Model suggestion for zero-bounded dependent variable I have a repeated measures dataset (8 measurements) with three experimental groups (Randomly generated). The dependent variable (Y) is on a continuous scale bounded inferiorly at 0. I am trying to model the effect of the different groups and time on Y. What would be the appropriate model here? -

*

*repeated ANOVA is compromised by the non-normal distribution of Y
(see histogram -  I tried adding a minuscule amount and logging, but
still really to no help)

*Mixed linear models are not bounded inferiorly at 0. Perhaps one of the more advanced non-linear mixed models?

*Area under the curves for all timepoints stratified by group?

*Bayesian approaches?

Raw Y   
Logged Y
Histogram of logged Y

 A: Have you given any thought to the three parameter Weibull distribution?  Which would be SEV with log(x). Also known as Complimentary log-log ,or Gompit on log(x) With a threshold.  Another idea is to treat time zero issues like time zero failures like warranty claims for vehicles that have not been sold. Basically the cumulative percentage has a non zero intercept. You analyze the non zero values separately, then add the percentage of the zero values to them.
Though I am not clear on the actual response, I suspect the "0" values are actually Left Censored values. Left Censoring: we only know the events happened sometime prior (eg prior to Y=1 (log_vol=0), but do not know when. Looking at the histograms of "log_vol" there are no values less than log_vol=0 (which is Y=1) except for the log(0.0001) spike. I suspect the spike is an artifact of this left censoring @ ~ Y=1. The time variable, appears to be shifting the distribution snapshots leftward toward 1 (log_vol=0), resulting in higher counts of values less than 1 (log_vol=0) as I try to show in the figure below using Logistic Link to illustrate on log_vol. The histagrams appear to be left skewed, so a SEV (aka Gumbull, Gompertz, Complimentary log-log) link may fit better. This becomes Weibull (SEV of log(x) is ~ Weibull) with Weibull slope ß = l/scale. With SEV scale= 1 is actually the exponential distribution (Poisson counts, Exponential time between events). If so, I suggest that a Survival analysis might be what you may want. Here is a link with an answer you may find helpful.
https://stackoverflow.com/questions/41968606/left-censoring-for-survival-data-in-r


A: So I did fit a longitudinal bayesian proportional odds model using brlm as suggested by Frank Harrells. The fit is quite good and seems to model what I wanted while still retaining the inferior bounds. However, I would have liked to do a posterior predictive check, but I don't quite comprehend the calculation of the predicted probabilities given all these confusing intercepts and the other "standard" Bayesian toolboxes don't seem to recognize the brlm models. Moreover, I tried calculating the contrast between the different groups at t=2, but I am at odds as how I can convert the value into the raw Y-units. The calculated contrast between the green and red group at t=2 is 1.866.

