Understanding USRMR and SRMR output under DWLS

[Aaron Bradetich]

Hello all - I am extremely grateful for the content this group has provided over the last couple years. Thank you!

Curious about the differences in how SRMR and USRMR are calculated under DWLS.

Example output:
                           cor thresholds   total
srmr                     0.046       0.00   0.037
srmr.se                  0.003         NA   0.002
srmr.exactfit.z          7.506         NA   7.506
srmr.exactfit.pvalue     0.000         NA   0.000
usrmr                    0.040       0.00   0.032
usrmr.se                 0.006         NA   0.002
usrmr.ci.lower           0.030         NA   0.029
usrmr.ci.upper           0.049         NA   0.034
usrmr.closefit.h0.value  0.050       0.05   0.050
usrmr.closefit.z        -1.794         NA -12.057
usrmr.closefit.pvalue    0.964         NA   1.000

Using ML, output is:
cov
srmr                     0.046
srmr.se                  0.002
srmr.exactfit.z         13.576
srmr.exactfit.pvalue     0.000
usrmr                    0.043
usrmr.se                 0.004
usrmr.ci.lower           0.036
usrmr.ci.upper           0.050
usrmr.closefit.h0.value  0.050
usrmr.closefit.z        -1.637
usrmr.closefit.pvalue    0.949

Why does Lavaan report correlations, thresholds, and totals under DWLS but only covariance under ML?

Any help understanding would be greatly appreciated -- thank you!

[Yves Rosseel]

> Why does Lavaan report correlations, thresholds, and totals under DWLS
> but only covariance under ML?

It looks likes the DWLS run was treating the variables as categorical.
Then you get (tetrachoric/polychoric) correlations and thresholds.

In the ML run, you treated (implicitly?) the variables as continuous.
And therefore, there is only a covariance matrix. If you add
meanstructure = TRUE, there will also be a mean component.

Yves.