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When I am doing a statistical analysis, first I take the measures of each of the constructs I am measuring and I create an average score. With these averages, I calculate the correlation between different constructs.

But, when I am using Structural Equation Modeling (SEM), I understand the correlations between my latent variables (constructs) are calculated differently (Based on the loadings of the observed values).

Also, I understand that when the correlations matrices are found from composite values instead of loadings (SEM), they are slightly different. Can someone explain to me why? How do I calculate the correlations of my latent variables based on my loadings of the observed values)?

Hint: when I ran the analysis in different software, the correlations between the observed variables, are the same in SPSS and MPlus, but when it comes to comparing the correlations and covariances of the latent variables (TECH4), the values from MPlus are slightly smaller than the ones obtained through SPSS.

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  • $\begingroup$ You might do better on an Mplus forum. $\endgroup$
    – mdewey
    Jan 22, 2019 at 10:10
  • $\begingroup$ Mplus and SPSS do different things. It's not surprising that the results are different. (Is it?) $\endgroup$ Jan 22, 2019 at 19:43

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The difference here should be a function of composite reliability. Consider the classical test theory definition of reliability, which is the squared correlation among a latent true-score variable and the observed variable being used as a measure (Lord, 1955). Viewed this way, the difference from 1 in the correlation you've observed is due to unreliability, because composite reliability is your observed correlation squared.

Lord, F. M. (1955). Estimating test reliability. Educational and psychological measurement, 15(4), 325-336.

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