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I was reading in Brown book the theory of a random effect model and then I started searching about how can I apply it in R.

I read that when I am modeling a mixed model using R, I am referring to random effects as random intercepts and as random slopes. Also we now have random intercepts model and random slopes model.

Wanted to ask something about random intercept model. Is it correct to say that its the same as a random effect model or its a specific category of a random effect model?

For both models random effects (or intercepts) are uncorrelated.

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  • (IMO) a "random intercept" model is a model with only random intercepts (i.e. only the intercept or baseline value varies among groups)
  • a "random slopes" model usually has both intercepts and slopes models varying randomly across groups (random-slopes-only is an unusual special case)

Some people make a distinction between a "random effects model" (with no fixed effects other than the intercept) and a "mixed model" (with both fixed and random effects).

(I don't know what the "Brown book" is ... maybe you mean Brown, Violet A. “An Introduction to Linear Mixed-Effects Modeling in R.” Advances in Methods and Practices in Psychological Science 4, no. 1 (January 1, 2021): 2515245920960351. https://doi.org/10.1177/2515245920960351 ?)

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  • $\begingroup$ *Book is Helen Brown-Robin Prescott. In my case random effects model having both fixed and random effects. $\endgroup$
    – Superd
    Commented Jul 27, 2023 at 12:41

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