Co-clustering Spatial Data Using a Generalized Linear Mixed Model With Application to the Integrated Pest Management

  • Zhanpan Zhang
  • Daniel R. Jeske
  • Xinping Cui
  • Mark Hoddle


Co-clustering has been broadly applied to many domains such as bioinformatics and text mining. However, model-based spatial co-clustering has not been studied. In this paper, we develop a co-clustering method using a generalized linear mixed model for spatial data. To avoid the high computational demands associated with global optimization, we propose a heuristic optimization algorithm to search for a near optimal co-clustering. For an application pertinent to Integrated Pest Management, we combine the spatial co-clustering technique with a statistical inference method to make assessment of pest densities more accurate. We demonstrate the utility and power of our proposed pest assessment procedure through simulation studies and apply the procedure to studies of the persea mite (Oligonychus perseae), a pest of avocado trees, and the citricola scale (Coccus pseudomagnoliarum), a pest of citrus trees.

Key Words

GLMM Heuristic optimization Integrated pest management Spatial co-clustering 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Barchia, I. M., Herron, G. A., and Gilmour, A. R. (2003), “Use of a Generalized Linear Mixed Model to Reduce Excessive Heterogeneity in Petroleum Spray Oil Bioassy Data,” Journal of Economic Entomology, 96 (3), 983–989. CrossRefGoogle Scholar
  2. Bennett, K. E., Hopper, J. E., Stuart, M. A., West, M., and Drolet, B. S. (2008), “Blood-Feeding Behavior of Vesicular Stomatitis Virus Infected Culicoides Sonorensis (Diptera: Ceratopogonidae),” Journal of Medical Entomology, 45 (5), 921–926. CrossRefGoogle Scholar
  3. Bianchi, F. J. J. A., Goedhart, P. W., and Baveco, J. M. (2008), “Enhanced Pest Control in Cabbage Crops Near Forest in The Netherlands,” Landscape Ecology, 23 (5), 595–602. CrossRefGoogle Scholar
  4. Breslow, N. E., and Clayton, D. G. (1993), “Approximate Inference in Generalized Linear Mixed Models,” Journal of the American Statistical Association, 88 (421), 9–25. MATHCrossRefGoogle Scholar
  5. Busygin, S., Prokopyev, O., and Pardalos, P. M. (2008), “Biclustering in Data Mining,” Computers & Operations Research, 35 (9), 2964–2987. MathSciNetMATHCrossRefGoogle Scholar
  6. Candy, S. G. (2000), “The Application of Generalized Linear Mixed Models to Multi-level Sampling for Insect Population Monitoring,” Environmental and Ecological Statistics, 7 (3), 217–238. CrossRefGoogle Scholar
  7. Elias, S. P., Lubelczyk, C. B., Rand, P. W., Lacombe, E. H., Holman, M. S., and Smith, R. P. (2006), “Deer Browse Resistant Exotic-Invasive Understory: An Indicator of Elevated Human Risk of Exposure to Ixodes scapularis (Acari: Ixodidae) in Southern Coastal Maine Woodlands,” Journal of Medical Entomology, 43 (6), 1142–1152. CrossRefGoogle Scholar
  8. Elston, D. A., Moss, R., Boulinier, T., Arrowsmith, C., and Lambin, X. (2001), “Analysis of Aggregation, a Worked Example: Numbers of Ticks on Red Grouse Chicks,” Parasitology, 122 (5), 563–569. CrossRefGoogle Scholar
  9. Gotway, C. A., and Stroup, W. W. (1997), “A Generalized Linear Model Approach to Spatial Data Analysis and Prediction,” Journal of Agricultural, Biological, and Environmental Statistics, 2 (2), 157–178. MathSciNetCrossRefGoogle Scholar
  10. Gozé, E., Nibouche, S., and Deguine, J.-P. (2003), “Spatial and Probability Distribution of Helicoverpa armigera (Hübner) (Lepidoptera: Noctuidae) in Cotton: Systematic Sampling, Exact Confidence Intervals and Sequential Test,” Environmental Entomology, 32 (5), 1203–1210. CrossRefGoogle Scholar
  11. Hartigan, J. A. (1972), “Direct Clustering of a Data Matrix,” Journal of the American Statistical Association, 67 (337), 123–129. CrossRefGoogle Scholar
  12. Hoddle, M. S. (2005), “Invasions of Leaf Feeding Arthropods: Why Are So Many New Pests Attacking California-Grown Avocados?” California Avocado Society Yearbook (2004–2005), 87, 65–81. Google Scholar
  13. Ifoulis, A. A., and Savopoulou-Soultani, M. (2006), “Use of Geostatistical Analysis to Characterize the Spatial Distribution of Lobesia botrana (Lepidoptera: Tortricidae) Larvae in Northern Greece,” Environmental Entomology, 35 (2), 497–506. CrossRefGoogle Scholar
  14. Madeira, S. C., and Oliveira, A. L. (2004), “Biclustering Algorithms for Biological Data Analysis: A Survey,” IEEE/ACM Transactions on Computational Biology and Bioinformatics, 1 (1), 24–45. CrossRefGoogle Scholar
  15. Maoz, Y., Gal, S., Zilberstein, M., Izhar, Y., Alchanatis, V., Coll, M., and Palevsky, E. (2011), “Determining an Economic Injury Level for the Persea Mite Oligonychus perseae, a New Pest of Avocado in Israel,” Entomologia Experimentalis et Applicata, 138 (2), 110–116. CrossRefGoogle Scholar
  16. McCulloch, C. E., Searle, S. R., and Neuhaus, J. M. (2008), Generalized, Linear, and Mixed Models (2nd ed.), Hoboken: Wiley. MATHGoogle Scholar
  17. Mechelen, I. V., Bock, H.-H., and Boeck, P. D. (2004), “Two-mode Clustering Methods: A Structured Overview,” Statistical Methods in Medical Research, 13, 363–394. MathSciNetMATHCrossRefGoogle Scholar
  18. Olejnik, S., Li, J., Supattathum, S., and Huberty, C. J. (1997), “Multiple Testing and Statistical Power With Modified Bonferroni Procedures,” Journal of Educational and Behavioral Statistics, 22 (4), 389–406. Google Scholar
  19. Paterson, S., and Lello, J. (2003), “Mixed Models: Getting the Best Use of Parasitological Data,” Trends in Parasitology, 19 (8), 370–375. CrossRefGoogle Scholar
  20. Prelic, A., Bleuler, S., Zimmermann, P., Wille, A., Bühlmann, P., Gruissem, W., Hennig, L., Thiele, L., and Zitzler, E. (2006), “A Systematic Comparison and Evaluation of Biclustering Methods for Gene Expression Data,” Bioinformatics, 22 (9), 1122–1129. CrossRefGoogle Scholar
  21. Ramírez-Dávila, J. F., and Porcayo-Camargo, E. (2008), “Spatial Distribution of the Nymphs of Jacobiasca Lybica (Hemiptera: Cicadellidae) in a Vineyard in Andalucia, Spain,” Revista Colombiana de Entomologia, 34 (2), 169–175. Google Scholar
  22. Schotzko, D. J., and O’Keeffe, L. E. (1989), “Geostatistical Description of the Spatial Distribution of Lygus hesperus (Heteroptera: Miridae) in Lentils,” Journal of Economic Entomology, 82 (5), 1277–1288. Google Scholar
  23. Shah, P. (2006), “Sequential Sampling Methods Using Generalized Linear Models With Applications to Pest Density Estimation,” Ph.D. Dissertation, University of California, Riverside, CA. Google Scholar
  24. Takakura, K.-I. (2009), “Reconsiderations on Evaluating Methodology of Repellent Effects: Validation of Indices and Statistical Analyses,” Journal of Economic Entomology, 102 (5), 1977–1984. CrossRefGoogle Scholar
  25. Williams, L., Schotzko, D. J., and McCaffrey, J. P. (1992), “Geostatistical Description of the Spatial Distribution of Limonius Californicus (Coleoptera: Elateridae) Wireworms in the Northwestern United States, With Comments on Sampling,” Environmental Entomology, 21 (5), 983–995. Google Scholar
  26. Zhang, Z. (2011), “Clustering: Algorithm, Optimization and Inference,” Ph.D. Dissertation, University of California, Riverside, CA. Google Scholar

Copyright information

© International Biometric Society 2012

Authors and Affiliations

  • Zhanpan Zhang
    • 1
  • Daniel R. Jeske
    • 2
  • Xinping Cui
    • 2
  • Mark Hoddle
    • 3
  1. 1.One Research CircleGE Global ResearchNiskayunaUSA
  2. 2.Department of StatisticsUniversity of CaliforniaRiversideUSA
  3. 3.Department of EntomologyUniversity of CaliforniaRiversideUSA

Personalised recommendations