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Jun 29, 2018, 10:56:25 AM6/29/18

to lavaan

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

Degrees of freedom 0

Thank you very much for your help,

Below is my full output:

--------------------------------------------------------------------------------------------------------

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

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

Jun 29, 2018, 11:43:29 AM6/29/18

to lavaan

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

Jun 30, 2018, 5:16:29 AM6/30/18

to lavaan

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.

Jun 30, 2018, 5:59:54 AM6/30/18

to lavaan

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.

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