at RDA, the location of the rules for recording high-incidence fields (title and statement of responsibility, publication and distribution, physical description, and notes) are not organized as linearly as they are in AACR2. The rules for recording the title, statement of responsibility, publication and distribution details (as would be recorded in the MARC 100, 245, and 260 fields) are found in chapter 2, “Identifying Manifestations and Items,” and the rules for recording the physical description (MARC 300 field) are found in chapter 3, “Describing Carriers.” Rules for creating notes are found throughout both chapters. The material-specific rules—such as those for music, recorded sound, video, etc.—are mixed into each chapter of RDA rather than the AACR2 practice of giving them their own chapters. This can be illustrated by looking at five rules in RDA specific to printed music. In chapter 2, which contains 228 pages, the rule for type of musical composition, medium of performance, key, etc., is found on page 25; the rule for devised titles for music is on page 56; and the rule for publisher’s number for music is on page 194. Similarly, in chapter 3, which contains 141 pages, the rule for extent of notated music is on page 30 and the rule for score and parts in a single physical unit is on page 134. These five RDA rules correspond to rules 5.1B1, 5.1B2, 5.4D3, 5.5B, and 5.5B1 in AACR2, all of which are found within the twenty pages of chapter 5, which is dedicated to printed music. This is only a small selection of the rules specific to printed music in RDA; many other music specific rules are spread around other chapters. The same illustration could be made for any other kind of material.

These differences between RDA and AACR2 raise important questions about the accessibility of RDA to cataloging students as well as the ease of transition to the new rules by experienced catalogers. Whether the less direct correspondence between the organization of the rules in RDA and the most widely used MARC fields provide as clear a roadmap as AACR2 for students learning to catalog is an open question. Additionally, regarding the co-location of material-specific rules in AACR2, and the lack thereof in RDA, few situations require that catalogers use rules specific to two different kinds of materials in cataloging a single item. Further research will be necessary to show whether the new rule organization scheme in RDA speeds up or slows down catalogers, both novice and experienced, as they find and apply the less-used but still important material-specific rules.