Help understanding model fit measures

[Natalie Wells]

Hi all,

I'm very new to SEM and lavaan, so apologies if this is a basic question, worded poorly  or I'm completely on the wrong track.

I'm fitting a structural equation model in lavaan using WLSMV because my behavioural outcome is binary. My sample is also not normally distributed. Sample size is 313.

The model ran successfully and produced the following fit indices:

CFI = .899 TLI = .911 RMSEA = .072 SRMR = .063

However, the scaled fit indices are much lower:

Scaled CFI = .342 Scaled TLI = .421

The output also shows a large difference between the standard and scaled baseline model chi-square statistics. I have read that although this does not support a good model fit, it should be interpreted along with other fit indices.

Model Test User Model:

                                              Standard      Scaled

  Test Statistic                               458.730     521.100

  Degrees of freedom                               174         174

  P-value (Unknown)                                 NA       0.000

  Scaling correction factor                                  1.143

  Shift parameter                                          119.804

    simple second-order correction                               

 

Model Test Baseline Model:

 

  Test statistic                              2965.033     680.456

  Degrees of freedom                               153         153

  P-value                                           NA       0.000

  Scaling correction factor                                  5.331

My confusion is that the RMSEA and SRMR appear to suggest at least acceptable fit, yet the scaled CFI/TLI imply extremely poor fit. I believe as my data is not normally distributed I should be paying attention to the scaled outputs. There is no robust CFI, TLI or RMSEA available.

Could someone help me understand:

1. Why can scaled CFI/TLI differ so dramatically from the standard values under WLSMV?
2. When the scaled and standard incremental fit indices tell such different stories, how would experienced SEM researchers typically interpret or report the model?

Any explanations or recommended references would be greatly appreciated. I'm still learning SEM and trying to understand what these indices are actually telling me.

Thanks in advance!