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Now I'm having a hard time having a grasp on the difference between fixed and random effects of regression models. I believe I understand it's recommended to use random effects if you consider heterogeneity of slopes, when the data is nested among hierarchical levels, etc.
But here's the question.
Why don't we just put moderating variable(interaction term) if we want to reflect the changing effect among different groups? for example, if the effect of study time on GPA differs among different classrooms, then why not just make a dummy variable for classroom variable, and put an interaction term? I cannot understand what the point is here.
What is an overall intuition on the grand assumption of random effects model? what is the main idea that can penetrate the logic of random effects model? I don't want any mathematical or statistical explanation, I want to draw some hypothetical picture in my head.