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How are the parameters without variability handled?

Adding/removing inter-individual variability

By default, all parameters have inter-individual variability. To remove it, click on the checkbox of the random effect column:

Choosing a method for the parameters without variability

Parameters without variability are not estimated in the same way as parameter with variability. Indeed, the SAEM algorithm requires to draw parameter values from their marginal distribution, which exists only for parameters with variability.

Several methods can be used to estimate the parameters without variability. By default, these parameters are optimized using the Nelder-Mead simplex algorithm (Matlab’s fminsearch method). Other options are also available in the SAEM settings:

  • No variability (default): optimization via Nelder-Mead simplex algorithm
  • Add decreasing variability: an artificial variability (i.e random effects) is added for these parameters, allowing estimation via SAEM. The variability starts at omega=1 and is progressively decreased such that at the end of the estimation process, the parameter has a variability of 1e-5. The decrease in variability is exponential with a rate based on the maximum number of iterations for both the exploratory and smoothing phases. Note that if the autostop is triggered, the resulting variability might me higher.
  • Variability at the first stage: during the exploratory phase of SAEM, an artificial variability is added and progressively forced to 1e-5 (same as above). In the smoothing phase, the Nelder-Mead simplex algorithm is used.

Depending on the specific project, one or the other method may lead to a better convergence. If the default method does not provide satisfying results, it is worth trying the other methods.

Alternatively, the standard deviation of the random effects can be fixed to a small value, for instance 5% for log-normally distributed parameters. To enforce a fixed value, click on the wheel next to the initial omega value and select “Fixed”.

With this method, the SAEM algorithm can be used, and the variability is kept small.