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Generalized k-means in GLMs with applications to the outbreak of COVID-19 in the United States

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  • Zhang, Tonglin
  • Lin, Ge

Abstract

Generalized k-means can be combined with any similarity or dissimilarity measure for clustering. Using the well known likelihood ratio or F-statistic as the dissimilarity measure, a generalized k-means method is proposed to group generalized linear models (GLMs) for exponential family distributions. Given the number of clusters k, the proposed method is established by the uniform most powerful unbiased (UMPU) test statistic for the comparison between GLMs. If k is unknown, then the proposed method can be combined with generalized liformation criterion (GIC) to automatically select the best k for clustering. Both AIC and BIC are investigated as special cases of GIC. Theoretical and simulation results show that the number of clusters can be correctly identified by BIC but not AIC. The proposed method is applied to the state-level daily COVID-19 data in the United States, and it identifies 6 clusters. A further study shows that the models between clusters are significantly different from each other, which confirms the result with 6 clusters.

Suggested Citation

  • Zhang, Tonglin & Lin, Ge, 2021. "Generalized k-means in GLMs with applications to the outbreak of COVID-19 in the United States," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    • Handle: RePEc:eee:csdana:v:159:y:2021:i:c:s0167947321000517
    DOI: 10.1016/j.csda.2021.107217
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    References listed on IDEAS

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    1. Li-Xuan Qin & Steven G. Self, 2006. "The Clustering of Regression Models Method with Applications in Gene Expression Data," Biometrics, The International Biometric Society, vol. 62(2), pages 526-533, June.
    2. Jianqing Fan & Shaojun Guo & Ning Hao, 2012. "Variance estimation using refitted cross‐validation in ultrahigh dimensional regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(1), pages 37-65, January.
    3. Robert Tibshirani & Guenther Walther & Trevor Hastie, 2001. "Estimating the number of clusters in a data set via the gap statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 411-423.
    4. Zhang, Yiyun & Li, Runze & Tsai, Chih-Ling, 2010. "Regularization Parameter Selections via Generalized Information Criterion," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 312-323.
    5. J. A. Hartigan & M. A. Wong, 1979. "A K‐Means Clustering Algorithm," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 28(1), pages 100-108, March.
    6. Junhui Wang, 2010. "Consistent selection of the number of clusters via crossvalidation," Biometrika, Biometrika Trust, vol. 97(4), pages 893-904.
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    1. Cerqueti, Roy & Ficcadenti, Valerio, 2022. "Combining rank-size and k-means for clustering countries over the COVID-19 new deaths per million," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).

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