Abstract
Bandwagons are ubiquitous in social life. No one doubts that people vote at least sometimes for political candidates simply because they are winning and or embrace many fashions simply because they want to “follow the crowd.” But estimating how much a bourgeoning trend owes to pure “bandwagon effects” can be very difficult. Often other factors motivate the people taking action to an unknown degree. In this paper we investigate the use of two variable window scan statistics, the minimum P value scan statistic and the generalized likelihood ratio test (GLRT) statistic, to analyze one important form of the bandwagon problem. We show how these scan statistics can be used to detect the clustering of bandwagon events in a time interval. Once the events are identified, the information can be used to set boundaries on the extent of bandwagoning. The method is illustrated by reference to data on political contributions in the 2016 U.S. Senate elections.
Similar content being viewed by others
References
Alm SE (1997) On the distribution of scan statistics of two-dimensional Poisson processes. Adv Appl Probab 29:1–18
Alm SE (1998) Approximation and simulation of the distributions of scan statistics for Poisson process in higher dimensions. Extremes 1:111–126
Alm SE (1999) Approximations of the distribution of scan statistics of Poisson processes. In: Glaz J, Balakrishnan N (eds) Scan Statistics and Applications. Birkhauser, Boston, pp 113–139
Balakrishnan N, Koutras MV (2002) Runs and scans with applications. Wiley, New York
Chen, J. and Glaz, J. (1997). Approximations and inequalities for the distribution of scan statistics for 0-1 Bernoulli trials. Advances in the Theory and Practice of Statistics - a volume in honor of Samuel Katz. N. L. Johnson and N. Balakrishnan, es. Wiley & Sons, New York, pp. 285-298
Chen J, Glaz J (1999) Approximations of the distribution of the moments of siscrete scan statistics of Poisson processes. In: Glaz J, Balakrishnan N (eds) Scan Statistics and Applications. Birkhauser, Boston, pp 27–66
Chen J, Glaz J (2004) Approximations and bounds for moving sums of discrete random variables. Applied Sequential Methodologies. In: Mukhopadhyay N, Datta S, Chattopadhyay S (eds) STATISTICS: textbooks and monographs, vol 173. Marcel Dekker, New York, pp 105–122
Chen J, Glaz J (2005) Approximations for discrete multiple scan statistics scan statistics. In: Yates RB, Glaz J, Gzys H, Huler J, Palacios JL (eds) Recent Advances in Applied Probability. Springer, New York, pp 97–114
Chen J, Glaz J (2016) Scan Statistics for Monitoring Data Modeled by a Negative Binomial Distribution. Communication in Statistics Theory and Methods 45(6, March 2016):1632–1442
Chen J, Glaz J (2016a) Scan statistics for monitoring data modeled by a negative binomial distribution. Communications in Statistics-Theory and Methods Ser A 45:1632–1642
Davison AC, Hinkley DV (1997) Bootstrap methods and their applications. Cambridge University Press, Cambridge
Ferguson, T., Jorgensen, P., and Chen, J. (2016). How money drives US congressional elections. Institute for New Economic Thinking, Working Paper #48. On the web at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2817705 Accessed July 22, 2019
Ferguson T, Jorgensen P, Chen J (2018) Industrial structure and political outcomes: the case of the 2016 US presidential election. In: Cardinale I, Scazzieri R (eds) Chapter 11The Palgrave Handbook of Political Economy. Palgrave, London, pp 330–440
Fu, J. C. and Lou, W. Y. W. (2003). Distribution Theory of Runs and Patterns and Its Applications: A Finite Markov Chain Imbedding Approach world scientific, Singapore
Glaz J, Naus J (1991) Tight bounds and approximations for scan statistic probabilities for discrete data. Ann Appl Probab 1:306–318
Glaz J, Zhang Z (2004) Multiple window discrete scan statistics. J Appl Stat 31(8):967–980
Glaz J, Naus J, Wallenstein S (2001) Scan statistics. Springer-Verlag, New York
Haiman G, Preda C (2002) A new method for estimating the distribution of scan statistics for a two-dimensional Poisson process. Methodol Comput Appl Probab 4:393–407
Henschel R, Johnston W (1987) The emergence of bandwagon effects: a theory. Sociol Q 28(4):493–511
Hoh J, Ott J (2000) Scan statistics to scan markers for susceptibility genes. Proc Natl Acad Sci 97:9615–9617
Kulldorff M, Huang L, Konty K (2009) A scan statistic for continuous data based on the normal probability model. Int J Health Geogr 8:58
Loader C (1991) Large deviation approximations to the distribution of scan statistics. Adv Appl Probab 23:751–771
Nagarwalla N (1996) A scan statistic with a variable window. Stat Med 15:845–850
Naus JI (1966) Some probabilities, expectations and variances for the size of largest clusters and smallest intervals. J Am Stat Assoc 61:1191–1199
Naus JI (1982) Approximation for distribution s of scan statistics. J Am Stat Assoc 77:177–183
Wallenstein S, Neff N (1987) An approximation for the distribution of the scan statistic. Stat Med 6:197–207
Wang X, Glaz J (2014) Variable window scan statistics for normal data. Communication in Statistics – Theory and Methods 43:2489–2505
Wang X, Zhao B, Glaz J (2014) A multiple window scan statistic for time series models. Statist Probab Lett 94:196–203
Zhao B, Glaz J (2014) Scan statistics for detecting a local change in variance for normal data with known variances. Methodology and Computing in Applied Probability 18:563–573
Zhao B, Glaz J (2016) Scan statistics for detecting a local change in variance for normal data with unknown population variances. Statistics and Probability Letters 110:137–145
Acknowledgments
The authors would like to thank Francis Bator and Joseph Glaz for helpful suggestions and the Institute for New Economic Thinking for support of the data collection.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Chen, J., Ferguson, T. & Jorgensen, P. Using Scan Statistics for Cluster Detection: Recognizing Real Bandwagons. Methodol Comput Appl Probab 22, 1481–1491 (2020). https://doi.org/10.1007/s11009-019-09737-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11009-019-09737-1