Tests for Identifying Synergistic and Antagonistic Interactions under Linear Model
| Autor: | Thao, Li-Lun, 曹立綸 |
|---|---|
| Rok vydání: | 2017 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 105 In this thesis, we consider a linear model with two 2-level predictors A and B and a continuous response Y. The two levels of A and B are labeled by 0 and 1. The responses obtained on the four level combinations of A and B, i.e., (0, 0), (0, 1), (1, 0), and (1, 1), are denoted by Y_{00}, Y_{01}, Y_{10}, and Y_{11} respectively. They are assumed to be normally distributed with means µ_{00}, µ_{01}, µ_{10}, and µ_{11} respectively, and an unknown variance σ^{2}. The two predictors A and B are said to have a synergistic (or antagonistic) interaction on the response Y if µ_{00}=µ_{01}=µ_{10}=µ, and µ_{11} is larger (or smaller) than µ. In this thesis, we utilize the methods of intersection-union test (IUT) and equivalence test to resolve the test problem of identifying such intersections. Chen (2016) also studied this problem but under the stronger assumption that σ is known. When σ is unknown, the parameter space and the rejection region we develop are quite different from what presented in Chen (2016). Berger and Hsu (1996) gave some conditions under which the rejection region of an IUT is of size α. We prove that our rejection region satisfies these conditions, and therefore it is a size-α rejection region. We also identify the parameter values on which the probability of this rejection region reaches α, and use this result to conclude that it is unnecessary to consider the correlation between the test statistics in the construction of this rejection region. A computer simulation is performed to study and verify the power of our method. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
| Externí odkaz: |
|