Saturated mediation model?

[Maria Eduarda Guimaraes]

Hello all, 

I've been trying to run a mediation model using lavaan. My variables are observables, so I use continuous scores for the model. 

it looks like this: 

model <- '

#a path
M ~ a*X

#b path
Y ~ b*M + cprime*X

#Indirect effect
ind := a*b

#total effect
total := cprime + ind

#direct effect 

dir := Y ~ c*X
'

however, the model fit parameters are so weird. 

example: 

Model Test Baseline Model: Test statistic 84.589 

Degrees of freedom 3 P-value 0.000 

User Model versus Baseline Model: 

Comparative Fit Index (CFI) 1.000 

Tucker-Lewis Index (TLI) 1.000 

Loglikelihood and Information Criteria:

 Loglikelihood user model (H0) -2666.671 

Loglikelihood unrestricted model (H1) -2666.671 

Akaike (AIC) 5343.342

Bayesian (BIC) 5363.448 

Sample-size adjusted Bayesian (SABIC) 5347.581 

Root Mean Square Error of Approximation: RMSEA 0.000

90 Percent confidence interval - lower 0.000 90 

Percent confidence interval - upper 0.000 P-value H_0: 

RMSEA <= 0.050 NA P-value H_0: 

RMSEA >= 0.080 NA

What that could mean? how would I fix it? I tried different estimators, I did use bootstrap, the variables are expressively correlated... 

Thank you very much in advance.

[Edward Rigdon]

There is nothing unusual (that I can see) in these results. Your
mediation model has 3 observed variables. The model is saturated, so
it produces a chi-square of 0 with 0 degrees of freedom. The
"baseline" or "null" model specifies the diagonal elements of the
covariance matrix free and the off-diagonal elements constrained to 0,
so it has 3 degrees of freedom. The fit indices all show no lack of
fit in your ("user") model. What you are seeing is what you should
see, in a situation where the user model is saturated.

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