Comparing two means in count models having random effects – a UMPU test. (English) Zbl 0899.62022
Summary: We propose a model for bivariate count data that includes a common random effect; conditional on the random effects the marginal distributions consist of independent Poisson distributions. Uniformly most powerful tests are derived for comparing the unconditional means of the two components count distributions for a variety of random effects distributions. The optimal test turns out to be the standard binomial test obtained by conditioning on the total number of events from both components. A numerical calculation is performed to compare the power of the proposed test with the likelihood test under various conditions.
MSC:
| 62F03 | Parametric hypothesis testing |
| 62E10 | Characterization and structure theory of statistical distributions |
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
References:
| [1] | Breslow, N. E., Extra-Poisson variation in log-linear models, Appl. Statist., 33, 38-44 (1984) |
| [2] | Dean, C.; Lawless, J. W., Tests for detecting overdispersion in Poisson regression models, J Amer. Statist. Assoc., 84, 467-472 (1989) |
| [3] | Dean, C.; Lawless, J. W.; Willmot, G. E., A mixed Poisson-inverse-gaussian regression models, Canad. J. Statist., 17, 171-181 (1989) · Zbl 0679.62051 |
| [4] | Ghosh, J. K.; Singh, R., Unbiased estimation of location and scale parameters, Ann. Math. Statist., 37, 1671-1675 (1966) · Zbl 0146.40001 |
| [5] | Lawless, J. W., Regression methods for Poisson process data, J. Amer. Statist. Assoc., 82, 808-815 (1987) · Zbl 0657.62103 |
| [6] | Lawless, J. W., Negative binomial and mixed Poisson regression, Canad. J. Statist., 15, 209-225 (1987) · Zbl 0632.62060 |
| [7] | Lehmann, E. L., Testing Statistical Hypothesis (1986), Wiley: Wiley New York · Zbl 0608.62020 |
| [8] | Lehmann, E. L.; Schefé, H., Completeness, similar regions, and unbiased estimation - Part I, Sankhy \(a\), A, 10, 305-339 (1950) · Zbl 0041.46301 |
| [9] | Lehmann, E. L.; Scheffé, H., Completeness, similar regions, and unbiased estimation - Part II, Sankhy \(a\), A, 15, 219-236 (1955) · Zbl 0068.12907 |
| [10] | Michael, J. R.; Schucany, W. R.; Haas, R. W., Generating random variates using transformations with multiple roots, Amer. Statist., 30, 88-90 (1976) · Zbl 0331.65002 |
| [11] | Nelson, J. F., Multivariate gamma-Poisson models, J. Amer. Statist. Assoc., 80, 828-834 (1985) |
| [12] | Omori, Y., Random effects in survival analysis, (Ph.D. Thesis (1992), University of Wisconsin at Madison, Department of Statistics) |
| [13] | Shao, J.; Chow, S. C., Test for treatment effect based on binary data with random sample sizes, Austral. J. Statist., 32, 53-70 (1990) · Zbl 0707.62043 |
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