Low TLI but acceptable CFI, RMSEA and SRMR using lavaan.mi

[Emma Y]

Hello, 

A disclaimer that I am not experienced with lavaan, so I apologise if anything I've said below is incorrect or is poorly explained. 

I'm trying to run a 1-lag cross-lagged panel model using lavaan.mi. Traceplots for imputation convergence looked good and all my code is running without error, but fit indices are lower vs. a complete case analysis. Using MI, the sample size is increased from 841 to 1407. The Robust CFI drops from 0.994 to 0.942 which (from my understanding) isn't great but is still OK, but the Robust TLI decreases from  0.971 to 0.563. RMSEA and SRMR are both still below 0.08. 

I'm a bit confused as to what the low TLI means for overall model fit in this case and why it decreases to the degree that it has, while CFI, RMSEA and SRMR seem to be relatively similar to the complete case analysis. Could anybody please help me to understand what's happening here? Output at the end of the post.

Thanks very much,

Emma

Output as follows:

Convergence information:
The model converged on 50 imputed data sets.
Standard errors were available for all imputations.

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        34

  Number of observations                          1407
  Number of clusters [cluster]                      709

Model Test User Model:

                                                                         Standard      Scaled
  Test statistic                                       9.530       7.925
  Degrees of freedom                              4           4
  P-value                                                   0.049       0.094
  Average scaling correction factor                                1.203
  Pooling method                                          D4            
    Pooled statistic                              “standard”            
    “yuan.bentler.mplus” correction applied            AFTER     pooling

Model Test Baseline Model:

  Test statistic                               123.300      87.377
  Degrees of freedom                                30          30
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.411

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.941       0.932
  Tucker-Lewis Index (TLI)                         0.555       0.487
                                                                 
  Robust Comparative Fit Index (CFI)                       0.942
  Robust Tucker-Lewis Index (TLI)                            0.563

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -8211.783   -8211.783
  Scaling correction factor                                  1.591
      for the MLR correction                                      
  Loglikelihood unrestricted model (H1)      -8200.555   -8200.555
  Scaling correction factor                                  1.540
      for the MLR correction                                      
                                                                 
  Akaike (AIC)                               16491.567   16491.567
  Bayesian (BIC)                             16670.040   16670.040
  Sample-size adjusted Bayesian (SABIC)      16562.035   16562.035

Root Mean Square Error of Approximation:

  RMSEA                                          0.031       0.029
  90 Percent confidence interval - lower         0.002       0.000
  90 Percent confidence interval - upper         0.058       0.054
  P-value H_0: RMSEA <= 0.050                    0.867       0.912
  P-value H_0: RMSEA >= 0.080                    0.001       0.000
                                                                 
  Robust RMSEA                                               0.029
  90 Percent confidence interval - lower                     0.000
  90 Percent confidence interval - upper                     0.059
  P-value H_0: Robust RMSEA <= 0.050                         0.864
  P-value H_0: Robust RMSEA >= 0.080                         0.001

Standardized Root Mean Square Residual:

  SRMR                                           0.046       0.046

Parameter Estimates:

  Standard errors                              Robust.cluster
  Information                                        Observed
  Observed information based on                       Hessian
                                                             
  Pooled across imputations              Rubin's (1987) rules
  Augment within-imputation variance     Scale by average RIV
  Wald test for pooled parameters          t(df) distribution

[Terrence Jorgensen]

Have you inspected the formulas for CFI and TLI? Don’t worry about robust or scaled, that doesn’t have anything to do with why the CFI and TLI differ so much in this case. If you work out the math for each, you will notice that differences are much larger than ratios for these user and baseline models.