看到一篇文献这样写的:“Fot the multiple regression models,we used the variables decribed below and all possible two-way interactions to calculate the adjusted least square geometric mean(LSGM) concentrations(in mincrograms per liter) ,which provide geometric mean estimates for a variable after adjustment for the model covariates. ”LSGM是最小二乘几何均数吧?用SAS怎么样计算啊?请高手指点!!!
I guess, they merely do the multivariable regression on the log-transformed response variable of concentration first and then get the least square mean of the transformed response. When back to the concentration itself, the back-transformed least square mean is called the least square geometric mean of concentration. It looks like as the following formula:
Estimate of E[Y|X] = exp{[log(y1|x)+log(y2|x)+….]/n} = exp{log[(y1*y2*…)^(1/n)]} = exp{Estimate of E[log(Y)|X},
Where (y1*y2*…)^(1/n) is the geometric mean of Y, the concentration.