In this week, we’ve reviewed about some important distributions, such as binomial distribution, geometric distribution, Poisson distribution, and so on.

Also, we’ve learned about linear mixed model, which is a model we need to use when linear regression model is not feasible. There are several assumptions that needs to be satisfied before fitting the linear mixed model.

- continuous response variable
- Subjects are independent, however observations within each subjects are dependent.
- Random effect errors and within-unit residual errors have constant variance.

Suppose there is a large difference between the intercept of each group, in this case, we usually consider adding a random effect, in particular, a random intercept to modify this problem. Furthermore, Suppose the intercepts are similar but there is a large difference between the slope of each group, in this case, we need to use a random slope to fix this problem. When both cases happen, we can use both random slopes and random intercepts. The following plots can help us to determine which random effects to be included in our model.