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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 :) $\endgroup$
    – Richard Erickson
    Jun 12, 2015 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, 2015 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. $\endgroup$
    – Richard Erickson
    Jun 12, 2015 at 20:36
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    $\begingroup$ There's "Latent variable modeling using R". amazon.com/Latent-Variable-Modeling-Using-Step-/dp/1848726996/… $\endgroup$
    – Jeremy Miles
    Jun 12, 2015 at 20:59
  • $\begingroup$ @JeremyMiles, why not post the comment as an answer? $\endgroup$
    – Richard Hardy
    Apr 4, 2019 at 14:06

3 Answers 3

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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! $\endgroup$
    – Richard Hardy
    Mar 17, 2020 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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