Structural Equation Model Standardized Path Coefficients Greater than 1

lujc07

Hi! I just built a structural equation model including two latent variables. Each latent variable has three indicators. However, after running the model, there are three standardized path coefficients greater than 1 (water quality > St[Mac... MMI]; latent 1 > St[Mac... MMI]; St[Base...Index] > St[Mac... MMI]). Normally the standardized path coefficients should be less than 1. I did some search and it is maybe because of multicollinearity. However, I checked the correlation matrix and looks like there is no multicollinearity. I don't know why this happens and hope someone could give me the answer. Thanks!

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LauraCS

Hi @lujc07 ,

Indeed, as you noted, there are times when standardized estimates are greater than 1 and, given the images you shared, it's due to the variances and covariances involving the latent variables, which are omitted in the correlation matrix you provided. You can get a sense of the associations between latent variables and your MMI outcome by looking at the Model-Implied Covariances (under the red triangle menu of the fitted model). The standardized estimate for a regression is obtained by multiplying the unstandardized coefficient by the ratio of model-implied standard deviations of the from/to variables. For example, in your model, the standardized estimate for Latent 1 --> MMI (let's call it Beta) can be computed as:

Beta = unstandardized estimate * sqrt(model-implied variance of Latent 1) / sqrt(model-implied variance of Macroinvertebrate MMI)

I hope this helps answer your question!

~Laura