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.

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