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Interval estimation of the mean response in a log‐regression model
Author(s) -
Wu Jianrong,
Wong A. C. M.,
Wei Wei
Publication year - 2005
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.2329
Subject(s) - statistics , regression analysis , mathematics , sample size determination , prediction interval , confidence interval , interval estimation , interval (graph theory) , regression , inference , econometrics , computer science , combinatorics , artificial intelligence
A standard approach to the analysis of skewed response data with concomitant information is to use a log‐transformation to normalize the distribution of the response variable and then conduct a log‐ regression analysis. However, the mean response at original scale is often of interest. El‐Shaarawi and Viveros developed an interval estimation of the mean response of a log‐regression model based on large sample theory. There is however very little information available in the literature on constructing such estimates when the sample size is small. In this paper, we develop a small‐sample corrected interval by using the likelihood‐based inference method developed by Barndorff‐Nielson and Fraser et al . Simulation results show that the proposed interval provides almost exact coverage probability, even for small samples. Copyright © 2005 John Wiley & Sons, Ltd.