I fit three Bayesian binary multilevel logistic regression models. Schematically they look like this:

```
model1 <- brm(DEP.VAR ~ IND.VAR1 + (1|WORD), data = data, family = Bernoulli, warmup = 4000, iter=20000))
model2 <- DEP.VAR ~ IND.VAR1 + IND.VAR2 + (1|WORD), data = data, family = Bernoulli, warmup = 4000, iter=20000)
model3 <- DEP.VAR ~ IND.VAR1 + IND.VAR2 + IND.VAR3 + (1|WORD), data = data, family = Bernoulli, warmup = 4000, iter=20000)
```

I calculated the ICC for each model with `icc()` from the package `performance`. The ICC is calculated with the latent variable method:


$\frac{\tau^2}{\tau^2+ \frac{\pi^2}{3}}$

$\tau^2$ is the variance of the distribution of the varying intercepts.


With each additional covariate, the ICC increases. Why? I don't understand why adding predictor variables should increase the amount of within-group homogeneity.