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1$\begingroup$ Thanks Erik, Your answer is really helpful! I have indeed considered whether a model with time as factor could be a better fit. But, does adding linear random slopes over fixed time coded as a factor lead to the same problem or OK? alt_model <- lmer( BDI ~ as.factor(time) + (1+time | id), data = dat ) Also, I've seen models who use different splines (e.g. restricted cubic splines, natural splines, etc.) where they include linear random slopes. Do these models suffer from the same problems that you listed above? I would've thought so, but not sure? $\endgroup$AndroidPandroid– AndroidPandroid2025-11-26 11:15:45 +00:00Commented Nov 26, 2025 at 11:15
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$\begingroup$ No problem, @AndroidPandroid! A spline approach is probably also out of reach, however I added some additional information in an edit that you can estimate something like your original model using SEM. $\endgroup$Erik Ruzek– Erik Ruzek2025-11-26 15:38:00 +00:00Commented Nov 26, 2025 at 15:38
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1$\begingroup$ Thanks Erik, I think moving on to SEM would be a bit too much for me at the moment. I'm really intrigued by your initial feedback since it seems to clash with what I've heard from others, so I truly appreciate it. If you do not mind, I've a couple of follow up questions: Would your critique still apply if I used restricted cubic splines (assuming I had more data, say around 20 time points and modeled random linear slopes)? And in your categorical model, would I need to model random time as a factor as well or could I use linear random time in that case? Again, assuming I had more data. $\endgroup$AndroidPandroid– AndroidPandroid2025-11-26 18:44:41 +00:00Commented Nov 26, 2025 at 18:44
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$\begingroup$ Pt.1. Assuming more time points, your options open up considerably. You could model the fixed (mean) effects of time flexibly using piecewise linear splines. With this model, you can allow for a continuous time random slope, such that for a given subject, the same amount is added to the slope of each line segment. For restricted cubic splines, you generally would want to model the spline variables themselves as random slopes (not continuous time). $\endgroup$Erik Ruzek– Erik Ruzek2025-11-26 20:04:59 +00:00Commented Nov 26, 2025 at 20:04
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$\begingroup$ Pt. 2. With the categorical model, you are essentially reproducing an ANOVA that can handle unbalanced data. You would not include random continuous time for the reasons discussed in my response, but you could look at random categorical time, This will be a tricky estimation problem, so be very careful. See stats.stackexchange.com/questions/78928/… $\endgroup$Erik Ruzek– Erik Ruzek2025-11-26 20:06:08 +00:00Commented Nov 26, 2025 at 20:06
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