I have a question about normal linear models vs mixed models.
Say I'm predicting prices for certain products, and I know two things: store and brand:
In a linear model (lm), this would be:
price ~ 1 + store + brand
in a mixed effects model (lmer from lme4), this would be
price ~ 1 + (1 | store) + (1 | brand)
I keep on reading that mixed effects models are great because e.g. different stores have different effects (think Whole Foods vs Costco, expensive vs cheap), but I don't see how a normal linear model doesn't track that anyways. If store and brand are factors, then doesn't each unique store get transformed into its own boolean variable? (For each price i, it was or it was not gathered from store j, so if there are ten different stores, that'll be turned into ten different indicator columns in the data matrix X).
How exactly does a mixed effects model do better than this?