TY - JOUR
T1 - Modelling count data via copulas
AU - Safari-Katesari, Hadi
AU - Samadi, S. Yaser
AU - Zaroudi, Samira
N1 - Publisher Copyright:
© 2021 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2020
Y1 - 2020
N2 - Copula models have been widely used to model the dependence between continuous random variables, but modelling count data via copulas has recently become popular in the statistics literature. Spearman's rho is an appropriate and effective tool to measure the degree of dependence between two random variables. In this paper, we derive the population version of Spearman's rho via copulas when both random variables are discrete. The closed-form expressions of the Spearman correlation are obtained for some copulas with different marginal distributions. We derive the upper and lower bounds of Spearman's rho for Bernoulli marginals. The proposed Spearman's rho correlations are compared with their corresponding Kendall's tau values and their functional relationships are characterized in some special cases. An extensive simulation study is conducted to demonstrate the validity of our theoretical results. Finally, we propose a bivariate copula regression model to analyse the count data of a cervical cancer dataset.
AB - Copula models have been widely used to model the dependence between continuous random variables, but modelling count data via copulas has recently become popular in the statistics literature. Spearman's rho is an appropriate and effective tool to measure the degree of dependence between two random variables. In this paper, we derive the population version of Spearman's rho via copulas when both random variables are discrete. The closed-form expressions of the Spearman correlation are obtained for some copulas with different marginal distributions. We derive the upper and lower bounds of Spearman's rho for Bernoulli marginals. The proposed Spearman's rho correlations are compared with their corresponding Kendall's tau values and their functional relationships are characterized in some special cases. An extensive simulation study is conducted to demonstrate the validity of our theoretical results. Finally, we propose a bivariate copula regression model to analyse the count data of a cervical cancer dataset.
KW - Spearman's rho
KW - bivariate measure of association
KW - concordance discordance dependence
KW - copula
UR - http://www.scopus.com/inward/record.url?scp=85099319090&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85099319090&partnerID=8YFLogxK
U2 - 10.1080/02331888.2020.1867140
DO - 10.1080/02331888.2020.1867140
M3 - Article
AN - SCOPUS:85099319090
SN - 0233-1888
VL - 54
SP - 1329
EP - 1355
JO - Statistics
JF - Statistics
IS - 6
ER -