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Longitudinal or repeated measures studies are appropriate if subjects are observed repeatedly over time (balanced or unbalanced).

Is it important to keep subjects that have records only for one time or it is possible to discard these subjects without any changes in the analysis? What does happen if we discard these subjects?

Is there any difference between classic and Bayesian framework in this regard? Any reference is welcome.

Suppose we want to fit a linear mixed model. If we keep single observations, the intercept and slope will be changed from the case we discard them. I think this is a bad idea to keep these data, as they have nothing to add to our knowledge. They are measured once and have no value in modeling longitudinal changes. Then using them seems incorrect as they change our estimates without any sensible justification. Unfortunately, I cannot find any reference for this. It seems that this point has not been clarified in the literature. Does anybody know a reference for this problem??

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  • $\begingroup$ 1) What is the "classic framework"? 2) If you are interested in inferring things from longitudinal data, what could bring a single observation except noise? Longitudinal data as I understand it are about quantities evolution over time, right? I somehow don't see why you would want to keep single observations but I am not an expert in the field, so maybe you could precise why keeping them would be useful :) $\endgroup$
    – Eskapp
    Commented Jan 5, 2017 at 15:20
  • $\begingroup$ Trivially, you can't keep single observations if you plan on using cross-section fixed effects, rather than random effects. You need fixed effects if your identification strategy requires that you control for time-invariant heterogeneity. $\endgroup$
    – generic_user
    Commented Jan 5, 2017 at 15:52
  • $\begingroup$ By classic, I mean "frequentist" methods. I understand and explained that longitudinal methods study changes over time. However, in some applications that has been published in prominent statistical journals, single observations (response measured at single time point) have also been included in the analysis. $\endgroup$
    – T JJ
    Commented Jan 5, 2017 at 18:08

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With respect, I wouldn't be so quick to discard single-value observations from data arising from longitudinal studies. In the building of longitudinal models, I certainly support dropping such data. However, in STUDIES as opposed to models, you are often asked to report information at baseline (ie, cross-sectionally) for the entire population, whether or not they continue to provide information subsequently.

For example, CONSORT guidelines for the reporting of randomised controlled trials require the description of baseline information regardless of the nature of a patient's subsequent participation in the trial (e.g., the patient might not receive an intervention, may choose to withdraw, or may experience the outcome of interest before the second measurement period). Another example in which baseline effects were important in and of themselves is in panel studies of AIDS (see Multicenter AIDS Cohort Study that has been collecting information semi-annually since 1984).

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  • $\begingroup$ I agree with you. However, if these data provide no information with respect to the longitudinal process, how can one justify their presence in the analysis as the aim of longitudinal studies is the study of change??A subject may receive a treatment at baseline and distort baseline distribution and then leave the study. In this case, he may shift the baseline average and by leaving the study, following averages become higher or lower, not because of the treatment, but because of including a group of people with single observations in the analysis. Therefore I am not comfortable with inclusion. $\endgroup$
    – T JJ
    Commented Jan 5, 2017 at 21:00
  • $\begingroup$ Right. There are a lot of issues here -- losses to follow-up, intention to treat analysis, external validity -- that go beyond the issue of the longitudinal models. Take, for example, the situation in which data are collected at three equally-spaced time points, baseline (T0), T1 and T2. It would be very meaningful to know that a model was run on 1,000 individuals, but 9,000 others who met inclusion criteria and provided T0 data were not included because they all dropped out. What is the external validity of your model? $\endgroup$
    – user140401
    Commented Jan 5, 2017 at 21:23
  • $\begingroup$ To be clear, though, I'm taking issue at the concept of discarding data versus non-inclusion of observations because they don't meet criteria specific to the requirements of the analysis. For example, you could easily state, as some have done, that you're limiting the analysis to those that provide at least two data points -- baseline plus one other. Good luck to you! $\endgroup$
    – user140401
    Commented Jan 5, 2017 at 21:25

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