So Here is the LDA Generative Model
The $\alpha$ and $\beta$ nodes represent the parameters for two Dirichlet distributions. The $\theta$ and $\phi$ nodes represent the parameters for two multinomial distributions. My question is about the $Z$ node (the topic assignment for the word). It represents a sampled topic from the topic distribution for a document from $\theta$. So I don't think it is actually a random variable, it is a sample. But then why is it a node in the generative model if it is not a random variable? This has me confused. Is $Z$ a random variable or not?