ANOVA vs LMER for discrete explanatory variables with stan

Figure: Comparisons between complete pooling, no pooling and partial pooling strategies (source)

In this blog, we focus on understanding and comparing the generative processes of analysis of variance (ANOVA) vs. linear mixed effects regression model (lmer) for discrete explanatory variables. Even though there has been an overall shift from ANOVA to lmer model in the community of science, it is still helpful to first look at the data generating process of ANOVA.