Correlation coefficient in SPSS is lower when constructs are treated as sum of separate items when compared with Mplus output when they are latent?

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Marina Goroshit Popular answer

Hello, Witold.

The reason for this phenomenon is that when you use composite scores, you don't take into account measurement errors. A major motivation for doing Structural Equation Modelling is to estimate parameters (e.g., correlations and regression coefficients) after adjusting for reliability of measurement (and measurement errors). This is called "correction for attenuation". I attach a wikipedia explanation for that and some explanation from SAGE.

Regards,

Marina

https://en.wikipedia.org/wiki/Correction_for_attenuation

https://srmo.sagepub.com/view/encyclopedia-of-survey-research-methods/n24.xml

Daniel Wright

The latent variable method will weight them differently when there are added together. There are lots of different methods that you can use that will give rise to different correlations. If you want to maximize the correlation find the first canonical correlate.

Marina Goroshit

Patrick S Malone

Coming back to Daniel's point, for most common estimation methods, the latent variable will use loadings that optimize reproducing the original variance/covariance matrix. The sum-score is equivalent to assuming equal loadings (and equal residual variances) for the items. It is not surprising that the results differ.