# Summary of SEM Model Fit Statistics

I can never keep track of the various model fit statistics. Thankfully, the Handbook of Structural Equation Modeling includes a chapter by West et al1 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 of 0/1, but is usually truncated. CLI will always in between 0 and 1 (inclusive).
• Only useful in large sample sizes or large degrees of freedom (DF).
• Minimum DF is 2.
• Muthén discusses it in this paper about TLI.

1. 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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