Hi @AWoodward,
Thanks so much for your reply! You are right, the association between these variables, especially lesion load, is nonlinear when plotting the predictions vs these predictors. I fit the model with the below adjustments:
mod2 <- brm(NORMED_MOTOR ~ s(Total_Percsub_Cramer_z, bs="cr", k=10) + s(Lesion_Volume_z, bs="cr", k=20) + (1|SITE), data=reduced_modeling_df, family=Beta(link="logit"), iter = 10000, chains = 6)
And got an improved fit but still not great:
I also notice that when I plot the density of the predicted values it seems like a “condensed” version of the density of the outcome (black = prediction, red=observed):
I think the different peaks are actually somewhat captured but in the wrong location and not spread over the whole distribution. The range for the predicted values is (0.31, 0.84) whereas the range for the true values is (0.01, 0.99). Is there a way to adjust the beta prior for the outcome to get a better “spread” over the domain and allow for predicting values over the whole range?
Please let me know if I can provide any more information and thanks again for the help!