Dataset Description: I use a dataset with neuropsychological (np) tests from several subjects. Every subject has more than one tests in his/her follow up i.e one test per year. I study the cognitive decline in these subjects. The information that I have are: Individual number(identity number), Education(years), Gender(M/F as factor), Age(years), Time from Baseline (= years after the first np test).
AIM: My aim is to measure the rate of change in their np tests i.e the cognitive decline per year for each of them. To do that I use Linear Mixture Effects Models (LMEM), taking into account the above parameters and I compute the slope for each subject.
Question: When I run the possible models (combining different parameters every time), I also check their singularity and the result in almost all cases is TRUE. So my models present singularity! In the case that I would like to use these models to do predictions this is not good as it means that the model overfits the data. But now that I just want to find the slope for each individual I think that this is not a problem, or even better I think that this is an advantage, as in that case singularity offers a more precise calculation for the subjects' slopes. Do you think that this thought is correct?
