Confirmatory factor analysis

[janetong]

Hi! Just wonder in the computation of confirmatory factor analysis, what input is putting in the formula in STATA, correlation matrix or covariance matrix? I understand the outcome analysis is based on covariance matrix.

[Weiwen Ng]

I am not sure if I understand you correctly, but it sounds like you're asking if Stata accepts either a correlation matrix or a covariance matrix for CFA in SEM. If you have individual-level data, you can just run SEM on that data.

If you do not have individual data but you have access to a correlation or covariance matrix for the set of items, you can actually conduct a CFA using that. The process is described in SEM example 2, using a summary statistics dataset. If you have many items, this is a lot of rows to enter. The example used a covariance matrix, but you can use the ssd command to specify a correlation matrix. Honestly, I have not ever done this because I have always had access to individual-level data.

[janetong]

Thank you, Weiwen for STATA's ability to perform SEM using a summary statistics dataset. I entered individual-level data for STATA to do the analysis. Just a further question, the goodness of fit indices are computed based the covariance analysis. Am I correct?

[Weiwen Ng]

... the goodness of fit indices are computed based the covariance analysis. Am I correct?

I am not sure exactly what you mean by this, but it could be because I'm not actually any sort of expert on traditional SEM. However, any SEM measurement model definitely involves an analysis of how the items covary. I do know that the goodness of fit indices stem from observed vs model-expected values of all the indicators. Say you assumed a unidimensional model - that means one latent trait causes the item responses, and that's the sole source of any covariance between them (or you could have added error covariances as appropriate, or other relatively minor stuff like that, or you could be fitting a multi-dimensional model, or whatever model). If you absolutely need more detail, I'd read the SEM manual's formulas. If those are too complex, one slightly better explanation I've seen is David Kenny's site.