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Is there any "state of the art" book on SEM/CFA that you can recommend? I am looking for something that offers both some theory and some practice and I am using R with lavaan.

I am a psychologist and mainly interested in CFA to test questionnaire structure, etc.

Please note why your book of choice is worth reading.

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    $\begingroup$ What is your your statistical background and area of study? For example, a mathematical statistician, computer scientist, and field biologist might all want to do SEM, but have very different backgrounds. Also, knowing your field would help us to provide better suggestions because we our suggestions would include story problems that better catch your interest :) $\endgroup$ Jun 12 '15 at 19:34
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    $\begingroup$ I am a psychologist, interested in testing a theoretically presumed structure of questionnaires with CFA, e.g. $\endgroup$
    – Jens
    Jun 12 '15 at 19:43
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    $\begingroup$ Thanks for that info. You might want to edit that into your question. For example, knowing that info, I won't suggest Jim Graces's book because he is an ecologist. $\endgroup$ Jun 12 '15 at 20:36
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    $\begingroup$ There's "Latent variable modeling using R". amazon.com/Latent-Variable-Modeling-Using-Step-/dp/1848726996/… $\endgroup$ Jun 12 '15 at 20:59
  • $\begingroup$ @JeremyMiles, why not post the comment as an answer? $\endgroup$ Apr 4 '19 at 14:06
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Mulaik, S. A. (2009). Foundations of factor analysis. Chapman and Hall/CRC.

This is a mathematically thorough (and demanding) treatment of the subject. It takes an algebraic perspective and is very clearly written. I did miss a probabilistic perspective in addition to the algebraic one, but I realize one should not require too much from an already great book. It will be too advanced for most beginners (except perhaps those who have solid skills in linear algebra).

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  • $\begingroup$ I have enjoyed the book a lot! $\endgroup$ Mar 17 '20 at 16:40
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Additional recommendation from a fellow psychologist/psychometrician.

State of the art books:

Bollen, K. (1989), Structural Equations with Latent Variables, John Wiley & Sons, New York, NY. Note: classical book, Kenneth Bollen is an influential figure in SEM

Brown, T. A. (2006). Confirmatory Factor Analysis for Applied Research. New York, NY: Guilford Press. Note there is a new 2015 version of this book. Deep coverage of CFA

Kline, R. B. (2015). Principles and practice of structural equation modeling. New York, NY: The Guilford Press. A lot of extra details on both SEM and CFA

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Mulaik, S. A. (2009). Linear Causal Modeling with Structural Equations. Chapman and Hall/CRC.

This seems to be a mathematically thorough treatment of the subject.

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