Structural Equation Model Standardized Path Coefficients Greater than 1

[#1]

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!

[#2]

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

[#3]

Hi Laura,

Thanks for the answer. I understand your explanation of the calculation of standardized coefficients. But I am still confused why the variances and covariances involving the latent variables cause the problem. Is there any specification error in my model such as I might create some paths between variables that have very low correlations? I attached correlation, covariance, implied-covariance matrix for you to check. Thank you very much.

[#4]

Hi @lujc07 ,

I appreciate you sharing those screenshots but there's still some ambiguity as to the model you're fitting. I don't see the covariances that are specified in the model other than that between Developed and Agriculture (are any edges hidden in the diagram?). From what I see in the screenshots, you seem to be missing covariances between Temperature, Water Quality, and Latent 1 (those would represent covariances among the residuals of those variables). Adding those covariances will change the model-implied covariance structure for the latent variables and their relations to Temperature AND your ultimate outcome (Macroinvertebrate MMI), so that could improve things a bit. I'm also curious about potential problems with the data and/or convergence of the model. Which warnings are you getting in the report? I can see you have a negative variance of MMI which is unsettling. I suggest you try adding those covariances (assuming they aren't specified already) and if you still have issues with a negative variance or convergence problems, please reach out to tech support at support@jmp.com where you can share your data and scripts so we can better assist you.

Best,

~Laura

[#5]

Hi Laura,

I followed your instruction to add these covariances. However, the problem still cannot be solved. So I shared my data to tech support to get help. Thanks.