Summary of SEM Model Fit Statistics
I can never keep track of the various model fit statistics. Thankfully, the
book
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 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.
Home 
Back to blog