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 al
including this handy chart:
A few other notes I’ve collected:
χ^{2}

For over ~400 obs, χ^{2} 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 χ^{2} which is "exact
fit" (and unrealistic in large data situations).

Muthén (author of Mplus)
suggests the
following steps:

If χ^{2} fails to reject, we have a good "exact fit" and
there’s no need to use SRMR to examine approximate fit.

If χ^{2} rejects, and SRMR is < .08, and there’s no large
residuals, model is approximately fit. (With larger samples, n > 200)
 χ^{2} rejects, SRMR > .08, poorly fitting model
TLI/CLI

Functions of χ^{2}/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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