世界大學學術排名(ARWU)自2003年起每年提供全球大學排名，是全球最早的大學排名。ARWU使用六個指標衡量大學的學術表現。自2004年起，全球最佳500所大學即透過六個指標之線性組合予以排名。本文針對ARWU探討二個部分。第一部分為採用自然對數迴歸，建構得分－名次模型，呈現2004年至2016年每年的得分變數與名次變數之間的關係。接著，也提出一個經由兩階段所建立的趨勢模型，用來預測未來得分與名次間之關係：第一階段，建立包含兩個參數（在t年的at及bt）的線性迴歸模型；第二階段，建立一個ARIMA模型以預測bt值。趨勢模型可用於預測某一特定名次所對應的得分，或預測某一特定得分在未來年度的名次。經實證研究，使用2005年至2015年的排名數據資料透過趨勢模型預測2016年前500名大學的得分，結果顯示該趨勢模型是有效的。此外，將2016年所預測的排名結果與2016年實際排名結果進行比較時，亦呈現出兩條非常相近且幾乎重疊的曲線。本文第二部分為採用逐步迴歸分析，建立2004年至2016年排名之五個逐步迴歸模型，以簡化ARWU排名指標與計分公式。所建立之五個模型中，有三個模型具最佳配適度。經實證研究，這三個模型所產生之三項計分公式均適於取代原計分公式，且獲得相似之得分結果。

The Academic Ranking of World Universities (ARWU) has provided annual global rankings of universities since 2003, making it the earliest of its kind. The ARWU draws on six indicators to measure the academic performance of universities. Top 500 universities are ranked each year since 2004 by linear combinations of the six indicators. This paper presents two parts on the study of the ARWU. In the first part, we used a natural log regression model, called the Score-Rank Model, to present the relationship between the score variable and the rank variable for each year from 2004 to 2016. Then, we also presented the Trend Model, built by a two-stage process, to forecast the relationship of the variables in future years. In the first stage, a linear regression model between two parameters (at and bt in year t) was established; in the second stage, an ARIMA model was built to obtain the value of bt. The Trend Model can be used to forecast the total score of a particular rank, or the rank of a specific total score for future years. It is shown that the Trend Model is valid in an empirical study using ranking data from 2005 to 2015 to forecast the total scores of the top 500 ranks in 2016. When comparing the forecast results with the real ranking outcomes of 2016 in a graph, it presents two very similar and almost overlapping curves. In the second part of the paper, in attempt to simplify the indicators of the ARWU, we used a stepwise regression analysis for each ranking year and constructed five Stepwise Regression Models from 2004 to 2016. Among the five models, we found three models that had better model fitting. Furthermore, the new scoring formulas generated from the three Modified Stepwise Regression Models are all adequate to replace the original scoring formula. As shown in our empirical study, the three modified scoring formulas all produced very similar results when compared with the original outcomes.

TABLE OF CONTENTS

LIST OF TABLES	III
LIST OF FIGURES	V

CHAPTER 1  INTRODUCTION	1
1.1  Background of the Study	1
1.2  Statement of the Problem	3
1.3  Purpose of the Study	3
1.4  Summary	4
CHAPTER 2  LITERATURE REVIEW	6
2.1  The Global Ranking Phenomenon	6
2.2  The ARWU Methodology	8
2.3  Comments on the ARWU Methodology	11
2.4  Studies on the ARWU Methodology	13
2.5  Summary	15
CHAPTER 3  METHODOLOGY	16
3.1  Data Collection	16
3.2  Model Formulation	26
    3.2.1  Score-Rank Model	26
    3.2.2  Trend Model	27
    3.2.3  Stepwise Regression Model	27
3.3  Summary	28
CHAPTER 4  TREND MODELS ON THE ARWU	29
4.1  Trend Analysis	29
4.2  Score-Rank Models	32
4.3  Trend Models	34
4.4  Empirical Study	45
4.5  Summary	47
CHAPTER 5  MODIFIED STEPWISE REGRESSION MODELS ON SIMPLIFYING THE ARWU’S INDICATORS	48
5.1  Stepwise Regression Analysis for World’s Top 500 Universities	48
5.2  Modified Stepwise Regression Models	57
5.3  Empirical Study	61
5.4  Summary	66
CHAPTER 6  CONCLUSIONS AND FUTURE WORK	68
6.1  Conclusions	68
6.2  Practical Implications	69
6.3  Future Work	70
REFERENCES	72
APPENDIX	75
 
LIST OF TABLES

Table 2.1  Criteria, indicators, codes and weights for the ARWU (2004-2016)	9
Table 2.2  The ARWU indicators and data sources	10
Table 4.1  Top 1 to 11 Universities in 2004 and their ranges of ranks	31
Table 4.2  Top 78 to 100 universities in 2004 and their ranges of ranks	31
Table 4.3  Values of at , bt and in log-models	33
Table 4.4  Suitable ARIMA models and their Stationary R2 and R2 (in descending order)	37
Table 4.5  Best ARIMA models for 2017-2026 to forecast bt	38
Table 4.5  Best ARIMA models for 2017-2026 to forecast bt (continued)	39
Table 4.5  Best ARIMA models for 2017-2026 to forecast bt (continued)	40
Table 4.5  Best ARIMA models for 2017-2026 to forecast bt (continued)	41
Table 4.6  Goodness-of-fit measures except stationary R2 and R2	41
Table 4.7  Values of parameters at, bt and Trend Models from 2017 to 2026	43
Table 4.7  Values of parameters at, bt and Trend Models from 2017 to 2026  (continued)	44
Table 4.8  The most ideal Trend Model for 2016	46
Table 5.1  Correlation coefficients matrix of the total scores and the six indicator scores for world’s top 500 universities in the 2004 ARWU	48
Table 5.2  Correlation coefficients matrix of the total scores and the six indicator scores for world’s top 500 universities in the 2005 ARWU	48
Table 5.3  Correlation coefficients matrix of the total scores and the six indicator scores for world’s top 500 universities in the 2006 ARWU	49
Table 5.4  Correlation coefficients matrix of the total scores and the six indicator scores for world’s top 500 universities in the 2007 ARWU	49
Table 5.5  Correlation coefficients matrix of the total scores and the six indicator scores for world’s top 500 universities in the 2008 ARWU	49
Table 5.6  Correlation coefficients matrix of the total scores and the six indicator scores for world’s top 500 universities in the 2009 ARWU	50
Table 5.7  Correlation coefficients matrix of the total scores and the six indicator scores for world’s top 500 universities in the 2010 ARWU	50
Table 5.8  Correlation coefficients matrix of the total scores and the six indicator scores for world’s top 500 universities in the 2011 ARWU	50
Table 5.9  Correlation coefficients matrix of the total scores and the six indicator scores for world’s top 500 universities in the 2012 ARWU	51
Table 5.10  Correlation coefficients matrix of the total scores and the six indicator scores for world’s top 500 universities in the 2013 ARWU	51
Table 5.11  Correlation coefficients matrix of the total scores and the six indicator scores for world’s top 500 universities in the 2014 ARWU	51
Table 5.12  Correlation coefficients matrix of the total scores and the six indicator scores for world’s top 500 universities in the 2015 ARWU	52
Table 5.13  Correlation coefficients matrix of the total scores and the six indicator scores for world’s top 500 universities in the 2016 ARWU	52
Table 5.14  Stepwise Regression Models for world’s Top 500 universities in the 2013 ARWU	54
Table 5.15 Partial correlations of the Stepwise Regression Models for world’s top 500 universities in the 2013 ARWU	55
Table 5.16  Stepwise Regression Models and their corresponding R2 values from 2004 to 2016 for world’s top 500	57
Table 5.17  Stepwise Regression Model 5 without Constant from 2004 to 2016 for world’s top 500 universities	58
Table 5.18  Modified Stepwise Regression Model 5 from 2004 to 2016 for world’s top 500 universities	59
Table 5.19  Stepwise Regression Model 4 without Constants from 2004 to 2016 for world’s top 500 universities	59
Table 5.20  Modified Stepwise Regression Model 4 from 2004 to 2016 for world’s top 500 universities	60
Table 5.21  Stepwise Regression Model 3 without Constants from 2004 to 2016 for world’s top 500 universities	60
Table 5.22  Modified Stepwise Regression Model 3 from 2004 to 2016 for world’s top 500 universities	61

LIST OF FIGURES

Figure 1.1  Research design of the study	5
Figure 3.1  Score information of total score and Alumni score for top 500 in 2004	17
Figure 3.2  Score information of total score and Award score for top 500 in 2004	18
Figure 3.3  Score information of total score and HiCi score for top 500 in 2004	19
Figure 3.4  Score information of total score and N&S score for top 500 in 2004	20
Figure 3.5  Score information of total score and PUB score for top 500 in 2004	21
Figure 3.6  Score information of total score and PCP score for top 500 in 2004	22
Figure 3.7  Data Set A – Scores of the six indicators, Score and Rank for top 500 institutions in 2004	24
Figure 3.8  Data Set B – Scores of top 500 institutions from 2004 to 2016	25
Figure 4.1  Curves of score by rank from 2004 to 2016	30
Figure 4.2  Confidence interval of bt in ten ARIMA models in 2017-2026	42
Figure 4.3  Curves of real scores and forecast scores of top 500 ranks in 2016	46
Figure 5.1  Scores of modified Models 3, 4 and 5 with the actual scores of ranks 1 to 500 from 2004 to 2006	62
Figure 5.2  Scores of modified Models 3, 4 and 5 with the actual scores of ranks 1 to 500 from 2007 to 2009	63
Figure 5.3  Scores of modified Models 3, 4 and 5 with the actual scores of ranks 1 to 500 from 2010 to 2012	64
Figure 5.4  Scores of modified Models 3, 4 and 5 with the actual scores of ranks 1 to 500 from 2013 to 2015	65
Figure 5.5  Scores of modified Models 3, 4 and 5 with the actual scores of ranks 1 to 500 in 2016	66

Abramo, G., & D’Angelo, C. A. (2014). How do you define and measure research productivity? Scientometrics, 101, 1129-1144.

Altbach, P. G. (2004). Globalisation and the university: Myths and realities in an unequal world. Tertiary Education and Management, 10(1), 3-25. 

Altbach, P. G. (2008). The complex roles of universities in the period of globalization. In Global University Network for Innovation (GUNI) (Ed.), Higher Education in the World 3: Higher Education: New Challenges and Emerging Roles for Human and Social Development (3-14). UK: Palgrave MacMillan.

The ARWU. (2003). Academic Ranking of World Universities 2003 – Academic Ranking of World Universities 2003. Retrieved from http://www.shanghairanking.com/ARWU2003.html

The ARWU. (2004-2016). Academic Ranking of World Universities 2004 – Academic Ranking of World Universities 2016. Retrieved from http://www.shanghairanking.com/ARWU2004.html -http://www.shanghairanking.com/ARWU2016.html

The ARWU. (2004-2016). Academic Ranking of World Universities 2004 Methodology – Academic Ranking of World Universities 2016 Methodology. Retrieved from http://www.shanghairanking.com/ARWU-Methodology-2004.html – http://www.shanghairanking.com/ARWU-Methodology-2016.html

Bauer, J., Leydesdorff, L., & Bornmann, L. (2015). Highly-cited papers in Library and Information Science (LIS): Authors, Institutions, and Network Structures. Journal of the Association for Information Science and Technology, 67(12), 3095-3100.

Billaut, J. C., Bouyssou, D., & Vincke, P. (2010). Should you believe in the Shanghai ranking? Scientometrics, 84(1), 237-263.

Cantwell, B., & Maldonado-Maldonado, A. (2009). Four stories: Confronting contemporary ideas about globalization and internationalization in high education. Globalisation, Societies and Education, 7(3), 289-306.

Claassen, C. (2015). Measuring university quality. Scientometrics, 104(3), 793-807. 

Dehon, C., McCathie, A., & Verardi, V. (2010). Uncovering excellence in academic rankings: A closer look at the Shanghai ranking. Scientometrics, 83(2), 515-524.

Docampo, D. (2013). Reproducibility of the Shanghai academic ranking of world universities. Scientometrics, 94(2), 567-587.

Docampo, D., & Cram, L. (2015). On the effects of institutional size in university classifications: The case of the Shanghai ranking. Scientometrics, 102(2), 1325-1346.

Docampo, D., Egret, D., & Cram, L. (2015). The effect of university mergers on the Shanghai ranking. Scientometrics, 104(1), 175-191.
 
Florian, R. (2007). Irreproducibility of the results of the Shanghai academic ranking of world universities. Scientometrics, 72(1), 25-32.

Goetzmann, M. (2014). Shanghai Academic Ranking: A French Controversy, 2013-8-29, La Jeune Politique. Retrieved from http://lajeunepolitique.com

Huang, M. (2011). A comparison of three major academic rankings for world universities: From a research evaluation perspective. Journal of Library and Information Studies, 9(1), 1-25.

Jeremic, V., Bulajic, M., Martic, M., & Radojicic, Z. (2011). A fresh approach to evaluating the academic ranking of world universities. Scientometrics, 87, 587-596.

Jovanovic, M., Jeremic, V., Savic, G., Bulajic, M., & Martic, M. (2012). How does the normalization of data affect the ARWU ranking? Scientometrics, 93, 319-327.

Liu, N. C., & Cheng, Y. (2005). Academic ranking of world universities – methodologies and problems. Higher Education in Europe, 30(2), 127-136.

Liu, N. C. (2009). The story of academic ranking of world universities. International Higher Education, 54(Winter), 2-3.

Luque-Martínez, T., & Del Barrio-García, S. (2016). Constructing a synthetic indicator of research activity. Scientometrics, 108(3), 1049-1064.

Marginson, S. (2005). There must be some way out of here. Tertiary Education Management Conference. Perth: Keynote address.

Marginson, S. (2017). Do rankings drive better performance? International Higher Education, 89(Spring), 6-8.

Piro, F. N., & Sivertsen, G. (2016). How can differences in international university rankings be explained? Scientometrics, 109(3), 2263-2278.

QS Top Universities. (2016). Can financial investment buy university success? Retrieved from https://www.topuniversities.com/university-rankings-articles/world-university-rankings/can-financial-investment-buy-university-success

QS Top Universities. (2017). QS World University Rankings – methodology. Retrieved from https://www.topuniversities.com/qs-world-university-rankings/methodology

Romanov, D., Drozdov, A., & Gerashchenko, A. (2017). Citation-based criteria of the significance of the research activity of scientific teams. Scientometrics, 112(3), 1179-1202.

Sadlak, J. (2009). Ranking in higher education: Its place and impact. The Europa World of Learning 2010 (60th ed.). London: Taylor & Francis Ltd.

Salmi, J. (2009). The challenge of establishing world-class universities. In J. Sadlack, & N. C. Liu (Eds.), The World-Class University as Part of a New Higher Education Paradigm: From Institutional Qualities to Systemic Excellence (23-68). Romania: UNESCO-CEPES, Cluj University Press.

Times Higher Education. (2016). World University Rankings 2016-17 Methodology. Retrieved from https://www.timeshighereducation.com/world-university-rankings/methodology-world–university-rankings-2016-2017

Torrisi, B. (2014). A multidimensional approach to academic productivity. Scientometrics, 99(3), 755-783.

Van Raan, A. (2005a). Fatal attraction: Conceptual and methodological problems in the ranking of universities by bibliometric methods. Scientometrics, 62(1), 133-143.

Van Raan, A. (2005b). Challenges in ranking of Universities. Invited paper for the 1st International Conference on World-Class Universities. Shanghai: Shanghai Jaio Tong University, June 16-18.

Yonezawa, A. (2015). Will the ranking game continue after a decade? International Higher Education, 80, Spring, 19-20.

Zitt, M., & Filliatreau, G. (2007). Big is (made) beautiful: Some comments about the Shanghai ranking of world-class universities. In J. Sadlack, & N. C. Liu (Eds.), The World Class University and Ranking: Aiming beyond Status (141-160). Romania: UNESCO-CEPES, Cluj University Press.