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I used MCMC-lognormal to fit the data with random effect and also I used the normal model to do that , when I make exponential to the mean from lognormal it is different from that one in coming from Normal model, big differences I wonder why?
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If you post SAS program that you used for the analyses, we will be able to comment more confidently.
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The primary reason is that exponentiating the mean of a log normal yields the geometric mean, which is almost certainly less than the mean assuming normality. Take a look at any graphical description of the lognormal distribution, or see this https://en.wikipedia.org/wiki/Log-normal_distribution . There you will see that the mean (expected value) of the log-normal is exp(mu + variance/2). The geometric mean is an approximate estimator of the median, which in a right skewed distribution is less than the mean.
SteveDenham
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Thank you for your reply.
I am pretty sure that the mean as you explained needs to be adjusted by including the variance in it. I will post the code soon and also I adjust the mean to see the result.