文章基本信息

标题：Linear Maximum Likelihood Regression Analysis for Untransformed Log-Normally Distributed Data
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作者：Sara M. Gustavsson ; Sandra Johannesson ; Gerd Sallsten 等
期刊名称：Open Journal of Statistics
印刷版ISSN：2161-718X
电子版ISSN：2161-7198
出版年度：2012
卷号：2
期号：4
页码：389-400
DOI：10.4236/ojs.2012.24047
出版社：Scientific Research Publishing
摘要：Medical research data are often skewed and heteroscedastic. It has therefore become practice to log-transform data in regression analysis, in order to stabilize the variance. Regression analysis on log-transformed data estimates the relative effect, whereas it is often the absolute effect of a predictor that is of interest. We propose a maximum likelihood (ML)-based approach to estimate a linear regression model on log-normal, heteroscedastic data. The new method was evaluated with a large simulation study. Log-normal observations were generated according to the simulation models and parameters were estimated using the new ML method, ordinary least-squares regression (LS) and weighed least-squares regression (WLS). All three methods produced unbiased estimates of parameters and expected response, and ML and WLS yielded smaller standard errors than LS. The approximate normality of the Wald statistic, used for tests of the ML estimates, in most situations produced correct type I error risk. Only ML and WLS produced correct confidence intervals for the estimated expected value. ML had the highest power for tests regarding β₁.
关键词：Heteroscedasticity; Maximum Likelihood Estimation; Linear Regression Model; Log-Normal Distribution; Weighed Least-Squares Regression