CFA: chi-square value is 0 but with degrees of freedom

[axenox]

I want to do a SEM analysis with an actor-partner interdependence model in Mplus. I managed to calculate it and everything seems right if I look at the means, SD's, effects, etc. But I have a problem with the model fit. The fit indices are weird, and too good... So there must be something wrong with it. I read that if one has a chi-square value of 0 as well as 0 degrees of freedom, the model is saturated and therefore a model fit test isn't done. But even though my chi-square value is 0, my df is 12. Also all other model fit indices are perfect. This can't be right.. Does anyone know what the problem might be, or what this tells me? Because to be quiet frank, I have no plan. And I can't seem to find any information on it...

Please, please, please help me!

Best, Annie


This is the output:

MODEL FIT INFORMATION

Number of Free Parameters 15

Loglikelihood

H0 Value -927.087
H1 Value -927.087

Information Criteria

Akaike (AIC) 1884.173
Bayesian (BIC) 1928.082
Sample-Size Adjusted BIC 1880.627
(n* = (n + 2) / 24)

Chi-Square Test of Model Fit

Value 0.000
Degrees of Freedom 12
P-Value 1.0000

RMSEA (Root Mean Square Error Of Approximation)

Estimate 0.000
90 Percent C.I. 0.000 0.000
Probability RMSEA <= .05 1.000

CFI/TLI

CFI 1.000
TLI 1.000

Chi-Square Test of Model Fit for the Baseline Model

Value 90.763
Degrees of Freedom 14
P-Value 0.0000

SRMR (Standardized Root Mean Square Residual)

Value 0.000

 

[axenox]

There are 15 parameters as I am estimating an APIMeM, with two people in one model. The variables are 2x interpersonal mindfulness as independent variable (1x actor, 1x partner), 2x coworker exchange as mediators (actor, partner) and 2x work engagement (actor, partner). The APIMeM includes dyadic covariances between independent variables, error terms of the mediators and between the dependent variables. It also specifies the following effects of the dyad to be equal: actor effects, partner effects, predictor means, predictor variances, outcome intercepts, and residual variances...