Hi all -

I have two multilevel nonlinear Beta regression models. Both of them have the same number of parameters (i.e., k, s_1, h, s_2):

Model \ 1: RSV = 1 / (1 + \textit{k} * Delay^{s_1}) * (1 + \textit{h} * OAs^{s_2})

Model \ 2: RSV = 1 / (1 + \textit{k} * Delay)^{s_1} * (1 + \textit{h} * OAs)^{s_2}

I’ve tested them with three different datasets, and Model 1 is consistently better than Model 2 based on cross-validation. For example,

```
elpd_diff se_diff
model2 0.0 0.0
model1 -69.9 11.4
```

Then I tried to know why Model 1 is better than Model 2 by examining the difference between the ELPD for each data point:

I failed to notice any sizable reason why Model 1 is better than Model 2. I then simulated each participant’s data from each of the two models and compared them with the group mean data. Surprisingly, when I plot them, the two models produce comparable, or almost the same, results (visually) in fitting the observed data. As may be seen below, the two simulated curves are almost identical.

I’ve been scratching my head over why this can be the case. Or is there a way to know/visualize *why* one model is better than the other?

Any thoughts will be much, much appreciated. Many thanks.

Mat