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Although I dont fully understand why ... apparently in longitudinal regression models, you can have an unequal number of measurements per subject (ex: 3 for subject1, 5 for subject2, etc). I actually posted a question about this where I was told that longitudinal regression can handle unequal number of measurements per subject [https://stats.stackexchange.com/questions/627433/why-does-longitudinal-models-work-for-uneven-measurements-per-subject-analysis]... but I did not fully understand why

But in longitudinal regression model, is it better to have an equal number of measurements per subject?(ex: 3 for subject1, 3 for subject2, etc). Will the longitudinal model be expected to work better?

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    $\begingroup$ What exact model do you mean? Do you mean a multilevel model? Generalized estimating equations? Repeated measures ANOVA? Or just a regression with time as a covariate? Or something else? $\endgroup$
    – Peter Flom
    Oct 18, 2023 at 10:01

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When using “more exact” methods, I.e., methods that form a full likelihood function (generalized least squares, mixed effects models, Markov models, Bayesian models, etc.) the method properly treats varying number of measurements per subject so the only problem you usually have is that there is loss of efficiency when many subjects have few observations. Approximate methods such as GEE (generalized estimating equations) and the cluster bootstrap do not have this advantage since they don’t have a full likelihood that respects the interconnections between observations within subject. They tend to fail with wildly varying cluster sizes, and also with a small number of subjects. They work best with a large number of subjects with not many records per subject.

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  • $\begingroup$ thx! can you please explain "methods that form a full likelihood function .... properly treats varying number of measurements per subject"? Is ANOVA an example of incomplete likelihood? What is a full likelihood vs not-full likelihood? (ex: not-full likelihood = approximate methods)? $\endgroup$ Oct 19, 2023 at 1:53
  • $\begingroup$ why is GEE considered not-full likelihood? isnt GEE used in longitudinal regression .... therefore longitudinal regression requires balanced number of observations per cluster? $\endgroup$ Oct 19, 2023 at 1:55
  • $\begingroup$ can you please explain " respects the interconnections between observations within subject"? why doesnt GEE do this? why do these other methods do this? $\endgroup$ Oct 19, 2023 at 1:57
  • $\begingroup$ "there is loss of efficiency when many subjects have few observations." Does this mean high variance? in general, is it advisable to use longitudinal regression when you only have few measurements per subject because the variance will be very big? $\endgroup$ Oct 19, 2023 at 1:59
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    $\begingroup$ In this context marginal = non-subject-specific, conditional = has subject-specific random effects. GEE, GLS, and some Markov models are marginal. Marginal models are entirely appropriate if interested in group-level effects more than subject-level estimates. Regarding normal distribution there are plenty of full likelihood longitudinal models for non-normal, binary, categorical, or ordinal Y. See for example semiparametric Markov models which are excellent competitors of normal-theory models even if normality holds perfectly. $\endgroup$ Oct 20, 2023 at 20:05

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