Second Order Model

[car...@ucn.cl]

Hi Lavaan users group,

I am new in lavaan and I am trying to run a second order model. The model contains three variables: SS, EC, and AI. I run the model and I obtained the following results, which are not good enough. Is there any alternative form of calculating a second order model? or Is there any way to justify a second order model with these results?. I really appreciate the help in advance:

SOCIAL1 <- ' 

SS =~ SS1 + SS2 + SS3 +SS4 + SS5 

AI=~ AI1 + AI2 + AI4 + AI5 + AI3

EC =~ EC1 + EC2 + EC3

SOC =~ SS + AI + EC'

  Optimization method                           NLMINB

  Number of free parameters                         29

                                                              Used       Total

  Number of observations                       385         431

  Estimator                                             ML

  Model Fit Test Statistic                        227.336

  Degrees of freedom                                62

  P-value (Chi-square)                           0.000

Model test baseline model:

  Minimum Function Test Statistic     2551.735

  Degrees of freedom                        78

  P-value                                            0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    0.933

  Tucker-Lewis Index (TLI)                         0.916

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)                  -6053.464

  Loglikelihood unrestricted model (H1)      -5939.796

  Number of free parameters                         29

  Akaike (AIC)                                                12164.928

  Bayesian (BIC)                                            12279.572

  Sample-size adjusted Bayesian (BIC)        12187.558

Root Mean Square Error of Approximation:

  RMSEA                                                       0.083

  90 Percent Confidence Interval                  0.072  0.095

  P-value RMSEA <= 0.05                            0.000

Standardized Root Mean Square Residual:

  SRMR                                                         0.055

Parameter Estimates:

  Information                                            Expected

  Information saturated (h1) model          Structured

  Standard Errors                                     Standard

Best Regards,

Carolina

[Terrence Jorgensen]

I obtained the following results, which are not good enough.

That's a bit vague, are you only talking about fit?  You can reject the H0 of exact fit, but the fit indices are not so bad.  RMSEA's CI rejects H0 of close fit (< .05), but also rejects poor fit (> .10).

Is there any alternative form of calculating a second order model? or Is there any way to justify a second order model with these results?.

These don't sound like lavaan questions, just general SEM questions.  I would recommend asking on SEMNET, but debates about fit and model modification get quite heated without always being useful.  I can't really offer any concrete help, but a couple thoughts:

• You only have 3 factors, so a higher-order factor would be just-identified.  Thus, a higher-order model is statistically equivalent to this CFA, and will not provide any new information. So, not to be discouraging, but from a practical standpoint, perhaps the point is moot.
• If you are interested in exploring why you model fails to fit perfectly (perhaps discovering how fit could be improved), I would recommend you look at the correlation residuals (i.e., differences between the observed and model-implied correlations) to see which specific bivariate relationships are not well accounted for by your model.

resid(fit, type = "cor")

Here is an article I recommend reading before putting too much faith in any model.  We can't ever expect models to be anything more than simplifications of reality.  The question of whether it is "good enough" can only be addressed by defining "good enough to do what?" (e.g., are you using the scale to diagnose or classify, or are you using these factors to explain other factors?).

MacCallum, R. C. (2003). 2001 presidential address: Working with imperfect models. Multivariate behavioral research, 38(1), 113-139.

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

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

http://www.uva.nl/profile/t.d.jorgensen

[Carolina Rojas Cordova]

Dear Terrence, 

Thank you so much for your time and your answer!!!!, I was just trying to probe that my independent variable can be measured by the combination of these three variables as a second order model. Thats why I developed the CFA. 

Thank you so much for your recommendation, I am going to read what you recommend me. 

Best Regards

Carolina

En 2 de noviembre de 2018 en 8:44:33 a. m., Terrence Jorgensen (tjorge...@gmail.com) escrito:

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