Saturated model simplification issue

[Fülöp Attila]

Dear All, 

My question is rather statistically-related, than lavaan-related. However, I don't know how other SEM packages in R would handle this, therefore it could be just a "feature" of lavaan... 

When performing a path analysis, in my very firs path model my Chis-sq value, df value and P value are all "0.000" or "NA" (when evaluating model fit). I suppose my model is saturated and this is the reason.. 

My problem is, that I want to simplify my initial model by deleting non significant paths from it, however I'm not sure if is correct to use the P values of the paths, if the model fit cannot be evaluated. How should I handle this issue?

Thank you in advance!

Attila

ps. See above an example for my problem..

 

summary(fit.path.hole.mlm.br1, fit.measures=TRUE)

lavaan (0.5-16) converged normally after  42 iterations

  Number of observations                            48

  Estimator                                         ML      Robust

  Minimum Function Test Statistic                0.000       0.000

  Degrees of freedom                                 0           0

  P-value (Chi-square)                           0.000       0.000

  Scaling correction factor                                     NA

    for the Satorra-Bentler correction

Model test baseline model:

  Minimum Function Test Statistic               37.975      37.497

  Degrees of freedom                                10          10

  P-value                                        0.000       0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    1.000       1.000

  Tucker-Lewis Index (TLI)                       1.000       1.000

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)               -336.784    -336.784

  Loglikelihood unrestricted model (H1)       -336.784    -336.784

  Number of free parameters                         18          18

  Akaike (AIC)                                 709.568     709.568

  Bayesian (BIC)                               743.250     743.250

  Sample-size adjusted Bayesian (BIC)          686.779     686.779

Root Mean Square Error of Approximation:

  RMSEA                                          0.000       0.000

  90 Percent Confidence Interval          0.000  0.000       0.000  0.000

  P-value RMSEA <= 0.05                          1.000       1.000

Standardized Root Mean Square Residual:

  SRMR                                           0.000       0.000

Parameter estimates:

  Information                                 Expected

  Standard Errors                           Robust.sem

                   Estimate  Std.err  Z-value  P(>|z|)

Regressions:

  holetot ~

    ug.scaled        -0.898    0.525   -1.711    0.087

    logfdb.scaled     1.351    0.387    3.493    0.000

    SMI.scaled       -0.652    0.302   -2.161    0.031

    sex              -1.235    0.671   -1.841    0.066

  ug.scaled ~

    SMI.scaled       -0.168    0.117   -1.431    0.152

    sex               0.845    0.265    3.186    0.001

  logfdb.scaled ~

    SMI.scaled       -0.078    0.144   -0.542    0.588

    ug.scaled         0.331    0.164    2.019    0.043

    sex               0.109    0.273    0.399    0.690

  SMI.scaled ~

    sex               0.067    0.296    0.227    0.820

Intercepts:

    holetot           5.030    1.086    4.633    0.000

    ug.scaled        -1.233    0.391   -3.155    0.002

    logfdb.scaled    -0.159    0.402   -0.395    0.693

    SMI.scaled       -0.098    0.416   -0.236    0.813

Variances:

    holetot           5.380    1.280

    ug.scaled         0.779    0.176

    logfdb.scaled     0.840    0.147

    SMI.scaled        0.978    0.242

[Sunthud Pornprasertmanit]

You might find this note from David Kenny useful:

http://davidakenny.net/cm/respec.htm

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[Fülöp Attila]

Thank you very much for the link! 

The problem is that I have a path analysis with observed variables only.. Does these tips refer to my case as well?

[Terrence Jorgensen]

The problem is that I have a path analysis with observed variables only.. Does these tips refer to my case as well?

Yes, the principles in the link apply to your model.  You don't have latent variables, so ignore the notes about factor loadings, but you do have several regression parameters, so pay attention to the notes about the "structural" model parameters.

Terry

[Fülöp Attila]

Okay! Thank you very much for your help! 

Best wishes,

Attila