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Is there a good book on Multilevel models (random intercept, random slope, fixed effects, etc.) written for mathematicians which treat the theory rigorously?

My background is essentially is in the area of stochastic analysis, stochastic partial differential equations, Markov chain Monte Carlo and computer graphics (beyond that, I'm interested in machine learning). So, I'm new to this stuff and don't whether there might be something out there which is appropriate for me.

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  • $\begingroup$ Given multilevel models have extensive application, I think you will struggle to find such a book that only focuses on theory. $\endgroup$
    – Earlien
    Commented Jul 14, 2020 at 1:03
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    $\begingroup$ @Earlien It doesn't not necessarily need to focus on theory only, but it should present the theory in a rigorous way. $\endgroup$
    – 0xbadf00d
    Commented Jul 14, 2020 at 4:15

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Yes, the book by Eugene Demidenko, "Mixed Models: Theory and Applications with R" is a good one for a mathematician.

You will see from the "why I wrote this book" that he is coming from a mathematical perspective: https://www.eugened.org/why-i-wrote-this-book

Amazon has quite of lot of preview pages: https://www.amazon.com/Mixed-Models-Theory-Applications-R/dp/1118091574

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