I've run a binary logistic regression using brms. I have one independent variable (Age) and 3 dependent variables, Y1, Y2, and Y3. These dependent variables are all pass/fail tasks. For each task, I want to model the probability of passing as a function of age. But, I also want to test the hypothesis that those who pass task 2 (Y2 = 1) tend to also pass task 3 (Y3 = 1).
Here is the call & summary:
fit1 <- brm(mvbind(Y1,Y2,Y3) ~ Age + (1|p|Age), data = MyData, family = bernoulli) add_ic(fit1) <- "loo" summary(fit1)
I'm new to brms, so there are two things I'm a little unsure about. First, how do I interpret the correlation estimates? I understand how to interpret the coefficients under "Population-Level Effects", but how do I interpret those under "Group-Level Effects"? For instance, how do I interpret the estimate of 0.09 for "cor(Y2_Intercept,Y3_Intercept)"? Second, the confidence intervals are very large for each correlation. Is the model suggesting that, in each case, there is no credible correlation? If so, this confuses me, because when I run cor.test, I get the following, which suggests a (statistically significant) moderate correlation:
Can anyone help me square this all away?