# Summary of SEM Model Fit Statistics

I can never keep track of the various model fit statistics. Thankfully, the book Handbook of Structural Equation Modeling1 includes a chapter by West et al2 including this handy chart:

A few other notes I’ve collected:

χ2:

• For over ~400 obs, χ2 is less useful because it almost always rejects. (Citation is the Muthén article linked below under SRMR.)
• We want it to fail to reject, so that saturated model is NOT better.
• A lot of people recommend ignoring this.

SRMR:

• Measure of “approximate fit”, as opposed to χ2 which is “exact fit” (and unrealistic in large data situations).
• Muthén (author of Mplus) suggests the following steps:
1. If χ2 fails to reject, we have a good “exact fit” and there’s no need to use SRMR to examine approximate fit.
2. If χ2 rejects, and SRMR is < .08, and there’s no large residuals, model is approximately fit. (With larger samples, n > 200)
3. χ2 rejects, SRMR > .08, poorly fitting model

TLI/CLI:

• Functions of χ2/df ratio
• TLI can be outside 0/1, but usually truncated. CLI always in [0,1].
• Only useful in large sample sizes or large DF
• Minimum DF is 2
• Muthén discusses it here.

1. Hoyle, Rick H., ed. Handbook of structural equation modeling. Guilford press, 2012.↩︎

2. West, Stephen G., Aaron B. Taylor, and Wei Wu. “Model fit and model selection in structural equation modeling.” Handbook of structural equation modeling (2012): 209-231.↩︎

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