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Augmented Factor Correlation Matrix for Measurement Model in SEM platform

Since JMP emphasizes visualization, the augmented factor correlation matrix with color coding will be a useful piece of information in the SEM platform. The factor correlation matrix is a useful for researchers during scale construction. For multi-item constructs scale builders look for convergent and discriminant validity. This piece of information can be obtained easily since JMP 15 can now compute factor scores for latent variables. This correlation matrix can be augmented as follows:

 

  1. 1. Correlation values on the lower diagonal
  2. 2. Correlation-squared values reflecting shared variance between factors on the upper diagonal
  3. 3. Average Variance Extracted (AVE) which is the variance each factor shares with its own indicators on the diagonals. This can also be thought of as the average communality of the construct.

 

Here is an example:image.png

 

For convergent validity, we want AVE > 0.5 indicating the construct explains > 50% of the variance of its indicators
 
For discriminant validity, we want the diagonal values to be higher than values to the right or above since this establishes that the factor shares more variance with its own indicators than other factors. When such is not the case, color coding the violations will be more useful.

6 Comments
LauraCS
Staff

Thank you for the suggestion Narayanan! I agree this will make a nice addition to the platform!

Jeff_Perkinson
Community Manager
Status changed to: Yes, Stay Tuned!

We are working on this for JMP 16. A menu item for "Assess Measurement Model" will provide other statistics to assess construct and composite reliability of the survey, in addition to construct validity.

Narayanan
Level IV

Good to hear that.   Looking forward to it.

Jeff_Perkinson
Community Manager
Status changed to: Delivered

With the release of JMP 16 the Assess Measurement Model option shows a variety of statistics and graphs for quantifying the reliability and validity of tests and measures, including indicator reliability, coefficients omega and H, and a construct validity matrix. 

2021-03-31_13-47-14.710.png

Narayanan
Level IV

Laura & Jeff:  Thank you for implementing this idea.  It is quite useful for people doing scale construction in the social sciences.  I just noticed something in that option.  The rows under the table in Composite Reliability and Construct Maximal Reliability do not line up with the rows of the histogram next to it.  This could be a font issue in the different displays.  Lining them up will make it much easier to read.

 

 

Narayanan
Level IV

Laura:  Since we now have a reliability measure, can I also request a confidence interval for that reliability measure with two columns of lower and upper in the table (at some default confidence level) and an error bar in the histogram next to it? The confidence interval could be computed using one of several ways including the Monte Carlo method.