Stern Chart and Research Articles, writing homework help

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For this assignment You will complete the Stern Note Taking table chart. You will use the 5 articles to complete the Stern Chart attached is the stern chart and the 5 articles.Be sure to complete with proper APA citation, form, and style as needed.


How will you find the purpose of the study?

How will you locate the methodology and findings in each study?



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Author One Type and purpose of study Type means qualitative, quantitative, or mixed methods research. Hypothesis or Research Questions Both quantitative and qualitative research can have research questions, but only quantitative can have hypotheses. Author Two Author Three Author Four Author Five Population and Sample Methodology Examples are case study, grounded theory, ethnography, quasiexperimental design etc. Findings We call it findings in qualitative research and results in quantitative research. Evaluation notes Look for the limitations to the study. Small sample size, not generalizable, bias of researcher etc. How will the study help your research or why are you rejecting it? Stern’s (2015) Note Taking Table State of Practice for Language and Literacy Research: A Review of Methods Carla Wood Autumn McIlraith Lisa Fitton Florida State University, Tallahassee T he interests of scientists from a variety of disciplines overlap at the focal point of literacy development and intervention. Literacy has been targeted nationwide as a high priority area for external funding to promote improved outcomes in reading, understanding, and subsequent academic progress consistent with the No Child Left Behind Act (NCLB, 2003). This area of research is relevant to multiple fields such as psychology, education, special education, and speech-language pathology. ABSTRACT: Purpose: In an effort to build capacity of future doctoral leaders in speech-language pathology, this review examined journals relevant to language and literacy research for trends in the size of data sets and the use of statistical analyses, randomization, and replication. Method: A systematic review of empirical studies was conducted. Investigators examined 120 randomly selected scholarly articles published in 2013 and 2014 in 10 journals, including 4 focused on communication disorders and 6 with relevancy to the study of language and literacy. Results: Based on trends in the randomly selected sample of 120 journal articles, data sets varied largely in terms of size. Random assignment was used 22% 306 Given that a variety of disciplines conduct literacy research, a wide distribution of methods used in language and literacy research is to be expected. This diversity of methods is beneficial in that it provides a variety of angles from which to examine current theory and practice, which in turn strengthens our confidence in findings that are consistently replicated across different methods. However, in order to continue to contribute to the body of research, scholars must have a basic understanding of the wide range of methods available in order to of the time. Studies used a wide variety of types of designs and statistical analyses. Larger data sets and statistical methods using multiple levels of analysis were more prevalent in journals that were not specifically within the field of speech-language pathology. Conclusion: The findings of this systematic review support the need to prepare future scholars to employ rigorous methods and analyses in their research. Potential ways to enhance the infrastructure required for utilization of innovative statistical advances, large-scale data sets, experimental design, and replication are discussed. KEY WORDS: systematic review, speech-language pathology, reading, literacy Contemporary Issues in C ommunication Science andScience Disorders • Volume 43 • 306–317 • Fall• Fall 20162016 Contemporary Issues in Communication and D isorders • Volume 43 • 306–317 1092-5171/16/4302-0306 © NSSLHA recognize their influence on research findings and their implications for interpretation. In response to this need, we reviewed the current state of practice in language and literacy research in an effort to identify methodologies that are important for next-generation scholars who wish to continue to consume and produce research effectively. Research evidence is considered one of the pillars of evidence-based practice (EBP) and is critical to clinical practice (American Speech-Language-Hearing Association [ASHA], 2005a; McCurtin & Roddam, 2012). EBP in speech-language pathology values both internal and external evidence, including consulting the published literature for the best available scientific evidence to support the use or disuse of specific speech and language intervention approaches. Among valued skills, speech-language pathologists (SLPs) are expected to demonstrate knowledge of various research practices and integration of research principles into EBP (ASHA, 2005b). Although practitioners and researchers alike greatly value EBP, there is no general consensus on what constitutes best available scientific evidence and which methods and analyses are necessary or appropriate for future consumers and producers of research in our field. By definition, rigor is used in research to refer to strict precision; however, the criterion for acceptable precision may vary across fields. Varied standards and hierarchies are applied within and across disciplines (McCurtin & Roddam, 2012), but the focus of the present article is to examine methodology in language and literacy research from a perspective of pursuing diversity. Different methods of research have different strengths and weaknesses that influence their utility to scholars. However, there is a need to address the suggestion that research in some fields, such as speech-language pathology, is not broadening to include newer advanced methods and statistics (e.g., Ioannidis, 2005). Given the national movement toward large data sets, randomization, and large-scale replication (Ioannidis, 2005), it is critical to examine the use of these methods within and outside of speech-language pathology research. Ioannidis (2005), a widely acclaimed researcher, has called for a revolution in research practices, with a focus on replication by independent research teams with large data sets (Ebrahim et al., 2014). After extensive review of the research literature in medicine, Ioannidis made a convincing case for the need for better powered evidence from large studies. He concluded that small n studies without random assignment were underpowered and were at risk for leading practitioners to inaccurate conclusions. Ioannidis exposed a plethora of research findings with large effect sizes that could not be replicated, resulting in a call for more rigorous research methods and a focus on replication. In addition to the use of larger data sets, the educational research community has increasingly incorporated statistics within the families of hierarchical linear modeling (HLM) and structural equations modeling (SEM). These techniques have expanded researchers’ abilities to answer more complex research questions through simultaneously examining interactions between predictor variables and their impacts on outcome variables. Recent research findings have suggested that the unique characteristics of individual participants interact considerably to influence observed results. For example, there have been repeated calls in bilingual literacy research to report more background characteristics such as age of first exposure to languages and type of classroom instruction because these characteristics have been found to be critically influential (e.g., August & Shanahan, 2006; Branum-Martin, Tao, & Garnaat, 2015). Although more traditional statistical models, including analyses of covariance (ANCOVAs) and multiple regression, allow for statistical inclusion of these background characteristics, they are limited in their ability to account for the interactions between variables. Rather, relationships between included variables are often evaluated individually in the order dictated by the researcher. This is appropriate when there is a strong theoretical basis for the chosen order, but poses a challenge when an established theoretical foundation for the research is lacking. In the latter case, it may be appropriate to consider statistical models such as HLM and SEM, which offer the benefit of examining relationships between all variables simultaneously (see Kline, 2015). An additional advantage of multilevel techniques such as HLM is that they allow the statistical model to more accurately represent the structure of the data. For example, if children are presented with a set of words and are asked to read them, the individual responses to each item by each child are not independent. All responses from a single child are dependent in the sense that they originate from the same child, and certain child-related features potentially influence the responses of that child, such as the child’s previous exposure to those words or the child’s phonological awareness skills. All responses to a single word are similarly dependent, because word-related features such as regularity and frequency of occurrence may influence the accuracy of responses across all children. Using HLM, this dependence can be taken into account by “nesting” the individual responses within children and within items. Without accounting for this nesting in HLM or SEM to include both levels Wood et al.: Language and Literacy Research 307 of features in the same model, statistical analysis may inaccurately estimate effects attributable to each independent variable, resulting in inaccurate conclusions (Baayen, Davidson, & Bates, 2008). Multilevel modeling provides an excellent tool for researchers to use to scale statistical model complexity to match the structure of more complex data sets, resulting in more accurate estimates of effects (Compton, Miller, Gilbert, & Steacy, 2013). from low-incidence populations, presents challenges. Further, within the populations we research, it is difficult to employ true experimental designs with random assignment given that participant characteristics cannot be assigned and treatment often cannot be ethically withheld. Low-incidence populations of interest can also have high degrees of heterogeneity. This is exemplified in the area of aural rehabilitation for individuals who are deaf or hard of hearing. Among other variables, participants in such research commonly present with differences in age of onset, age of identification, underlying cause, severity, use of sensory device, comorbidity, communication method, and educational settings or approaches. Such an array of complex characteristics, coupled with the low incidence of deafness, presents methodological challenges for research in aural rehabilitation techniques, and many other specializations face similar complexities Perhaps equally as powerful as these methodological challenges is the current lack of infrastructure that would be required to support and sustain change or a revolution in methodology. Sharpe (2013) identified several infrastructure components that are necessary to support the inclusion of more complex methods in research practices, including (a) better access to continuing education in advanced methods and statistics, and (b) better use of mavens in the field. With regard to continuing education, SLPs and researchers in our field readily access continuing education in content across big areas (e.g., language, speech, hearing, fluency, voice, social communication, communication modalities, and cognition). However, continuing education regarding methodological or statistical innovations for consumers or producers of research is less available. One might argue that this level of continuing education is not feasible given that our field has multiple areas of content specialty to master. Sharpe also raised the notion of statistical mavens, or individuals who serve as liaisons between statistical innovators and contentarea experts. The presence of mavens could serve to provide practitioners and researchers with the information and new skills needed to be effective consumers and producers of advanced methods research. Although a promising concept, using mavens to enhance research design and analyses has received limited attention in the field of speech-language pathology. Without access to large data sets or infrastructure for continuing education on innovative research methodologies, research in speech-language pathology may be at risk for being “left behind” as new methods and statistical practices are developed and adopted by other fields in order to support more robust, generalizable research. Our resistance to including innovative techniques in our statistical toolboxes could come at great cost as external funding becomes increasingly Modeling Revolution The rise in the use of multilevel modeling in many academic fields has led some researchers to refer to a “modeling revolution” (Rodgers, 2010). The term modeling is used to refer to “a set of assumptions together with implications drawn from them by mathematical reasoning” (Neimark & Estes, 1967, p. v). Evidence for an increase in the use of multilevel modeling was demonstrated by Reinhart, Haring, Levin, Patall, and Robinson (2013), who examined methods used in 275 empirical articles from five primary research journals that were published between 2000 and 2010. They found that the use of modeling increased from 15% of empirical studies in 2000 (nine out of 61) to 54% in 2010 (50 out of 93). Challenges of Advanced Modeling and Methodology Despite the development of innovative statistical techniques and Ioannidis’s (2005) call for larger sample sizes, exclusive reliance on traditional statistical practices persists among many scholars. Considering the abundant support in place for traditional systems and the lack of support and resources available for novel procedures, the adoption of new practices is difficult. In the field of speech-language pathology in particular, there are several notable challenges restricting the incorporation of newer and more complex methodologies into our research practice. A few barriers that will be discussed throughout the article include the prevalence of small n studies due to the low incidence of disabilities of interest, challenges to random assignment due to the inherent participant characteristic of presenting with a disability or not (e.g., researchers cannot randomly assign cochlear implants), and (c) ethical conflicts of random assignment to a treatment versus comparison control group when early intervention is warranted. The prevalence of small n studies has been perpetuated by several factors. In speech-language pathology, the tendency toward small data sets may be partially attributed to our interest in low-incidence populations. Recruiting children and youth, particularly 308 Contemporary Issues in Communication Science and Disorders • Volume 43 • 306–317 • Fall 2016 competitive and as related fields continue to publish research that was conducted using these complex methods. Researchers with access to large data sets and those who can leverage the most appropriate designs and employ random assignment have the upper hand in competing for external funding. When we consider the disorders that are studied within speechlanguage pathology, the heterogeneity of affected individuals, and the number of variables we know to be important, it is critical that we expand our methodological skills to include approaches that recognize and account for these levels of complexity. Given the importance of rigor and of methodological diversity in research, we decided to examine the literature in language and literacy-related journals in order to foster discussion of the range and distribution of research methodologies that are currently being used. We decided to examine and describe general characteristics (e.g., number of participants, number of research institutions involved, population studied, methods, statistical analyses, and funding) of 2013–2014 publications in 10 journals related to child language and literacy based on a review of a subset of randomly selected articles. Specifically, we asked the following research questions: • What were the average sample sizes and general characteristics of studies published in 2013–2014 in 10 journals that are recognized as publishing language and literacy research (based on a randomly selected sample of 120 articles)? • What was the proportion of different types of analyses (e.g., qualitative; single-case; nonparametric; ordinary least squares [OLS] or linear least squares; and advanced statistics, such as SEM, HLM, item response theory) in 2013–2014 publications in 10 journals related to child language and literacy (based on a randomly selected sample of 120 articles)? • To what extent was random assignment and replication used in publications in the sample of 2013–2014 articles in 10 journals? Finally, a secondary interest of the current research (although not a specific research question) was to discuss the possible implications of these findings for current practices for scholars in higher education programs in communication disorders and specifically for those with interests in language and literacy. Method Journals of Interest We selected 10 journals to review, including four journals of speech-language pathology: Language, Speech, and Hearing Services in Schools (LSHSS); American Journal of Speech-Language Pathology (AJSLP); Journal of Speech, Language, and Hearing Research (JSLHR); and Journal of Communication Disorders. Six additional journals relevant to language and literacy were selected for inclusion due to their relevance to the aim of exploring journals that publish language and literacy research: Journal of Education Psychology (JEP), Scientific Study of Reading (SSR), Reading Research Quarterly (RRQ), Reading and Writing, Journal of Learning Disabilities, and Journal of Research for Educational Effectiveness (JREE). LSHSS. LSHSS is a quarterly journal that is produced by ASHA. The journal focuses on research that is relevant to SLPs and audiologists in schools. The journal is designed to address the needs of researchers, clinicians, and students who are interested in school-based issues. In 2012, LSHSS reported an impact factor of 1.256 and a 5-year impact factor of 1.520. In 2013, the journal published four issues containing a total of 26 research articles and in 2014, 17 research articles, reporting research on typically developing children and children with communication disorders ranging in age from toddlers to high-school students and adults who serve as SLPs. AJSLP. AJSLP is a quarterly journal that is also produced by ASHA. It is designed to disseminate research findings applicable to clinical practice in speech-language pathology. In 2012, AJSLP reported an impact factor of 2.448 and a 5-year impact factor of 2.897. Overlapping in school-based topics with LSHSS, AJSLP publishes on all aspects of clinical practice, not restricted to school-based topics. In 2013, the journal published four issues containing 27 research articles, and in 2014, published four issues containing 50 research articles. JSLHR. JSLHR is a bimonthly journal that is also produced by ASHA. It is designed to disseminate basic and applied research that focuses on normal and disordered communication processes. The mission of JSLHR focuses on advancing evidence-based practices as well as providing new information and theoretical approaches that are relevant to speech, language, and hearing processes, assessment, and management. In 2012, JSLHR reported an impact factor of 1.971 and a 5-year impact factor of 2.745. In 2013, the journal published six issues containing 149 articles, and in 2014, published six issues containing 171 articles. Journal of Communication Disorders. The Journal of Communication Disorders, published six times a year, disseminates articles with a focus on disorders of speech, language, and hearing. Although the journal does not exclusively publish language and literacy research, the assessment, diagnosis, and treatment of Wood et al.: Language and Literacy Research 309 reading disorders is a focus of the journal in addition to the reading-related implications of other communication disorders. The Journal of Communication Disorders reported an impact factor of 1.278 in 2015 and a 5-year impact factor of 1.864. In 2013, this journal published one volume (46) with six issues containing a total of 38 research articles; in 2014, the journal published six volumes (47–52) containing a total of 40 articles. Journal of Learning Disabilities. The Journal of Learning Disabilities, a journal of the Hammill Institute on Disabilities by Sage, publishes six issues per year, with articles on the science of learning disabilities. The journal reports an impact factor of 1.901 and a ranking of 4 out of 39 in special education. In 2013, this journal produced one volume (46) with six issues containing 44 research articles. In 2014, the journal produced one volume (47) with six issues containing 43 research articles. JREE. JREE is a quarterly publication of the Society for Research on Educational Effectiveness. Among the journal’s aims are to disseminate findings of intervention and evaluation studies or methodological studies that focus on the process and implementation of educational research, specifically related to problems in school classrooms. It was reported to have an impact factor of 3.154. In 2013, the journal published 15 research articles. In 2014, the journal published four issues with 16 research articles, including a special issue (number 3) on learning disabilities research studies reporting findings from projects funded by the National Institute of Child Health and Human Development. The introduction to a special issue and two commentaries were excluded from review. JEP. JEP is a quarterly journal designed to disseminate research pertaining to education across the lifespan, from early childhood to geriatrics. Not exclusively focused on language and literacy research, the journal includes general research in the area of educational psychology. JEP identifies several key focus areas, including scholarship on learning, cognition, instruction, motivation, social issues, emotion, development, special populations, and individual differences. In 2012, JEP reported an impact factor of 3.08 and a 5-year impact factor of 4.93. In 2013, the journal published 81 research articles; in 2014, it published 79 research articles. SSR. SSR is a bimonthly journal that is produced by the Society for the Scientific Study of Reading. It focuses on empirical studies related to language and literacy, although it also accepts literature reviews, papers on theory and constructs, and policy papers. The journal indicates that it places value on both theoretical and practical significance. SSR reports a 310 Contemporary Issues in Communication Science 5-year impact factor of 3.124. In 2013, the journal published 26 research articles; in 2014, it published 21 research articles. RRQ. RRQ is a quarterly journal that is produced by the International Reading Association. It is designed to facilitate connections between researchers in an effort to build a knowledge base in reading and literacy. The journal identifies empirical studies; multidisciplinary research; various modes of investigation; and diverse perspectives on teaching, practices, and learning as valued areas. RRQ reports an impact factor of 2.382. In 2013, the journal published 21 research articles; in 2014, it published 22 research articles. Reading and Writing: An Interdisciplinary Journal. Reading and Writing is a quarterly journal published by Springer with a primary aim of disseminating scientific articles related to the process, acquisition, and loss of reading and writing skills. The journal description highlights that the focus of the journal spans several disciplines including neuropsychology, cognitive psychology, speech and hearing science, and education. Based on data from 2001 to 2005, the impact factor is reported to be 3.85. In 2013, this journal published nine issues containing a total of 69 articles. In 2014, the journal published nine issues containing 80 articles, 79 of which were research articles and one article that was an introduction to a special issue. Procedure In approaching the task of identifying and describing research designs and analyses used in each study, we first had to establish definitions of relevant terms across disciplines. For this review, we included only research studies and excluded general literature reviews, editorials, commentaries, tutorials, and position papers. We categorized studies by design using broad categories (refer to the Appendix for definitions and categorizations). Additionally, we identified basic characteristics such as number of participants, age range, number of research institutions involved, method(s) of analyses, presence of random assignment, and inclusion of replication. We pulled a random sample of 12 articles from each journal, six from each of 2 years—2013 and 2014. Although six is a notably small proportion of articles for some of the journals, the quantity of six was selected in part because a few of the journals had a relatively small corpus of articles published in a given year (e.g., 17 articles in total for LSHSS and 15 for JREE in 2013). Albeit an arbitrary number, 12 was equivalent to bimonthly distribution. To complete this task, we entered each research article in a journal and Disorders • Volume 43 • 306–317 • Fall 2016 on a line in an Excel database, organized by year and journal title. Initially, we considered excluding articles that did not explicitly discuss literacy implications; however, upon further consideration, it was apparent that a case could be made that literacy components and implications of disorders are quite vast. For example, an article on phonetic processing during the acquisition of new words by children with cochlear implants may not explicitly discuss literacy, yet the research has implicit relevance to phonological awareness. As a result, we used an inclusive approach such that every research article in the relevant journals had an equal chance of being selected for review. We entered the range of numbers associated with the rows of the Excel database into a random number generator (i.e., select six numbers between 1 and 132). The random numbers generated served to identify which articles would be reviewed for the journal. Six articles were selected in this manner for each year of the journal. In the event that the selected article did not qualify for the study (e.g., a literature review or editorial without data), the article was excluded and the random number generator was used to derive a new line number corresponding to another article. This occurred in three instances for JREE; twice for RRQ; and once for AJSLP, JLD, Journal of Communication Disorders, and SSR. Each author independently coded four articles from each of the first six journals in an Excel database using mutually agreed-on criteria. A month into the process, we met to discuss the parameters for categorization and to adjust and refine the definitions for distinction of categories. The rules of coding were further defined to clarify the process based on our initial reviews. We agreed that in the event that there were multiple studies or experiments within the same scholarly article, the study with the most advanced statistical design would be included, and if the studies had the same design, which was the case in all instances, then the study with the largest number of participants would be included in the review. Of the articles reviewed, nine articles included multiple research studies within the scholarly article. Categorizing statistical analyses. We coded each article with one of four categorical codes based on the type of research analysis included in it. The codes included four types: qualitative research, single-case methods or a case study, traditional estimation, or advanced statistics. Qualitative studies included research that employed qualitative analyses such as open-ended interviewing to describe and develop themes. The single-case code was assigned to studies that employed single-case design methods (e.g., A-B-A withdrawal, multiple baseline, or alternating treatments; Horner et al., 2005) or reported a case study. Traditional estimation included singlelevel analyses such as OLS approaches (e.g., analysis of variance [ANOVA], regression, t tests), which had single variance terms including correlations, descriptive statistics, and nonparametric analyses. Advanced statistics included methods that employed multiple levels of analysis (e.g., SEM or HLM) or considered multiple dimensions of sampling (e.g., subjects and time or subjects and items) such as growth curves and mixed models (Garson, 2013). During the review process, we identified that several of the randomly selected studies used a metaanalysis. As a result, meta-analysis was added as an additional category. In addition to the assignment of categorical types, we also identified specific analyses used by name (e.g., hierarchical regression) to further describe the statistical methodology used in a study. Randomization was coded with a binary code for the presence or absence of random sampling. This category was included because of the recent focus on randomization (Ioannidis, 2005); however, we recognized that the use of randomization may be less feasible or practical for studies examining individuals with communication disorders. Notably, randomization is not always possible in clinically relevant research in speech-language pathology. For example, researchers cannot randomize who has Down syndrome and who is typically developing, or which participants receive a cochlear implant at an early age versus those receiving treatment B (e.g., hearing aids). Agreement. Of the articles reviewed, 14 were randomly selected to assess interrater agreement. Agreement was calculated by dividing the number of agreements by the total (disagreements plus agreements) × 100. There was 100% agreement for the type of design (e.g., qualitative, single-case design/ case study, traditional, or advanced) across coders for the six journals. For other data elements (e.g., number of participants, random assignment), there were three cases of confusion where one aspect of interest (e.g., replication) was not explicitly stated in the article. All instances of disagreement were discussed until we reached consensus. Results Following completion of the review process and agreement consensus gathering, we conducted descriptive data analyses to identify trends in designs and analyses in order to address the research aims, which included describing (a) the average sample size and general characteristics, (b) the proportion of different types of statistical analyses used, and (c) the extent to which random assignment and replication was used. Wood et al.: Language and Literacy Research 311 General Characteristics The population of interest and the characteristics of the data set also varied by population type (Table 2). The articles in the journals either focused on typical populations exclusively (60%), focused on participants with atypical development or disorders (20%), or included both groups of participants with typical and atypical characteristics (20%). The studies largely reported on children in grades K–12 (57%), but the age group of focus was somewhat distributed: infant-toddler (9%), preschool (6%), college attendees (9%), and adults (17%). A large portion of the studies reported that the research was grant funded (65%), although some authors may not have reported grant funding as it did not appear to be a customary practice for all of the journals To address the first research aim, we aggregated data across the 12 articles selected from each journal and across the complete set of 120 articles. On average, the studies in the articles showed wide variability in the sample size, with a mean of 973 (SD = 4282). The extreme ends of the range were typically large n survey studies (n = 5) and single-case studies (n = 5). When the five survey studies were excluded from the average number of participants, the adjusted mean sample size was 699 (SD = 3,313). On average, the sample studies were conducted by two research institutes, with a range of one to five institutes. Large standard deviations are partially explained by the fact that the average sample size and number of research institutes varied across journals. Table 1 reflects detailed descriptive data by journal. The size of the participant pool tended to be smaller for journals that focused on populations with communication disorders (e.g., LSHSS, AJSLP, JSLHR, JCD) where the average number of participants ranged from 27 to 108. Journals that tended to include populations with typical development (e.g., JEP, SSR, RRQ, JREE) tended to have a larger average number of participants, with means ranging from 140 to 6,241. Three journals, Journal of Learning Disabilities, Reading and Writing, and JREE, appeared to be exceptions to that trend. These three journals included populations with learning disabilities and reading disorders but also had large mean sample sizes (215, 139, and 2,765, respectively). Types of Analyses The 120 articles reviewed used six types of design, including qualitative (n = 4), single-case design or case study (n = 7), traditional quantitative (n = 69), advanced statistics (n = 37), meta-analysis (n = 2), and one simulation that was not specified in our original coding scheme. The prevalence of advanced statistics varied considerably across journals and particularly between journals that focused on communication disorders and other journals (refer to Table 3). Based on the descriptive data in Table 3, six of the 10 journals employed advanced statistics on 25% or more of the randomly selected articles (RRQ, RW, JLD, JREE, SSR, and JEP). Journals that focused more exclusively on participants with communica- Table 1. Summary of data set size based on 120 randomly selected articles reviewed. Universities Journal M SD LSHSS AJSLP JSLHR JCD JLD JREE JEP SSR RRQ RW 1.70 1.60 1.75 2.20 2.20 2.60 2.50 1.80 1.70 2.08 0.89 0.67 0.75 1.29 1.21 1.38 1.31 0.72 0.78 1.16 Participants More than Range of M SD 50 participantsa sample size 108 27 54 61 215 2765 6,241 140 276 139 147 17 40 76 292 4584 11,746 122 494 101 50% 0% 33% 33% 92% 100% 92% 83% 67% 83% 1–461 3–48 8-165 4–250 29–1,031 114–13,803 47–31,038 40–466 1–649 28–386 Participants: surveys excludedb M SD 108 27 54 61 215 2,765 4,151 140 143 139 147 17 40 76 292 4,584 9,684 122 187 101 Note. LSHSS = Language, Speech, and Hearing Services in Schools; AJSLP = American Journal of Speech, Language Pathology; JSLHR = Journal of Speech, Language, and Hering; JCD = Journal of Communication Disorders, JLD = Journal of Learning Disabilities; JREE = Journal of Research for Educational Effectiveness; JEP = Journal of Education Psychology; SSR = Scientific Study of Reading; RRQ = Reading Research Quarterly; and RW = Reading and Writing. Refers to the percentage of studies reporting more than 50 participants; bRepresents the mean number of participants without the studies that involved only surveyed participants. . a 312 Contemporary Issues in Communication Science and Disorders • Volume 43 • 306–317 • Fall 2016 Table 2. Summary of participant characteristics in the 120 articles. Typical populationsa LSHSS AJSLP JSLHR JCD JLD JEP SSR RRQ JREEd RW Infant toddlerb Preschoolc K–12 College age Adults 18% 33% 8% 17% 0% 8% 0% 0% 8% 0% 9% 8% 8% 17% 0% 0% 17% 0% 0% 0% 73% 8% 33% 42% 83% 33% 83% 83% 75% 67% 0% 0% 17% 0% 17% 25% 0% 8% 8% 17% 0% 50% 33% 25% 0% 33% 0% 8% 0% 17% 58% 25% 42% 25% 16% 92% 100% 100% 83% 75% The percentage of articles that included participants who were typically developing; bthe percent of articles that included participants who were under 3 years of age; cthe percentage of articles that included participants who were 3–5 years of age; d JREE does not equal 100% because one study did not include human subject participants. a Table 3. Proportion of analyses used in 120 randomly selected articles from 2013 to 2014. Qualitative LSHSS AJSLP JSLHR JCD JLD JEP SSR RRQ JREEa RW Single case or case study Traditional Advanced statistics n % n % n % n % 0 2 0 2 0 0 0 1 0 1 0 17 0 17 0 0 0 8 0 8 2 2 0 0 0 0 0 1 0 0 17 17 0 0 0 0 0 8 0 0 8 7 11 9 7 5 9 5 0 8 67 58 92 75 58 42 75 42 0 67 2 1 1 1 5 7 3 5 9 3 17 8 8 8 42 58 25 42 75* 25 JREE does not equal 100%. The other three randomly selected articles represented two types not captured in the above categories. Two (17%) were meta-analyses and one (8%) was a simulation with a methodological question. a tion disorders (LSHSS, AJSLP, JSLHR, JCD) demonstrated a lower proportion of advanced statistics but employed a variety of designs (i.e., qualitative, single case, traditional, and advanced). The majority of the sampled articles employed traditional methods (58%–92% of the time), most commonly reporting descriptive data, ANOVAs, or regression analyses. built replication into their design in order to replicate their own findings in a sequence of studies and one reported that a primary aim was to replicate another existing study. Randomization and Replication Key Findings Random assignment was not a predominating characteristic of the research studies reviewed, with only 22% using random assignment. Most of the studies did not report that the research was an attempt to replicate a previous study or did not include replication in their methods (92%). Of the studies in the review pool that addressed replication (n = 10), nine Discussion Based on trends in the randomly selected sample of 120 journal articles, multidimensional methods of analysis were commonly used, particularly in articles published in JREE, JLD, JEP, RW, RRQ, and SSSR. The common use of multidimensional methods seen here is consistent with trends reported in the literature, as noted by one methodologist: “Multilevel and Wood et al.: Language and Literacy Research 313 hierarchical modeling through various types of linear mixed models has rapidly become a required asset in the statistical toolkit of researchers worldwide” (Garson, 2013, p. 23). Trends in the current review suggest that the data sets used in the studies varied largely in terms of size, with 62% including 50 or more participants. Articles from journals in speech-language pathology showed lower average sample sizes. Across all journals, random assignment was the exception rather than the norm. Studies used a wide variety of types of design and statistical method. Advanced statistical methods that considered multiple levels of analysis and dimensions of sampling were more prevalent in journals that were not specifically within the field of speech-language pathology (e.g., JREE, JEP, RRQ, JLD, RW, and SSR). It is not surprising that studies from selected journals in speech-language pathology showed smaller sample sizes on average. The focus on low-incidence populations in speech-language pathology may partially explain the tendency toward small data sets. Consistent with this explanation, the out-of-field journals showed a higher percentage of articles pertaining to typical populations. Recruiting children and youth, particularly from low-incidence populations, may require innovative collaborations across institutions in order to access larger data sets. Further, the nature of our interest in populations with unique characteristics may impact the types of methods used, in that employing true experimental designs with random assignment may be challenging given that participant characteristics cannot be assigned and treatment often cannot be ethically withheld. commonly focused on furthering research competencies for consumers or producers of evidence-based practices. Further, there are not many examples of large open-access or multistate data sets available in the extant literature; however, the concept is aligned with Heilmann, Miller, and Nockerts’ (2010) description of the establishment of large language-sample databases. In this example, the establishment of multistate data using common language-sample protocols allowed for replication and ultimately a discriminant function analysis to validate the use of language sample measures in classifying children’s language status. Other potential change mechanisms noted in the literature include (a) fostering the establishment of mavens with content knowledge in our field, (b) providing social support such as setting up a special interest group on advanced statistics and methodology, and/or (c) creating blogs on statistical design (Sharpe, 2013). Leaders in the field of speechlanguage pathology have noted the critical need for building partnerships between highly qualified researchers and school-based SLPs to conduct welldesigned high-quality intervention studies focused on improving children’s language and literacy needs (Nippold, 2015). Becoming producers or consumers of rigorous research using more complex statistics and methodology is difficult, if not impossible, without access to comprehensible professional development. It would not be surprising to find that well-intentioned lifelong learners have purchased an advanced methods book hoping for professional guidance, only to find that they cannot easily digest it without a guide or interpreter. In response, increased offerings of short courses or research translation sessions may be considered that focus on innovative statistics and methodology with relevant application to our field and practices. There may be no immediate or simple solutions that emerge from the literature. In brainstorming possible options to overcome challenges of working with low-incidence populations, it would seem important for us to leverage incentives to build a useful body of evidence. National organizations could offer incentives for individual clinicians to register item responses on commonly administered assessments in order to facilitate the formation of national data sets that might have utility for difficult-to-answer research questions. It may also be beneficial for national organizations to have designated mavens or information brokers who are skilled at bundling evidence into meaningful, manageable information packages to facilitate use in clinical practices, as findings of rigorous research may otherwise go ignored without translation (Mullen, 2005). Mechanisms of Change One of the intentions of this article was to generate discussion of ways to enhance leadership training in order to prepare next-generation scholars to ensure rigor in research in our field. The results illuminate trends, similarities, and differences in the methods used in scholarly journals related to language and literacy. The discrepancies between journals highlight the need to ensure that scholars in speech-language pathology are poised to be consumers and producers of research who employ diverse methods in order to be competitive for external funding. Although the identification of levers of change is beyond the scope of this article, one of the aims was to generate such discussion. There are many possible mechanisms of change; among them, professional development, combining forces to establish large data sets, and Big Data at a multistate level. Although professional development is widely available in communication disorders programs, it is perhaps less 314 Contemporary Issues in Communication Science and Disorders • Volume 43 • 306–317 • Fall 2016 Although the role of SLPs in language and literacy research may be highly regarded, our field risks being left behind if there are lags in the time it takes us to incorporate novel statistics and methodology into our research repertoire. Some authors have suggested that preparation for scientific rigor begins at the undergraduate curriculum so as to optimally prepare students for scientific careers in our field (Koehnke, McNeil, Chapman, Folsom, & Nunez, 2014). Research experiences and course work in methodology and statistics should begin early in students’ career paths but also be present as a constant focus throughout training and beyond. Each decade also brings waves of innovations in research practices. SEM, HLM, and advances in statistical software bring new opportunities for rigorous research designs. In response, continuing education opportunities are needed to help CSD faculty compete in the research-funding climate. Within a relatively short time of obtaining a degree or even a terminal degree comes the sweeping realization that nothing is terminal about one’s understanding of research design, methodology, and statistics. Indeed, whether one’s desire is to produce high-quality research or to be a wise consumer of it, knowledge of best practices in research can quickly become archaic without continuing education opportunities to stay current. The end goal in advocating for reliable evidence is to better inform policy and practice. With their sails set on random assignment, massive data sets, and replication, researchers in educational and CSD research may benefit from strategic preparation to poise themselves to take full advantage of the new options to promote rigorous research. Study Limitations It cannot be assumed that the randomly selected sample of journal articles is representative of the collective set of articles in each journal or representative of the typical proportion of articles using each type of design. We may have derived different trends if we had characterized every article in each issue of each journal. Also, it should be noted that the current review is not an exhaustive review of all journals pertaining to language and literacy. Notably, there are numerous other journals that could be included to expand the review; however, we felt these journals to be of interest as flagship journals. Implications Despite limitations, the trends in the findings of the review support the need to prepare future faculty and scholars in speech-language pathology to be proficient consumers and producers of a variety of research designs and statistical methodology. Doctoral programs in speech-language pathology may want to carefully consider the research-related competencies to include a range of qualitative, single-case method, and multilevel models. Based on the trends, particularly in JEP, JREE, RRQ and SSR, there is regular use of SEM and hierarchical methods. The current review suggests that studies published in ASHA journals may be shifting a bit in the use of advanced methods as well, as noted by the use of multilevel models in some of the articles reviewed. It may be difficult to consider intensive systems change in preparing doctoral students for use of a range of methods when doctoral students in CSD programs are already in short supply. In response, mechanisms of change may need to be considered. References American Speech-Language-Hearing Association. (2005a). Evidence-based practice in communication disorders: Position statement and technical report. Retrieved from www.asha.org/policy doi:10.1044/policy American Speech-Language-Hearing Association. (2005b). Shortages in special education and U. S. Office of Related Services focus on new coalition—Shortages outstrip those in math, science. Rockville, MD: Author. August, D., & Shanahan, T. (Eds.). (2006). Developing literacy in second-language learners: Report of the National Literacy Panel on Language-Minority Children and Youth. Mahwah, NJ: Erlbaum. Baayen, R. H., Davidson, D. J., & Bates, D. M. (2008). Mixed-effects modeling with crossed random effects for subjects and items. Journal of Memory and Language, 59, 390–412. Branum-Martin, L., Tao, S., & Garnaat, S. (2015). Bilingual phonological awareness: Reexamining the evidence for relations within and across languages. Journal of Educational Psychology, 107(1), 111–125. Compton, D. L, Miller, A. C., Gilbert, J. K., & Steacy, L. M. (2013). What can be learned about the reading comprehension of poor readers through the use of advanced statistical modeling techniques? In B. Miller, L. E. Cutting, & P. McCardle (Eds.), Unraveling reading comprehension: Behavioral, neurobiological, and genetic components (pp 135–147). Baltimore, MD: Brookes. Ebrahim, S., Sohani, Z., Montoya, L., Agarwal, A., Thorlund, K., Mills, E. J., & Ioannidis, J. P. A. (2014). Reanalyses of randomized clinical trial data. Journal of the American Medical Association, 312(10), 1024–1032. doi:10.1001/jama.2014.9646 Garson, G. D. (2013). Fundamentals of hierarchical linear and multilevel modeling. In D. Garson (Ed.), Hierarchical linear modeling: Guide and applications (pp. 3–25). Thousand Oaks, CA: Sage. Wood et al.: Language and Literacy Research 315 Heilmann, J. J., Miller, J. F., & Nockerts, A. (2010). Large language sample databases. Language, Speech, and Hearing Services in Schools, 41, 84–95. Neimark, E. D., & Estes, W. K. (1967). Stimulus sampling theory. San Francisco, CA: Holdenday. Nippold, M. (2015). Call for studies in implementation science: Improving reading comprehension in school-age children. Language, Speech, and Hearing Services in Schools, 46, 65–67. doi:1044/2015_LSHSS-15-0010 Horner, R. H., Carr, E. G., Halle, J., McGee, G., Odom, S., & Wolery, M. (2005). The use of single-subject research to identify evidence-based practice in special education. Exceptional Children, 71(2) 165–179. doi:10.1 177/001440290507100203 No Child Left Behind (NCLB) Act of 2001, 10 U. S. C. A. 6301 et seq. (West 2003). Ioannidis, J. (2005). Why most published research findings are false. PLoS Medicine, 2(8), 696–701. doi:10.1371/ journal.pmed.0020124 Reinhart, A. L., Haring, S. H., Levin, J. R., Patall, E. A., & Robinson, D. H. (2013). Models of not-so-good behavior: Yet another way to squeeze causality and recommendations for practice out of correlational data. Journal of Educational Psychology, 105, 241–247. Kline, R. B. (2015). Principles and practice of structural equation modeling (4th ed.) New York, NY: Guilford Press. Rodgers, J. L. (2010). The epistemology of mathematical and statistical modeling: A quiet methodological revolution. American Psychologist, 65, 1–12. doi:10.1037/ a0018326 Koehnke, J., McNeil, M. Chapman, K., Folsom, R. C., & Nunez, L. (2014, April). Addressing the PhD shortage. Paper presented at the conference of the Council on Academic Programs in Communication Sciences and Disorders. Retrieved from www.capcsd.org/conference/ 2014Handouts/Addressing_the_PhD_Shortage_April11_ 2014.pdf Sharpe, D. (2013). Why the resistance to statistical innovations? Bridging the communication gap. Psychological Methods, 18(4), 572–582. doi:10.1037/a0034177 McCurtin, A., & Roddam, H. (2012). Evidence-based practice: SLTs under siege or opportunity for growth? The use and nature of research evidence in the profession. International Journal of Communication Disorders, 47(1), 11–26. doi:10.1111/j.14606984.2011.00074.x Contact author: Carla Wood, Florida State University, Communication Disorders, 201 W Bloxham, Tallahassee, FL 32309. Email: carla.wood@cci.fsu.edu Mullen, R. (2005, November 8). Survey tests members’ understanding of evidence-based practice. The ASHA Leader, 10, pp. 4–14. doi:10.1044:/leader.AN.10152005.4 316 Contemporary Issues in Communication Science and Disorders • Volume 43 • 306–317 • Fall 2016 Appendix. Description of Constructs for Coding Advanced was used to describe quantitative studies that utilized more complex statistical analyses including path analysis, item response theory, and approaches that used multiple dimensions of sampling, such as structural equation modeling and multilevel modeling, and meta-analyses. Quantitative was used to describe studies that employed any form of quantitative methodology, using probability statistics to make inferences or draw conclusions. Studies that employed only surveys for data collection were excluded from this category. Atypical sample was defined as a sample selected to target specifically members of an atypical population. Samples that were not specified to target specifically atypical populations were labeled as typical samples. Random assignment was defined as statistically-random assignment of groups or manipulations. Design was used to describe the methodological procedures employed to address the purpose of the article and was categorically labeled. Categories included single group: single case/case study; single group: manipulation; single group: observation; multiple group: observation; multiple group: manipulation without random assignment; and multiple group: manipulation with random assignment. Manipulation was defined as the experimenter changing or controlling some variable(s) in the research design. Most advanced analysis was defined as the most advanced statistical analysis employed in the study. Possible classifications were: 1) Qualitative; 2) Single Case/Case Study; 3) Traditional; 4) Advanced. Multiple group was used to describe any design with two or more groups. Replication was defined as the explicitly identified repeating of a previous research investigation with the intent to cross-examine conclusions obtained in that previous study. Research was defined as any design including systematic evaluation of data, excluding meta-analyses Single-Case or Small n was used to describe any single-group design with less than 5 participants or where participants served as their own controls. Research entities were counted as the separate institutions listed within each research article as having participated in the investigation through supporting or employing one or more of the authors. Sample size was defined as the total number of individuals participating in the investigation. Multiple studies was the label assigned to research articles including more than one explicitly identified research study. Single case/case study was used to describe quantitative studies that examined one or a few subjects using either single case research design or case study design; Single group was defined as a research design with one group for the entire duration of the research project. Number of groups was defined as the number of clusters or groups in which participants belonged or were placed. Survey was used to describe studies that employed only questionnaires or script-based interviews for data collection. Observation was defined as the experimenter obtaining data without changing or controlling some variable in the research design. Traditional was used to describe quantitative studies that utilized only OLS-based or equivalent nonparametric statistical analyses, such as regression, multiple regression, ANOVA, t test, Mann-Whitney, Pearson product–moment correlation, Spearman’s rank order correlation. Population was categorically labeled and was determined by the age of the participants included in the sample. Population categories included: infant/toddler, Pre-K, K-12, college students, adults, geriatric (ages 60+), or mixed. Qualitative was used to describe studies that employed only qualitative methodology, such as open-ended interviewing to describe and develop themes, rather than quantitative methodology. Type of study was defined categorically as the type of research conducted. Categories included: qualitative, quantitative, survey, and mixed. Typical sample was defined as a sample following a conventional and predictable pattern based on the majority of the general population. Wood et al.: Language and Literacy Research 317 Copyright of Contemporary Issues in Communication Science & Disorders is the property of National Student Speech Language Hearing Association and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. Social Impact of Scholarly Articles in a Citation Network Jose A. García, Rosa Rodriguez-Sánchez, and Joaquín Fdez-Valdivia Departamento de Ciencias de la Computación e I. A., CITIC-UGR, Universidad de Granada, 18071 Granada, Spain. E-mail: {jags, rosa, jfv}@decsai.ugr.es The intent of this article is to use cooperative game theory to predict the level of social impact of scholarly papers created by citation networks. Social impact of papers can be defined as the net effect of citations on a network. A publication exerts direct and indirect influence on others (e.g., by citing articles) and is itself influenced directly and indirectly (e.g., by cited articles). This network leads to an influence structure of citing and cited publications. Drawing on cooperative game theory, our research problem is to translate into mathematical equations the rules that govern the social impact of a paper in a citation network. In this article, we show that when citation relationships between academic papers function within a citation structure, the result is social impact instead of the (individual) citation impact of each paper. Mathematical equations explain the interaction between papers in such a citation structure. The equations show that the social impact of a paper is affected by the (individual) citation impact of citing publications, immediacy of citing articles, and number of both citing and cited papers. Examples are provided for several academic papers. Introduction Garfield (1955) proposed a citation index for the sciences (a list of papers along with the articles that cite them) to improve the scholarly communication process. He also suggested the possibility of using citations as a measure of the impact of a scholarly article within its research field. In this context, Garfield and Sher (1963) presented results concerning the citation behavior of research literature in 1961. It was shown that when plotting citation frequency (e.g., the number of times a paper is cited), a small subset of those papers receive the majority of citations. The evaluation of the impact of scholarly articles aims to identify the most influential works within research fields. Received April 19, 2013; revised October 4, 2013; accepted October 4, 2013 © 2014 ASIS&T • Published online 9 May 2014 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/asi.23156 In a situation, for example, in which the only influential articles are those that achieve a given number of citations, a published manuscript not receiving the minimum number of citations is assumed to be of less impact. However, the effect of citation relationships between academic papers (i.e., cites and is cited by) cannot be gauged in advance except in the roughest terms. It can easily happen that the structure of these citation relationships in a citation network conceals a bias in the distribution of influence among articles unsuspected and unobserved by those measuring the impact of scholarly papers. In this context, Garner (1967) was among the first to consider citation analysis as a kind of network study. Small (1973) provides one of the first applications of citation networks. Currently, few would not see citation analysis as a form of applied graph theory, as suggested by Hu, Rousseau, and Chen (2012), which exemplifies the state of the art using this approach. The intent of this article is to use an economic model of cooperative game theory to predict the level of social impact of scholarly papers created by specific citation networks. Lucio-Arias and Scharnhorst (2012) connect this proposal with the history of citation network analysis from a mathematical approach. Hereafter, “social impact” refers to the net effect of citations on a network: A scholarly paper exerts direct and indirect influence on other articles (by citing articles and by articles that cite citing articles) and is itself influenced directly and indirectly (by references and references of references). This citation network leads to an influence structure of citing and cited publications (i.e., the set of influence relations between the manuscripts in a given citation network). In our model of social impact, a cooperative game is a game where groups of articles (coalitions) may enforce cooperative behavior to gain further recognition and relevance, hence the game is a competition between coalitions of papers, rather than between individual articles. Here, we assume that articles choose which coalitions to form following the citation relationships in a citation network. These coalitions will be composed of (direct and indirect) citing and cited articles. JOURNAL OF THE ASSOCIATION FOR INFORMATION SCIENCE AND TECHNOLOGY, 66(1):117–127, 2015 A cooperative game is given by specifying a value for every coalition of articles. Formally, the game consists of a finite set of articles N , called the grand coalition, and a characteristic function v from the set of all possible coalitions of papers to a set of payments that satisfies that the value of the empty set is zero, v(0/ ) = 0. The function describes how much collective relevance (payoff) a set of articles can gain by forming a coalition, and the game is sometimes called a value game or a profit game. Recall that the players (articles) are assumed to choose which coalitions to form based on the citation relationships in a citation network (i.e., direct and indirect citing and cited papers). The challenge is then to allocate the collective relevance v( N ) among the individual articles in some fair way. A solution concept is a vector that represents the allocation to each player in the game. In game theory, researchers have proposed different solution concepts based on different notions of fairness. Some properties to look for in a solution concept include (see Aumann & Hart, 2002, for further details) efficiency, individual rationality, existence, uniqueness, computational ease, symmetry, additivity, and zero allocation to null players. For instance, the Shapley value is the unique payoff vector that is efficient, symmetric, additive, and assigns zero payoffs to dummy players (Shapley, 1953). Drawing on cooperative game theory, our research problem is to translate into mathematical equations the rules governing the social impact of a paper in a citation network. We also want to study the differences in value between the (individual) citation impact of a paper and its social impact in a citation network. Thus, in this article, we prove that when citation relationships between academic papers (cites and is cited by) function within a citation structure, the result is social impact instead of the (individual) citation impact of each paper (i.e., times cited). To this aim, we derive mathematical equations explaining the interaction between papers in such a citation structure. The equations will show that the social impact of a paper is affected by (individual) citation impact of citing publications, immediacy of citing articles, and number of both citing and cited papers. This theory of social impact of scholarly papers proves that the greater the number of citing publications in a citation network, the greater the social impact. Immediacy takes into account how direct or indirect was the influence that a citing publication exerts on other papers by citing articles, by citing citing articles, and so on. The derived equations illustrate that there is more social impact when the citing publications are highly cited papers, when the citing action is more immediate, and when there is a greater number of citing articles. But here we also uncover another rule of social impact of scholarly papers, which is divisions of impact in a citation structure. This rule states that the number of cited articles also plays a role in social impact. That is, the greater number of cited publications in a citation structure causes the social impact to be divided among all of the cited publications. 118 Drawing on an economic model of cooperative game theory, the social impact theory of scholarly articles is both a generalizable and a specific theory. It uses one set of equations that are applicable to many citation relationships. Social impact theory of scholarly papers is also useful, because it can be used to understand which citation relationships between academic papers result in the greatest impact. Hence, social impact theory explores citation relationships and can help predict the outcomes of such citation relationships finding more accurate ways to measure social impact, understanding the role of each element in a citation network. In summary, in this article, we show the use of cooperative game theory to attack the problem of the measurement of impact of a scholarly manuscript in a citation network. The main contributions are: • A mathematical treatment for the network approach to citation analysis • The concept of “social impact” of an article and its measure that yields an effective way to analyze the influence of papers in a citation network • The comparative study of the citation impact of a paper and its social impact The following section proves that without taking account of the influence structure (in a citation network) on the manuscripts, the value of social impact of a paper equals its individual citation impact. Next, the Social Impact in a Citation Network section analyzes the social impact of scholarly articles taking account of the influence structure in a citation network. It predicts a shift in individual impact; that is, the citation impact of a paper is equally spread over itself and its superiors in the influence structure given by a citation network. A mathematical model of the cooperative game theory allows the exact calculation of the factor of social impact that results in such a case. The comparative value of social impact and (individual) citation impact of scholarly articles are analyzed using a set of experiments in the Social Impact in a Citation Network section. Finally, we summarize the main conclusions of this work. The “Social Impact” of Scholarly Articles There are papers of high citation impact that retain the power to wield single-handed influence within their research field. At the same time, most of the scholarly articles are often individually of low citation impact as measured by the number of received citations (see, e.g., Garfield & Sher, 1963; Redner, 1998). Generally, the measurement of the influence of a scholarly article is carried out based on a large number of manuscripts with low citation impact. However, if papers form coalitions based on citation relationships, their collective impact may be great enough to achieve a significant influence. In that case, the question is how to attribute to each JOURNAL OF THE ASSOCIATION FOR INFORMATION SCIENCE AND TECHNOLOGY—January 2015 DOI: 10.1002/asi article its “fair share” of collective impact for the different coalitions (which arise from citation relationships) in a citation network. This problem falls naturally into the realm of cooperative game theory (Aumann & Hart, 2002). There, too, we have players who can form coalitions and gain by doing so; some coalitions may gain more than others. The question there, too, is how to divide the benefits of the cooperation among the players. Depending on the criteria we want our solution to satisfy, we get different solutions. In our problem, a cooperative game consists of a set of scholarly articles N and a characteristic function v that describes the worth (joint impact) that every coalition (subset) of articles could normally obtain in a citation network. Because interactions among all the possible coalitions of papers may be complex, we simplify by assuming that the cooperative possibilities of the game can be described by the function v that assigns a number v(S ) to every coalition S of published papers, with the value of the empty subset being zero, v(0/ ) = 0. What each coalition S of scholarly articles can achieve on its own regarding the joint impact, its worth v(S ), depends on the complementaries between the individual impact of the manuscripts in S . In this article, we consider that the cooperative game is additive, and the worth of coalition S is then as follows: v(S ) = ∑ wi i ∈S (1) where wi denotes the number of received citations of manuscript i in S (i.e., its citation impact). That is, following Garfield (1955), it is assumed that the individual impact of each article i ∈ N is represented by the number of received citations wi (citation impact). Now, by means of this cooperative game, we study the distribution of the impact within the set of scholarly articles. For instance, Table 1 shows a possible coalition S of articles in N . In this example, N is the set of articles published in academic journals—included in the Web of Science (WoS)—during 2012. The coalition S of scholarly articles illustrated in Table 1 is composed of four papers, S = {1, 2, 3, 4}, and the worth of S is the sum of (individual) citation impacts of the papers in the coalition: v(S ) = ∑ wi = 3 + 2 + 5 + 9 = 19 i ∈S (2) TABLE 1. An example of a coalition of scholarly articles. Paper 1 2 3 4 Title Authors Which Are the Best Performing Regions in Information Science in Terms of Highly Cited Papers? Some Improvements of Our Previous Mapping Approaches Percentile Ranks and the Integrated Impact Indicator (I3) The New Excellence Indicator in the World Report of the SCImago Institutions Rankings 2011 Basic Properties of Both Percentile Rank Scores and the I3 Indicator Times cited, wi L. Bornmann & L. Leydesdorff 3 L. Leydesdorff & L. Bornmann 2 L. Bornmann, F. de Moya-Anegón, L. Leydesdorff 5 R. Rousseau 9 scholarly articles N ; and (b) an additive characteristic function v, v({i}) = wi for all i in N , determined by the worth (joint impact) of coalitions of articles (i.e., the sum of [individual] citation impacts of the papers in the coalition). This definition does not take account of the influence structure in a citation network (the set of influence relations between the manuscripts in a given citation network) beyond the individual citation impacts that were summed to obtain the worth of coalitions. However, it can easily happen that the structure of these citation relationships in a citation network conceals a bias in the distribution of influence among articles. This will be analyzed in the following section (see Social Impact in a Citation Network section). Let S and P be two coalitions of papers; where S may be a subset of P. Following Harsanyi (1959), the game v can then be expressed as v( P ) = ∑ Δ v (S ) ⋅ uS (P ); P ⊆ N (3) S ⊆ N :S =/ 0/ where the quantity Δ v (S ) is referred to as the dividend of coalition S in game of influence (v, N ), and where uS denotes the unanimity game (i.e., a game in which coalition S is trying to maximize the joint impact of another coalition P only if coalition S is a subset of P ) given by uS (P ) = 1 if S ⊆ P ; 0 otherwise. (4) where the wi values were calculated using the citations received by the articles in the WoS database (accessed January 2013). We can now define the concept of “game of influence” as follows: From Equation (3), to analyze the game of influence (v, N ) properly, we study its behavior on the collection of all unanimity games uS , where S ⊆ N : S =/ 0/ . Because the unanimity games form a basis, Equation (3) is uniquely determined. To this end, we first need the following result. Definition 1: Game of influence. A game of influence (v, N ) is a cooperative game that consists of: (a) the set of Proposition 1: Dividends of a game of influence. In a game of influence for measuring the impact of scholarly JOURNAL OF THE ASSOCIATION FOR INFORMATION SCIENCE AND TECHNOLOGY—January 2015 DOI: 10.1002/asi 119 manuscripts, the dividend S ⊆ N : S =/ 0/ , is given by ⎧wi Δ v (S ) = ⎨ ⎩0 Δ v (S ) of coalition if S = {i} for some i ∈ N ⎫ ⎬ otherwise. ⎭ S, Paper (5) where wi is the number of received citations of manuscript i ∈ N (its citation impact). Proof. See Proof of Proposition 1 section in the Appendix. From Proposition 1, it follows that the only coalitions of papers that have positive dividends are those composed of one manuscript. This is a direct consequence of Definition 1 that does not take into account the set of influence relations in a citation network (beyond the individual citation impacts). We have that manuscripts with low individual citation impact (as given by the number of received citations) may be influential via coalitions in a citation network. A payoff x = {x i (v); i ∈ N } for the game of influence (v, N ) is a correspondence that associates with each manuscript i a possible payment for being involved in the game. It charges each manuscript its fair share of coalitional influence (which we are looking for). Hence a payoff x for the game (v, N ) provides an estimation of the cooperative influence of scholarly articles in N . In game theory, Shapley (1953) defined a value for games to be a function that assigns to each game v a payoff xi(v) for each i ∈ N , which can be described by x i (v) = Δ v (S ) S S ⊆ N :i ∈S ∑ (6) with S being the cardinal of subset S, where Δ v (S ) denotes the dividend of coalition S. In our problem, the Shapley value is a unique function that satisfies three axioms: (symmetry axiom) manuscripts that are treated identically by the game v be treated identically by the value xi(v); (carrier axiom) the sum of xi(v) over all manuscripts i in any N equals v( N ); and (additivity axiom) for any games v and w, xi(v + w) = xi(v) + xi(w). Also, Driessen (1988) proved that the Shapley value of a superadditive game (i.e., a game such that v(S ) + v(T ) ≤ v(S ∪ T ) for any S , T ⊆ N ) is individually rational. Based on the Shapley value of a game of influence, we can now define the concept of “social impact” of a manuscript as follows: Definition 2: Social impact of scholarly articles. Given a game of influence (v, N ), the social impact SIv(i) of a manuscript i ∈ N is SI v (i ) = Δ v (S ) . S S ⊆ N :i ∈S ∑ (7) The following result is a direct consequence of the definition of a game of influence given in Definition 1. It shows 120 TABLE 2. Social impact and times cited (citation impact) of manuscripts in S (see Table 1). 1 2 3 4 Social impact, SIv(i) Times cited 3 2 5 9 3 2 5 9 that if citation relationships between academic papers (i.e., cites and is cited by) do not give rise to an influence structure on scholarly articles, the social impact is equal to the (individual) citation impact of each paper. Proposition 2. In a game of influence (v, N ) as given in Definition 1, the social impact of a manuscript i equals its individual citation impact (times cited wi): SI v (i ) = wi , with i ∈ N . (8) Proof. It simply follows from substituting Equation (5) in the social impact SIv(i) of a manuscript as given in Definition 2. Following Proposition 2, Table 2 shows the values of social impact for the manuscripts in coalition S = {1, 2, 3, 4} given in Table 1. As discussed earlier, to achieve the result given by Proposition 2, we assumed that there is no influence structure on the articles that can bias social impact. However, it is unrealistic because a citation network would cause an influence structure on scholarly articles, as demonstrated in the following section. Social Impact in a Citation Network The influence structure in a citation network (the set of influence relations between the manuscripts in a given citation network) may go beyond the individual citation impacts that were summed to obtain the worth of earlier coalitions. In this case, it can easily happen that the structure of these citation relationships in a citation network conceals a bias in the distribution of influence among articles unsuspected and unintended by the methods that were used to measure the impact of scholarly papers in the previous section. Following Hu et al. (2012), we have that, within a citation network, a manuscript exerts direct and indirect influence on other papers (by citing articles and by articles that cite citing articles), and is itself influenced directly and indirectly (by references and references of references). This leads to an influence structure of citing and cited publications. This section studies the social impact of scholarly articles, taking into account the influence structure in a citation network. It predicts a shift in individual impact; that is, the citation impact of a paper is equally spread over itself and its superiors in the influence structure given by a citation JOURNAL OF THE ASSOCIATION FOR INFORMATION SCIENCE AND TECHNOLOGY—January 2015 DOI: 10.1002/asi FIG. 1. All descendants and superiors of paper 2 in the influence structure O (see Table 3). FIG. 2. All descendants and superiors of paper 3 in the influence structure O (see Table 3). network. Again, a mathematical model of the cooperative game theory allows the exact calculation of the factor of social impact in this case. Influence Structure in a Citation Network First, we need to define how the citation relationships (i.e., cites and is cited by) in a given citation network may give rise to an influence structure on scholarly articles. We assume that all references have already been published by an academic journal before being cited by another manuscript of N . Definition 3: Influence structure in a citation network. Let a direct descendant of paper i be a manuscript that cites i. Given a citation network, the influence structure on the set N of manuscripts is a mapping O on N such that O(i), with i ∈ N, is the set of direct descendants of i in the citation network. Therefore, O(i), with i ∈ N, is the subset of manuscripts where paper i is being cited. Given an influence structure O, we have that the collection of all (direct and indirect) descendants of the published article i, name after D(i), defines the transitive closure of the influence structure O. That is, the descendants of manuscript i are the subset of (direct and indirect) citing articles of the manuscript i. In the following, we also denote by D −1 (i ) = {k ∈ N | i ∈ D(k )} (9) the set of all superiors of manuscript i ∈ N in the influence structure O on N . The superiors of manuscript i are the subset of direct and indirect references of the manuscript i. Figures 1 through 4 show the collection of all descendants (transitive closure of O) and superiors for the manuscripts in the coalition S = {1, 2, 3, 4}, which is illustrated in Table 1. Again, in this example, N is the set of articles published in academic journals—included in the WoS— during 2012. The set of descendants of coalition S, that is, FIG. 3. All descendants and superiors of paper 1 in the influence structure O (see Table 3). D({1, 2, 3, 4}), is simply given by D(S) = D(1) ∪ D(2) ∪ D(3) ∪ D(4). Table 3 shows the set of papers and their descendants for this coalition S of example: {1, 2, 3, 4} ∪ D({1, 2, 3, 4}). For each paper, this table also illustrates the accession number and times cited in the WoS database (accessed January 2013). In Figures 1 through 4, using a directed graph, we illustrate the descendants and superiors of each paper in the coalition S = {1, 2, 3, 4}. In these four figures, each manuscript is represented by a node in the graph. A directed edge from node i to j means that paper i is being cited by paper j. A paper k is a descendant of i if there exists a path from i to k in the graph. For instance, paper 5 is a descendant of paper 1 (see Figure 3): 5 ∈ D(1). Hence Figures 1 through 4 show all descendants (and superiors) of papers 2, 3, 1, and 4, in the influence structure O on N . These examples show a given citation structure with the same number of nodes (papers) and links (“is cited by”), but they focus on different papers having a distinct level of (more or less) social influence. JOURNAL OF THE ASSOCIATION FOR INFORMATION SCIENCE AND TECHNOLOGY—January 2015 DOI: 10.1002/asi 121 FIG. 5. Superiors of S: D−1(S) = D−1(1) ∪ D−1(2) ∪ D−1(3) ∪ D−1(4). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] FIG. 4. All descendants and superiors of paper 4 in the influence structure O (see Table 3). TABLE 3. Papers and all (direct and indirect) descendants (in N ) for coalition S = {1, 2, 3, 4}. Paper 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Accession number Times cited WoS:000301364100018 WoS:000307730000017 WoS:000301364100017 WoS:000302157900016 WoS:000310550000019 WoS:000308516300002 WoS:000308581700016 WoS:000308888400013 WoS:000310550000010 WoS:000311853600006 WoS:000305233900015 WoS:000311234600025 WoS:000308581700021 WoS:000306547000013 WoS:000305434900004 WoS:000306547000017 WoS:000306547000012 WoS:000306547000018 WoS:000311515900011 3 2 5 9 0 0 0 1 0 0 1 0 0 1 0 2 1 0 0 Note. N is the set of articles published in academic journals—included in the WoS—during 2012. Next, we define a class of coalitions of articles that are productive without papers outside those coalitions, because all superiors (references) of the manuscripts in that “autonomous” coalition are also members of the coalition. Definition 4: Autonomous collections of manuscripts. Let O be an influence structure on N . The coalition S ⊆ N is autonomous in the influence structure O if D −1 (S ) ⊂ S ; with D −1 (S ) = ∪ i∈S D −1 (i ) . Figure 5 shows the set of all superiors in N for the coalition S = {1, 2, 3, 4} of the example given in Table 1. A Venn diagram is used to illustrate that coalition S = {1, 2, 3, 4} is autonomous in the influence structure O, because D −1 (S ) ⊂ S (see Figure 6). 122 FIG. 6. Venn diagram that shows that S is autonomous in the influence structure O: D −1 (S ) ⊂ S . [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] We can now address the game theoretic analysis taking account of the influence structure. There, the citation relationships impose asymmetric constraints on the manuscripts. That is, for every i, k ∈ N , k ∈O(i ) implies that i ∈ / O(k ), because we assumed that all references have already been published before being cited by another manuscript of N ; thus, if k ∈ O(i), we have that manuscript i was published before being cited by manuscript k and the manuscript i cannot be a descendant of k in the influence structure, that is, i ∉ O(k). Finally, we are now in conditions to define the basic concept as follows: Definition 5: Game with an influence structure. A game of influence (v, N , O) is a cooperative game on the set of scholarly articles N , where an additive characteristic JOURNAL OF THE ASSOCIATION FOR INFORMATION SCIENCE AND TECHNOLOGY—January 2015 DOI: 10.1002/asi function v, v(i) = wi for all i in N , determines the worth (joint impact) that coalitions could normally obtain were it not for the influence structure O on N in a citation network. Restricted Game In the definition of game with an influence structure (Definition 5), the worth of articles (and their coalitions) is still independent of the influence structure O. Following Gilles, Owen, and van den Brink (1992), we need to transform this game of influence (v, N , O) into a new game. It describes all possibilities open to the scholarly articles in the influence structure O, given their potential abilities as described by the additive game v. The resulting game is called restricted game as defined in the following: Definition 6: Restricted game. Let (v, N , O) be a game of influence with a given influence structure O. The restricted game (vO, N ) is a cooperative game on the set of scholarly manuscripts N , where the worth of the coalitions S ⊆ N determines which they can achieve (in terms of collective influence), taking account of the influence structure O: SI vO (i ) = Δ vO (S ) . S S ⊆ N :i ∈S ∑ with Δ vO (S ) being the dividend of coalition S in restricted game (vO, N ). The following proposition predicts a substantial shift in (individual) citation impact of scholarly articles, when considering the influence structure O. It explains the interaction between papers in such a citation structure. This proposition shows that the social impact of a paper is affected by (individual) citation impact of citing papers, immediacy of citing publications, and number of both citing and cited articles. It is based on the social impact of a scholarly manuscript in a restricted game (vO, N ): Proposition 4: Shift in (individual) citation impact of papers. In a restricted game (vO, N ), the social impact of a scholarly article i ∈ N is given by SI vO (i ) = ∑ k ∈{i} ∪ D ( i ) vO (S ) = v(σ (S )), for all S ⊆ N Proposition 3: Dividends of a restricted game. In a restricted game (vO, N ) with an influence structure O, the dividend Δ vO (S ) of coalition S, S ⊆ N : S =/ 0/ , is given by if S = α ({i}) for some i ∈ N ⎫ ⎬ otherwise. ⎭ wk D (k ) + 1 −1 (13) (10) where σ (S ) is the largest autonomous subset of S. That is, the worth of coalition S when taking into account the influence structure O is simply the worth (joint impact) that the largest autonomous subset of S could normally obtain. In this study, we can also analyze the restricted game (vO, N ) on the collection of all unanimity games uS as given in Equation (4), where S ⊆ N : S =/ 0/. To this aim, we first need a new proposition that gives the form of the dividends of a restricted game as follows: ⎧wi Δ vO (S ) = ⎨ ⎩0 (12) (11) where wi is the (individual) citation impact of manuscript i ∈ N , and with α (R ) being the smallest autonomous coalition that contains all members of R, as well as their superiors in the influence structure, for example, α ({i}) = {i} ∪ D −1 (i ) . Proof. See Proof of Proposition 3 section in the Appendix. Based on the Shapley value of a restricted game, we can now define the concept of social impact of a scholarly manuscript taking account of the influence structure in a citation network: Definition 7: Social impact in a restricted game with an influence structure. Given a restricted game (vO, N ), the social impact SI vO (i ) of an article i ∈ N when taking account of an influence structure O is where wk is the number of received citations of article k (its citation impact), D(i) is the set of all descendants of article i in the influence structure, and with |D−1(k)| being the cardinal of the set of all superiors of manuscript k. Proof. See Proof of Proposition 4 section in the Appendix. This mathematical result shows that the greater the number of citing publications in a citation network, the greater the social impact. Also, there is more social impact when citing publications are highly cited papers, when the citing action is more immediate, and when there is a greater number of citing articles. It also proves that the greater number of cited publications in a citation structure causes the social impact to be divided among all of the cited publications. In summary, this proposition proves the existence of a shift in individual citation impact that arises from the influence structure in a citation network. This is a main result of this study because, from The “Social Impact” of Scholarly Articles section, it follows that, without taking account of the influence structure, the social impact value of a manuscript equals its individual impact. This shift in individual citation impact of scholarly articles is best illustrated in one example as follows. Figure 7 shows the individual citation impacts (times cited) of articles {1, 2, 3, 4}. Following Proposition 2, without taking account of the influence structure, the social impact of the articles in the unrestricted game is simply given by the respective number of received citations. However, it is unrealistic given the citation relationships in the citation networks, which were illustrated in Figures 1 through 4. Figure 7 shows the social impact of the scholarly manuscripts, when considering the influence structure O, as given in Proposition 4. It shows the substantial shift in their indi- JOURNAL OF THE ASSOCIATION FOR INFORMATION SCIENCE AND TECHNOLOGY—January 2015 DOI: 10.1002/asi 123 Tables 4 through 7 show the respective computations of the social impact values of papers 1, 2, 3, and 4, taking account of the influence structure, which was illustrated in Figures 1 through 5 and 8. Each table shows its descendants k, with the corresponding accession number, times cited, and wk −1 D (k ) + 1 value. At the bottom of each table, the value of social impact is computed following Proposition 4. Conclusions FIG. 7. Shift in individual citation impact (times cited) of scholarly articles {1, 2, 3, 4} in the influence structure given by citation relationships in a citation network. FIG. 8. Descendants and superiors for papers with higher and lower social impact. vidual citation impact that results from the influence structure. A new figure (Figure 8) illustrates descendants and superiors for individual papers with higher and lower social impact. Figure 8 complements Figures 1 through 4. It can be used to better understand the concept of social impact: (a) the greater the number of citing publications in a citation network, the greater the social impact would be; and (b) the greater number of cited publications in a citation network causes the social impact to be divided among all of the references. 124 We have developed a formal theory for the division of influence among scholarly manuscripts that follows from the mathematical theory of games to social power. The concept of “social impact” of an article and its measure yield an effective way to analyze the impact of papers in a citation structure. Here, social impact refers to the net effect of citations on a network. The use of game theory to attack the problem of the measurement of the social impact of a scholarly manuscript in a citation network provides a rigorous mathematical treatment for the network approach to citation analysis. This mathematical model allows the exact calculation of the social impact value. Drawing on cooperative game theory, we have proved that, if citation relationships between academic papers do not give rise to an influence structure on scholarly articles, the social impact value of a manuscript equals its individual citation impact (e.g., number of received citations). However, the influence structure in a citation network may go beyond the individual citation impacts that were summed to obtain the worth of coalitions of papers. Following Hu et al. (2012), we have that, within a citation network, a manuscript exerts direct and indirect influence on other papers (by citing articles and by articles that cite citing articles) and is itself influenced directly and indirectly (by references and references of references). This leads to a more complex influence structure of citing and cited publications. Again, drawing on cooperative game theory, we proved that when citation relationships between academic papers function within a citation structure, the result is social impact instead of individual impact. The equations showed how the social impact of a paper is affected by individual impact of citing papers, immediacy of citing publications, and number of both citing and cited articles. This theory of the social impact of scholarly papers proved that the greater the number of citing publications in a citation network, the greater the social impact. Also, the derived equations illustrated that there is more social impact when citing publications are highly cited papers, when the citing action is more immediate, and when there is a greater number of citing articles. We also uncovered another rule relating to the social impact of scholarly papers, which is divisions of impact in a citation structure. Thus, the greater number of cited publications in a citation structure causes JOURNAL OF THE ASSOCIATION FOR INFORMATION SCIENCE AND TECHNOLOGY—January 2015 DOI: 10.1002/asi TABLE 4. Social impact of paper 1, with an influence structure. Paper 1 (times cited: 3; |D−1(1)| = 1) Descendant 2 3 5 6 7 8 9 10 11 ∑ Accession number Times cited (wk) |D−1(k)| WoS:000307730000017 WoS:000301364100017 WoS:000310550000019 WoS:000308516300002 WoS:000308581700016 WoS:000308888400013 WoS:000310550000010 WoS:000311853600006 WoS:000305233900015 2 5 0 0 0 1 0 0 1 3 2 6 4 2 5 5 4 4 Accession number Times cited (wk) |D−1(k)| WoS:000310550000019 WoS:000308888400013 0 1 6 5 Accession number Times cited (wk) |D−1(k)| WoS:000307730000017 WoS:000310550000019 WoS:000308516300002 WoS:000308888400013 WoS:000310550000010 WoS:000311853600006 WoS:000305233900015 2 0 0 1 0 0 1 3 6 4 5 5 4 4 wk D −1 (k ) + 1 0.5 1.67 0 0 0 0.17 0 0 0.2 2.53 k ∈D (1) Social impact: SI vo (1) = ∑ k ∈{1}∪D (1) TABLE 5. wk 3 = + 2.53 = 4.03 D −1 (k ) + 1 1 + 1 Social impact of paper 2, with an influence structure. Paper 2 (times cited: 2; |D−1(2)| = 3) Descendant 5 8 ∑ wk D −1 (k ) + 1 0 0.17 0.17 k ∈D ( 2 ) Social impact: SI vo (2) = ∑ k ∈{2}∪D ( 2 ) TABLE 6. wk 2 = + 0.17 = 0.67 D −1 (k ) + 1 3 + 1 Social impact of paper 3, with an influence structure. Paper 3 (times cited: 5; |D−1(3)| = 2) Descendant 2 5 6 8 9 10 11 ∑ wk D −1 (k ) + 1 k ∈D ( 3 ) Social impact: SI vo (3) = ∑ k ∈{3}∪D (3) 0.5 0 0 0.17 0 0 0.2 0.87 wk 5 = + 0.87 = 2.53 D −1 (k ) + 1 2 + 1 the social impact to be divided among all of the cited publications. To illustrate this main result, the comparative value of the social impact of a scholarly article with and without taking account of the influence structure in a citation network has also been analyzed in a set of experiments. Assuming there is no asymmetric constraint on the scholarly articles imposed by some influence structure, the social impact of papers in the unrestricted game is simply given by the respective number of received citations (its individual citation impact). For instance, papers 1, 2, 3, and 4 in the example have a social impact of 3, 2, 5, 9, respectively (see Table 2). Instead, scholarly manuscripts exhibit a substantial shift in (individual) citation impact that results from the influence structure. In this case, the same papers 1, 2, 3, and 4 have a social impact of 4.03, 0.67, 2.53, and 13.74 (see Tables 4 through 7). The intent of this article is to present a novel theory of social impact of scholarly articles. As regards future JOURNAL OF THE ASSOCIATION FOR INFORMATION SCIENCE AND TECHNOLOGY—January 2015 DOI: 10.1002/asi 125 TABLE 7. Social impact of paper 4, with an influence structure. Paper 4 (times cited: 9; |D−1(4)|=0) Descendant 1 2 3 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ∑ Accession number Times cited (wk) |D−1(k)| WoS:000301364100018 WoS:000307730000017 WoS:000301364100017 WoS:000310550000019 WoS:000308516300002 WoS:000308581700016 WoS:000308888400013 WoS:000310550000010 WoS:000311853600006 WoS:000305233900015 WoS:000311234600025 WoS:000308581700021 WoS:000306547000013 WoS:000305434900004 WoS:000306547000017 WoS:000306547000012 WoS:000306547000018 WoS:000311515900011 3 2 5 0 0 0 1 0 0 1 0 0 1 0 2 1 0 0 1 3 2 6 4 2 5 5 4 4 3 1 2 5 6 10 9 12 wk D −1 (k ) + 1 1.5 0.5 1.67 0 0 0 0.17 0 0 0.2 0 0 0.33 0 0.29 0.09 0 0 4.74 k ∈D ( 4 ) Social impact: SI vo (4) = ∑ k ∈{4}∪D ( 4 ) wk 9 = + 4.74 = 13.74 D −1 (k ) + 1 0 + 1 directions, we are developing a publicly available suite of web-based tools designed to calculate the social impact value of academic papers. In addition, we will provide an interface for the analysis of social impact, which will be freely available to the scientific community. Of course, the selection of the Shapley value of a game of influence to define the concept of social impact is a limitation of the proposed method because other solution concepts could be applied to our problem where cooperative game theory implies a strategy and an intention from the actors, that is, the “articles” and the “citations.” Future work includes the analysis of alternative solution concepts to the Shapley value that was used in this paper. Going forward, we will also consider several questions; for example, what is the role of self-citations, and how does this influence the joint impact and the individual share? Can this method be used in evaluation practices, and what are the limitations? Acknowledgments Garfield, E. (1955). Citation Indexes for Science: A new dimension in documentation through association of ideas. Science, 122(3159), 108–111. Garfield, E., & Sher, I.H. (1963). New factors in the evaluation of scientific literature through citation indexing. American Documentation, 14(3), 195–201. Garner, R. (1967). A computer oriented, graph theoretic analysis of citation index structures. In B. Flood (Ed.), Three Drexel Information Science Research Studies (pp. 3–46). Philadelphia, PA: Drexel Press. Gilles, R.P., Owen, G., & van den Brink, R. (1992). Games with permission structures: The conjunctive approach. International Journal of Game Theory, 20, 277–293. Harsanyi, J.C. (1959). A bargaining model for cooperative n-person games. In A. W. Tucker & R. D. Luce (Eds.), Contributions to the Theory of Games IV (pp. 325–355). Princeton, NJ: Princeton University Press. Hu, X.J., Rousseau, R., & Chen, J. (2012). Structural indicators in citation networks. Scientometrics, 91, 451–460. Lucio-Arias, D., & Scharnhorst, A. (2012). Mathematical approaches to modeling science from an algorithmic-historiography perspective. Understanding Complex Systems, 23–66. Redner, S. (1998). How popular is your paper? An empirical study of the citation distribution. The European Physical Journal B Condensed Matter and Complex Systems, 4(2), 131–134. Shapley, L.S. (1953). A value for n-person games. In H. W. Kuhn & A. W. Tucker (Eds.), Contributions to the Theory of Games II (pp. 307–317). Princeton, NJ: Princeton University Press. Small, H. (1973). Co-citation in the scientific literature: A new measure of the relationship between two documents. Journal of the American Society for Information Science, 24(4), 265–269. This research was sponsored by the Spanish Board for Science and Technology under grant TIN2010-15157 cofinanced with European FEDER funds. Sincere thanks are given to the reviewers for their, constructive suggestions. Appendix References Proof of Proposition 1 Aumann, R., & Hart, S. (Eds.). (2002). Handbook of Game Theory (Vol. 1). Handbooks in Economics Series No. 11. North-Holland, Elsevier Science B.V., Amsterdam, The Netherlands. Driessen, T. (1988). Cooperative Games, Solutions and Applications. Kluwer Academic Publishers, Dordrecht, The Netherlands. 126 From Harsanyi (1959), the dividends Δ v (S ) are given by Δ v (S ) = ∑ (−1) S −T T ⊆S JOURNAL OF THE ASSOCIATION FOR INFORMATION SCIENCE AND TECHNOLOGY—January 2015 DOI: 10.1002/asi v(T ) (14) for all S, where S ⊆ N : S =/ 0/. Given that v is an additive game, we have that Δ v (S ) = ∑ (−1) S − T × T ⊆S ( ) ∑ wi i ∈T (16) The proof is completed by noting that the expression in brackets vanishes except for S = 1. Proof of Proposition 3 From the de...
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