Measurement Model Checker
A measurement model links each construct, such as perceived value, to the questionnaire items that measure it. Before testing relationships between constructs, check that each construct’s items hang together (convergent validity and reliability) and that different constructs measure different things (discriminant validity). This tool computes the standard checks from the output JASP gives you.
The tool opens on a confirmatory factor analysis of the 3 scales in event-survey-data.csv: Content, Value and Network, 4 items each. The loadings and fit indices come from that CFA, and HTMT is computed from the item correlations in the same file. Paste your own loadings from JASP’s CFA output, and a correlation matrix or a data file, to check your model.
How it works
Here λ is a standardised loading and k the number of items. The thresholds and their sources:
- AVE of 0.50 or more. Fornell, C. and Larcker, D. F. (1981), “Evaluating structural equation models with unobservable variables and measurement error”, Journal of Marketing Research, 18(1), 39 to 50.
- Composite reliability of 0.70 or more, and loadings of 0.70 or more, with 0.50 as the floor. Hair, J. F., Black, W. C., Babin, B. J. and Anderson, R. E. (2019), Multivariate Data Analysis, 8th edition, Cengage.
- HTMT below 0.85, or below 0.90 as the more lenient threshold. Henseler, J., Ringle, C. M. and Sarstedt, M. (2015), “A new criterion for assessing discriminant validity in variance-based structural equation modeling”, Journal of the Academy of Marketing Science, 43(1), 115 to 135.
- CFI and TLI close to 0.95 or above, RMSEA close to 0.06 or below, SRMR close to 0.08 or below. Hu, L. and Bentler, P. M. (1999), “Cutoff criteria for fit indexes in covariance structure analysis”, Structural Equation Modeling, 6(1), 1 to 55.
In the sample, Content has loadings of 0.767, 0.838, 0.828 and 0.762, so AVE = 0.639 and CR = 0.876. The 3 constructs are almost uncorrelated in this file, so every HTMT value sits close to 0. These cutoffs come from simulation studies and published practice, and Hu and Bentler themselves recommend reading 2 indices together.
Frequently Asked Questions
What is average variance extracted?
Average variance extracted (AVE) is the mean of the squared standardised loadings of a construct's items. It is the share of the items' variance that the construct explains. Fornell and Larcker (1981) set 0.50 as the minimum, meaning the construct explains more variance than measurement error does.
How is composite reliability calculated?
Composite reliability is the squared sum of the standardised loadings divided by that same squared sum plus the sum of the error variances, 1 minus each squared loading. Values of 0.70 or more indicate good reliability (Hair et al., 2019).
What is HTMT and what threshold should I use?
The heterotrait-monotrait ratio compares correlations between items of different constructs with correlations between items of the same construct. Henseler, Ringle and Sarstedt (2015) discuss 0.85 as the stricter threshold and 0.90 as the more lenient one.
What are good CFI, TLI, RMSEA and SRMR values?
Hu and Bentler (1999) suggest CFI and TLI close to 0.95 or above, RMSEA close to 0.06 or below and SRMR close to 0.08 or below. Treat these as guidelines and report the values themselves.
Can I paste output from JASP?
Yes. Copy the factor loadings table from JASP's confirmatory factor analysis and paste it in. The tool reads the factor, indicator and standardised estimate columns. Plain lines of construct, item and loading work too.