First, I’m interested in why people left. Did you examine what variables predicted attrition?

Two potential reasons. (a) The T1 of our data collection took place right before the onset of the Covid-19 pandemic. The pandemic having disrupted daily routines and priorities for many people, we believe it may have had an impact on the participant's motivation to complete the survey as it focused on psychological distress. (b) All of our participants were in grade 11 or 12 in high school at T1 and had provided us with their high school emails (study limitation). At T2, they had either graduated from high school or were out of school because of social distancing, meaning it was difficult to contact them through their school emails.

I don t know what is your exact measure of psychological distress, but as you speak of linear regression, I assumed that it is a continuous variable. If you want to identify a pattern evolution maybe you can use a time-series cluster analysis.

I remember having this question as well when I was researching and analyzing a longitudinal study of customers both who churned and who stayed over their lifecycle. In order to reduce the effects of missing data or uncontactable source. as well as factor in pandemic related effects, I used MER (Mixed Effect Regression) as my statistical tool to analyze as its able to factor in irregularly timed data. Anova/Manova is not flexible enough to account for the irregularities. The good thing about MER is that when it correlates repeated responses, it quantifies variation among random effects and can serve to describe cluster specific trends over time. Which is different from Anova (the assumption here is outcomes have equal variances over time - which in reality is not) and Manova (no specific assumptions at all). Try it out maybe it'll give you an outcome that may be able to explain your random effects of the pandemic.

Do any of your T1 variables predict retention at T2 and T3? The drop from T1 to T2 seems a casualty of COVID, but it is surprising that a lot who did T1 and T2 did not do T3. I assume your goal is looking at growth/decline over time, so growth models (e.g., first example in lmer, in the R package lme4). However, the choice of model depends on what your measures and research questions. There are a few caveats, but consider one technical and one conceptual one. The technical one is that with longitudinal data looking at growth you would often use a random slope model, which assumes people's slopes vary around some overall slope, and you can estimate those (if you choose). However, with only three time points, even if you had no missing data, this procedure can have problems estimating these slopes (some alternatives are described here https://www.frontiersin.org/articles/10.3389/feduc.2017.00058/full). The conceptual issue relates to why there are missing. This can become an important (post hoc) research question to address. I assume that there are other studies that you can look at for T1-T2 loss in similar groups (e.g., similar proportion of high school seniors [grade 12] move out of town) and see if you can estimate how much loss can be attributed to COVID. I think given the interest in how COVID affected research this could be interesting.

When dealing with a low retention rate of participants in a longitudinal study, it's crucial to employ alternative statistical analyses to tackle the challenges posed by missing data and participant dropout. Here's a summary of the alternative approaches and statistical techniques to consider:

In conclusion, the choice of analysis method should align with the data's nature and reasons for dropout. Transparent reporting of methods used to address missing data and conducting sensitivity analyses are essential for assessing result robustness. Collaboration with an experienced statistician or data analyst skilled in managing longitudinal data with missingness can be highly beneficial in such scenarios.