# Interpretation of Residual Covariance

I have recently begun using the Structural Equations Modeling (SEM) Method of confirmatory factor analysis for a research endeavor in educational science. My question is, suppose I have two latent variables each with many of its own manifest variables. If I observe a covariance between the two latent variables (I'm not sure if specifically what program I used to reach this point matters but if so I use the lavaan package in R), what does it mean?

I believe it means that it is a residual covariance indicating the presence of a common factor not shown by their predictors but I am unsure. If this is the case what would the level of residual covariance mean? i.e. is there a cut-off point where it could be considered statistically insignificant? Thank you!

• As the latent variables are standard normal the covariance is just correlation. I think it is just this – it seems reasonable for factors to correlate when they are identifying traits / behaviours - although you can set the correlation to zero if it suits your hypothesis. If you think their may be a second level of latent factors you can examine this. – user20650 Mar 28 '13 at 17:15
• Thank you so much for your response! What you say makes sense. That the two latent variables would have some degree of correlation, in fact I had thought about the idea of a multilevel cfa, but is the covariance really just correlation? In my particular case, if that were so I would expect them to correlate much more but instead the value is around .03. Which I am assuming is rather low for a correlation but perhaps not for a residual covariance. (hence the part of my question about statistical significance). I know this is a little vague without a more concrete example. – StatiStudent Mar 28 '13 at 17:35
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