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I need to write a computer program to estimate the fixed-effects and random-effects parameters for a linear mixed-effects model. Is there a paper or book that clearly describes how to do this? Can you please give me a bibliographic-like citation?

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As far as I know, this book presents all the necessary details that you need to implement a program to estimate the fixed-effects and random-effects parameters for a linear mixed-effects model from scratch:

Generalized Linear Mixed Models: Modern Concepts, Methods and Applications

If you intend to use a software like R, you may find information in this tutorial:

Linear Mixed Models

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