Posted 25 July 2013 - 07:02 PM
Dear colleague
If you do not have etas at all, then I guess you used the simulation versus simple option when unclicking population. As far as I know this will give you only the predicted responses and not the the response + noise. If you want to get the noise too added to your response (CObs versus C), then just add a random effect and out a very small variance. In the population mode, you will get both the predicted response © without noise and what could be an observation CObs which includes the noise. If you are still in trouble, let me know and I will send you a demo example.
When you shift to the population mode, you model parameter is now defined in terms of both fixed and random effect.
For example
stparm(Cl=tvCl*exp(nCl))
ranef(diag(nCl)=c(0.1))
tvCl is the fixed effect which is what you used when you did not have any random effect.
Now, nCl is a sample from a normal distribution with mean 0 and variance you defined just below in the statement ranef. ranef stands for random effect, diag means no covariance, c means vector and then you put the variance, here 0.1.
The program will always simulate from a normal distribution with mean 0 and variance defined in the ranef statement.
However Cl is equal to tvCl*exp(simulated random effect) and therefore you will get what we call a lognormal distribution for Cl. The median of that distribution is tvCl.
If you want a pure normal distribution for cl, you can change the option by clicking on parameter/structural and look under style where you can select different options for distribution (default is lognormal). Suppose you define sum + eta. This stands for normal distribution for your parameter. The mathematical formula is
stparm(Cl=tvCl+nCl)
same meaning for nCl but since you add tvCl to it, the result will be a normal distribution for Cl
Every time you shift to another individual, the program selects a new random sample (nCl)
You are talking about uncertainty here and not population variability, These are two completely different things. However there is a way to quantify the impact of the uncertainty in your fixed effect and reflect it through simulation. The problem is often the confidence intervals are asymmetrical and therefore it is more difficult to define the uncertainty distribution. You can make an assumption that the standard error give to you can be used to simulate a normal distribution with mean at the estimate and variance equal to the square of your given standard error. This is risky because you can get negative values for your parameter. If you have the standard error of your parameter in the log domain, then you can take the log of your estimate and use that standard error as the standard deviation for your simulation, then you exponentiate the result to get the values of your model parameters that now will never be negative.
I hope it helped.
best
Serge