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# Linear Maximum Likelihood Regression Analysis For Untransformed Log-Normally Distributed Data

Artikel i vetenskaplig tidskrift
Författare Sara Gustavsson Sandra Johannesson Gerd Sällsten Eva M. Andersson Open Journal of Statistics 2 4 389-400 2161-718X 2012 Institutionen för medicin, avdelningen för samhällsmedicin och folkhälsa 389-400 en dx.doi.org/10.4236/ojs.2012.24047 Heteroscedasticity, Maximum Likelihood Estimation, Linear Regression Model, Log-Normal Distribution, Weighed Least-Squares Regression Statistik

## Sammanfattning

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

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