In the study in here, it is said that mixed effects models are better in estimating parameters of a ODE system when there is only very small number of data to estimate the parameters. So, in a situation where viral load data are measured over time across several subjects how does mixed effects improve parameter estimation than simply using a nonlinear optimisation technique to minimise an objective function that considers minimising the sum of squared errors?
Is it because the mixed effects models estimate a population mean for the parameters and the individual variability is explained through the random effects?
So, does mixed effects consider the data points of all subjects together when estimating the population parameters?How does it overcome the issue of limited data?
Also, is this mixed effects method effective when the data across subjects show various patterns? For example, the viral load data in the above article all show a similar pattern, although there is individual variation. But in a situation where the patterns are totally different, is this method still effective?