Zero degrees of freedom in Outputs from mediation.

[Cedric Ginestet (KCL)]

Dear all,

I have fitted a mediation model in Lavaan, but I have difficulties in interpreting the ouputs.

What do the following indicate? I don't understand how my degrees of freedom can be zero in this case. And how can the test (objective) function attain a minimum of zero?

  Minimum Function Test Statistic                0.000
  Degrees of freedom                                 0

Thank you very much for your help,

Below is my full output:

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lavaan (0.5-23.1097) converged normally after  61 iterations

  Number of observations                           280

  Number of missing patterns                         9

  Estimator                                         ML
  Minimum Function Test Statistic                0.000
  Degrees of freedom                                 0

Parameter Estimates:

  Information                                 Observed
  Standard Errors                             Standard

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)
  Y ~                                                
    X          (c)    1.694    0.951    1.782    0.075
    M          (b)   -0.361    0.268   -1.343    0.179
    C1                0.459    0.055    8.363    0.000
    C2                0.308    0.249    1.236    0.217
    C3                0.027    0.040    0.669    0.503
    C4               -0.874    1.028   -0.851    0.395
  M ~                                                
    X          (a)    0.524    0.227    2.312    0.021
    C1                0.001    0.013    0.109    0.913
    C2                0.608    0.046   13.149    0.000
    C3               -0.007    0.010   -0.725    0.468
    C4               -0.128    0.253   -0.505    0.613

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)
   .Y                 2.932    3.120    0.940    0.347
   .M                 3.136    0.725    4.325    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .Y                52.382    4.791   10.934    0.000
   .M                 3.232    0.289   11.202    0.000

Defined Parameters:
                   Estimate  Std.Err  z-value  P(>|z|)
    Direct            1.694    0.951    1.782    0.075
    Indirect         -0.189    0.164   -1.153    0.249
    Total             1.505    0.940    1.601    0.109

--
Cedric Ginestet, PhD
Department of Biostatistics and Health Informatics (S2.06)
Institute of Psychiatry, Psychology and Neuroscience
King's College London, PO20, 16 De Crespigny Park,
London SE5 8AF, UK

[Terrence Jorgensen]

I don't understand how my degrees of freedom can be zero in this case.

Because every pair of variables is directly connected, so there are no relationships posited to be completely explained as a function of other relationships.  df are not a function of sample size in SEM.  SEM developed as covariance-structure analysis, so its df are a function of the number of observed (co)variances that are treated as input data.

And how can the test (objective) function attain a minimum of zero? 

Because with zero df, your model fits perfectly (zero discrepancy between the observed and model-implied covariance matrix).  Any introductory SEM text should explain this, if you want more details.

Terrence D. Jorgensen

Postdoctoral Researcher, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

UvA web page: http://www.uva.nl/profile/t.d.jorgensen

[Cedric Ginestet (KCL)]

Thanks a lot Terrence for your prompt reply,

It makes a lot of sense. I guess that what was confusing is that this mediation model is, in fact, correctly specified; even though the nulll values of these quantities seem to indicate otherwise. (I had followed the example from the Lavaan website, and the same issues are visible there: http://lavaan.ugent.be/tutorial/mediation.html)

So, the routine chi-square test performed by Lavaan doesn't apply to the case of a mediation model. It would be perhaps helpful for future users to add a few words to that effect for the mediation example on the webpage cited above.

[Terrence Jorgensen]

So, the routine chi-square test performed by Lavaan doesn't apply to the case of a mediation model.

No, it doesn't apply to saturated models. It applies to models that have degrees of freedom.  Since you only have observed variables, you could get degrees of freedom in a model of full (rather than partial) mediation.