MCMC Lognormal.

[AlexDaher]

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?

[Rick_SAS]

If you post SAS program that you used for the analyses, we will be able to comment more confidently.

[SteveDenham]

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

[AlexDaher]

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.