## 2.8 Assumptions for interpretation and statistical inference

### 2.8.1 Linearity.

I have nothing to add, here.

### 2.8.2 Normality.

The brms package is quite general and allows users to fit models from a variety of likelihoods other than the Gaussian. For example, users can accommodate outliers/extreme values with Student’s t regression. You can do count regression with the Poisson or the negative binomial… For more, see McElreath’s lecture introducing the generalized linear model or Bürkner’s vignette, *Parameterization of Response Distributions in brms*

### 2.8.3 Homoscedasticity.

The brms package can also accommodate homoscedasticity with distributional modeling. In short, one simply models \(\sigma\) in addition to the mean, \(\mu\). See Bürkner’s handy vignette on the topic.

### 2.8.4 Independence.

And the issue of independence is where the multilevel model comes on. See any relevant text, such as *Statistical Rethinking* or *Data Analysis Using Regression and Multilevel/Hierarchical Models*.