Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Tests for Equality of Dispersions in the Generalized Bivariate Negative Binomial Regression Model with Heterogeneous Dispersions

서로 다른 산포를 갖는 이변량 음이항 회귀모형에서 산포의 동일성에 대한 검정

  • 한상문 (서울시립대학교 통계학과) ;
  • 정병철 (서울시립대학교 통계학과)
  • Received : 20101200
  • Accepted : 20110100
  • Published : 2011.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we proposed a generalized bivariate negative binomial distribution allowing heterogeneous dispersions on two dependent variables based on a trivariate reduction technique. In this model, we propose the score and LR tests for testing the equality of dispersions and compare the efficiencies of the proposed tests using a Monte Carlo study. The Monte Carlo study shows that the proposed score and LR tests prove to be an efficient test for the equality of dispersions in the view of the significance level and power. However, the score test is easier to compute than the LR test and it shows a slightly better performance than the LR test from the Monte Carlo study, we suggest the use of score tests for testing the equality of dispersions on two dependent variables. In addition, an empirical example is provided to illustrate the results.

본 연구에서는 두 반응변수의 이질적 산포를 허용하는 좀 더 일반적인 형태의 이변량 음이항 회귀모형을 삼각소거법(trivariate reduction technique)을 이용하여 제안하였다. 이 분포에서 산포의 동일성에 대한 스코어 검정과 LR 검정을 유도하고 모의실험을 통하여 각 검정법의 효율성을 비교하였다. 모의실험 결과 스코어 검정과 LR 검정 모두 명목유의수준을 제대로 유지하고 검정력도 높게 나타나 산포의 동일성을 검정하는데 효율적인 검정법으로 나타났다. 하지만 스코어 검정은 LR 검정에 비하여 계산이 간편하다는 장점이 존재하고 모의실험을 통하여 스코어 검정이 LR 검정보다 약간 나은 효율을 보였으므로 산포의 동일성에 대한 검정에서 스코어 검정의 사용을 제안하고자 한다. 더불어 실제 사례에 두 검정법을 적용하고 그 결과를 제시하였다.

Keywords

References

  1. Cameron, A. C. and Trivedi, P. K. (1998). Regression Analysis of Count Data, Cambridge University Press, Cambridge.
  2. Deb, P. and Trivedi, P. K. (1997). Demand for medical care by the elderly: A finite mixture approach, Journal of Applied Econometrics, 12, 313–336. https://doi.org/10.1002/(SICI)1099-1255(199705)12:3<313::AID-JAE440>3.0.CO;2-G
  3. Faymoe, F. and Consul, P. C. (1995). Bivariate generalized poisson distribution with some applications, Metrika, 42, 127–138. https://doi.org/10.1007/BF01894293
  4. Holgate, P. (1964). Estimation for the bivariate poisson distribution, Biometrika, 51, 241–245.
  5. Kocherlakota, S. and Kocherlakota, K. (2001). Regression in the bivariate poisson distribution, Communications in Statistics - Theory and Methods, 30, 815–825. https://doi.org/10.1081/STA-100002259
  6. Kocherlakota, S. and Kocherlakota, K. (1992). Bivariate Discrete Distributions, Marcel Dekker, New York.
  7. Marshall, A. W. and Olkin, I. (1990). Multivariate distributions generated from mixtures of convolution and product families, In H.W. Block, A.R. Sampson and T.H. Savits(eds), Topics in Statistical Dependence, IMS Lecture Notes - Monograph Series, 16, 372–393. https://doi.org/10.1214/lnms/1215457574
  8. Munkin, M. K. and Trivedi, P. K. (1999). Simulated maximum likelihood estimation of multivariate mixedpoisson regression models with application, Econometrics Journal, 2, 29–48. https://doi.org/10.1111/1368-423X.00019
  9. So, S., Chun, H. and Jung, B. C. (2011). Bivariate negative binomial regression model with heterogeneous dispersions, Communications in Statistics - Theory and Methods, Submitted.
  10. Subrahmaniam, K. (1966). A test for “Intrinsic Correlation” in the theory of accident proneness, Journal of the Royal Statistical Society B, 28, 180–189.