Modeling multivariate count data using copulas. (English) Zbl 1183.62100
Summary: Multivariate count data occur in several different disciplines. However, existing models do not offer great flexibility for dependence modeling. Models based on copulas nowadays are widely used for continuous data dependence modeling. Modeling count data via copulas is still in its infancy; see C. Genest and J. Nešlehová [Astin Bull. 37, No. 2, 475–515 (2007 (2007; Zbl 1274.62398)]. A series of different copula models providing various residual dependence structures are considered for vectors of count response variables whose marginal distributions depend on covariates through negative binomial regressions. A real data application related to the number of purchases of different products is provided.
MSC:
| 62H20 | Measures of association (correlation, canonical correlation, etc.) |
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
| 91B42 | Consumer behavior, demand theory |
Keywords:
Archimedean copulas; Kendall’s tau; market basket count data; mixtures of Max-id copulas; partially symmetric copulasCitations:
Zbl 1274.62398References:
| [1] | DOI: 10.1007/0-387-24555-3_1 · doi:10.1007/0-387-24555-3_1 |
| [2] | Aitchinson J., Biometrika 75 pp 621– (1989) |
| [3] | DOI: 10.1111/j.1467-9574.2004.00126.x · Zbl 1059.62011 · doi:10.1111/j.1467-9574.2004.00126.x |
| [4] | DOI: 10.1111/j.1467-9574.2004.00125.x · Zbl 1059.62121 · doi:10.1111/j.1467-9574.2004.00125.x |
| [5] | Brijs , T. , Swinnen , G. , Vanhoof , K. , Wets , G. ( 1999 ). Using association rules for product assortment decisions: A case study . In:Proceedings of the Fifth International Conference on Knowledge Discovery and Data Mining. San Diego , CA , pp. 254 – 260 . |
| [6] | DOI: 10.1111/j.1368-423X.2004.00144.x · Zbl 1115.62329 · doi:10.1111/j.1368-423X.2004.00144.x |
| [7] | Cameron A. C., Regression Analysis of Count Data (1998) · Zbl 0924.62004 |
| [8] | DOI: 10.1198/07350010152596673 · doi:10.1198/07350010152596673 |
| [9] | DOI: 10.1016/j.jmva.2004.01.004 · Zbl 1095.62065 · doi:10.1016/j.jmva.2004.01.004 |
| [10] | DOI: 10.1080/03067310290024030 · doi:10.1080/03067310290024030 |
| [11] | DOI: 10.2143/AST.37.2.2024077 · Zbl 1274.62398 · doi:10.2143/AST.37.2.2024077 |
| [12] | DOI: 10.2307/2281536 · Zbl 0056.12801 · doi:10.2307/2281536 |
| [13] | DOI: 10.1111/1467-9574.00095 · Zbl 0921.62138 · doi:10.1111/1467-9574.00095 |
| [14] | DOI: 10.1006/jmva.1993.1061 · Zbl 0778.62045 · doi:10.1006/jmva.1993.1061 |
| [15] | DOI: 10.2307/2291331 · Zbl 0843.62016 · doi:10.2307/2291331 |
| [16] | Joe H., Multivariate Models and Dependence Concepts (1997) · Zbl 0990.62517 |
| [17] | DOI: 10.1016/j.jmva.2004.06.003 · Zbl 1066.62061 · doi:10.1016/j.jmva.2004.06.003 |
| [18] | DOI: 10.1006/jmva.1996.0032 · Zbl 0863.62047 · doi:10.1006/jmva.1996.0032 |
| [19] | Johnson N., Discrete Multivariate Distributions (1997) · Zbl 0868.62048 |
| [20] | DOI: 10.1111/j.1751-5823.2005.tb00250.x · Zbl 1104.62010 · doi:10.1111/j.1751-5823.2005.tb00250.x |
| [21] | DOI: 10.2307/3314912 · Zbl 0632.62060 · doi:10.2307/3314912 |
| [22] | DOI: 10.1111/1467-842X.00070 · Zbl 0946.62101 · doi:10.1111/1467-842X.00070 |
| [23] | DOI: 10.1017/S0266466601171082 · Zbl 1179.62083 · doi:10.1017/S0266466601171082 |
| [24] | DOI: 10.1093/biomet/73.1.13 · Zbl 0595.62110 · doi:10.1093/biomet/73.1.13 |
| [25] | DOI: 10.1111/j.1467-9574.2007.00368.x · Zbl 1149.62338 · doi:10.1111/j.1467-9574.2007.00368.x |
| [26] | DOI: 10.1214/07-AOS556 · Zbl 1173.62044 · doi:10.1214/07-AOS556 |
| [27] | DOI: 10.2307/2533435 · Zbl 0825.62788 · doi:10.2307/2533435 |
| [28] | DOI: 10.1080/10485250500038967 · Zbl 1135.60303 · doi:10.1080/10485250500038967 |
| [29] | Nelsen R. B., An Introduction to Copulas (2006) |
| [30] | DOI: 10.1016/j.jmva.2005.11.007 · Zbl 1107.62047 · doi:10.1016/j.jmva.2005.11.007 |
| [31] | Nikoloulopoulos , A. K. ( 2007 ). Application of Copula Functions in Statistics. Ph.D. thesis, Department of Statistics, Athens University of Economics . |
| [32] | DOI: 10.1002/sim.3449 · doi:10.1002/sim.3449 |
| [33] | DOI: 10.1016/j.jspi.2009.05.034 · Zbl 1169.62044 · doi:10.1016/j.jspi.2009.05.034 |
| [34] | DOI: 10.1016/j.jspi.2009.05.023 · Zbl 1169.62328 · doi:10.1016/j.jspi.2009.05.023 |
| [35] | DOI: 10.1111/1467-9469.00191 · Zbl 0955.62054 · doi:10.1111/1467-9469.00191 |
| [36] | Song P. X.-K., Correlated Data Analysis: Modeling, Analytics, and Application (2007) · Zbl 1132.62002 |
| [37] | DOI: 10.1086/302279 · doi:10.1086/302279 |
| [38] | DOI: 10.1017/S0266466699152058 · Zbl 0964.62110 · doi:10.1017/S0266466699152058 |
| [39] | DOI: 10.1016/S0047-259X(03)00020-4 · Zbl 1035.62061 · doi:10.1016/S0047-259X(03)00020-4 |
| [40] | DOI: 10.1111/1468-0084.00188 · doi:10.1111/1468-0084.00188 |
| [41] | DOI: 10.1198/073500105000000153 · doi:10.1198/073500105000000153 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
