# Interpretation of FIT indices for cfa

I am running a confirmatory factor analysis on a very simple model. It is intended to confirm the structure of a brief rating scale for the evaluation of one social emotional domain. As usual, I split the sample (N = 307) in two parts (i.e., calibration and validation samples) and tested the same model (one-factor solution) on the two sub-samples separately and then re-tested it on the full sample. The fit indices looked very good for the calibration sample, but then when I re-ran the same analysis on the validation sample I obtained these (weird?) values. In particular, chi-square is highly nonsign., CFI is equal to 1, TLI greater than 1 (which I know it is mathematically possible but it never happened to me nor I have ever seen it in other publications), and the RMSEA is equal to zero. I also obtained similar values when I tested the model on the full sample. Am I missing anything? Or I can go ahead and write up the results of the manuscript? Are there other parts of the model I can check to make sure I am not running into some issues?

Thanks to anyone who will take the time to help!

lavaan 0.6-8 ended normally after 32 iterations

Estimator                                         ML
Optimization method                           NLMINB
Number of model parameters                         8

Number of observations                           152

Model Test User Model:
Standard      Robust
Test Statistic                                  0.413       0.238
Degrees of freedom                                  2           2
P-value (Chi-square)                            0.813       0.888
Scaling correction factor                                   1.739
Yuan-Bentler correction (Mplus variant)

Model Test Baseline Model:

Test statistic                               229.862     106.486
Degrees of freedom                                 6           6
P-value                                        0.000       0.000
Scaling correction factor                                  2.159

User Model versus Baseline Model:

Comparative Fit Index (CFI)                    1.000       1.000
Tucker-Lewis Index (TLI)                       1.021       1.053

Robust Comparative Fit Index (CFI)                         1.000
Robust Tucker-Lewis Index (TLI)                            1.042

Loglikelihood and Information Criteria:

Loglikelihood user model (H0)               -940.922    -940.922
Scaling correction factor                                  2.458
for the MLR correction
Loglikelihood unrestricted model (H1)       -940.716    -940.716
Scaling correction factor                                  2.314
for the MLR correction

Akaike (AIC)                                1897.845    1897.845
Bayesian (BIC)                              1922.036    1922.036
Sample-size adjusted Bayesian (BIC)         1896.716    1896.716

Root Mean Square Error of Approximation:

RMSEA                                          0.000       0.000
90 Percent confidence interval - lower         0.000       0.000
90 Percent confidence interval - upper         0.098       0.000
P-value RMSEA <= 0.05                          0.867       0.981

Robust RMSEA                                               0.000
90 Percent confidence interval - lower                     0.000
90 Percent confidence interval - upper                     0.000

Standardized Root Mean Square Residual:

SRMR                                           0.010       0.010

Parameter Estimates:

Standard errors                             Sandwich
Observed information based on                Hessian

Latent Variables:
Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
F1 =~
Item33              1.000                               0.599    0.450
Item35              2.275    0.622    3.658    0.000    1.362    0.943
Item36              1.841    0.481    3.829    0.000    1.102    0.675
Item37              1.473    0.346    4.261    0.000    0.882    0.778

Variances:
Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
.Item33              1.414    0.240    5.886    0.000    1.414    0.798
.Item35              0.231    0.204    1.131    0.258    0.231    0.111
.Item36              1.453    0.250    5.802    0.000    1.453    0.545
.Item37              0.506    0.138    3.665    0.000    0.506    0.394
F1                  0.358    0.204    1.758    0.079    1.000    1.000