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I am just a novice in factor analysis.

I am writing some presentation about factor analysis and I am mainly reading about exploratory factor analysis.

Both EFA and CFA have diagrams. For EFA usually factor loadings are seen on the arrows. However, for CFA usually there are some "1" on some arrows, but not all. As I am a novice in this, I do not really understand yet what those mean.

Can you give me some clues?

For example, see here page 174, there is a picture : http://psychology.concordia.ca/fac/kline/Library/k13b.pdf

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    $\begingroup$ Not my field, nor my religion, but I thought CFA meant confirmatory factor analysis. But to increase your chance of a good answer from those who do this, could you give a reference or an example? $\endgroup$
    – Nick Cox
    Commented May 16, 2013 at 8:34
  • $\begingroup$ I have changed the title... And give a reference as an example $\endgroup$
    – renathy
    Commented May 16, 2013 at 10:27
  • $\begingroup$ It appears that you have received good answers. If you are happy with any of them, please accept one. $\endgroup$
    – LeelaSella
    Commented May 27, 2013 at 12:25

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The "1" means that the coefficient for that particular path has been set (fixed) to 1, as mentioned by Peter Flom. The diagram you refer to is reproduced here:

enter image description here

In order for a latent variable to have a scale either its variance must be fixed (often to 1), or a path to one of it's indicators must be fixed (usually to 1), as in this case. The same applies for the errors - although it would be possible to fix the error variances instead of their paths, it is usually of interest to estimate the error variances directly, so you hardly ever see models where error variances are fixed instead of their paths. Also, it is worth noting that in many books, papers and software packages, the 1s on the error paths are not usually shown.

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A "1" on diagrams like this usually means that the coefficient has been set to 1 by the person doing the analysis. Such settings are often necessary to allow model identification.

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There is a complete explanation p176: http://psychology.concordia.ca/fac/kline/Library/k13b.pdf

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