Negative factor loading and Different estimated factor score vs Mplus

[Dai Duong]

1. In my SEM model, a factor loading is negative. This negative sign is theoretical justified and expected. However, an SEM expert warns me that this negative loading is abnormal because factor loadings are usually positive in many published SEM academic articles. Also, this negative loading will make the estimation of factor score incorrect. So, does this negative loading undermine factor score estimation?

2. What method is used to estimate factor score in lavaan? I use both Mplus and lavaan to get factor scores but estimated scores are completely different. I am wondering which one is more reliable and correct, especially how each method treat negative factor loading?

Estimated factor scores by Mplus                                                                             

    stats |     CTRLL      KHOE      KNOW    DECENT

---------+----------------------------------------

    mean |  .0040838 -.0459148  .0002261 -.0053508

     p50 |     -.004      .069     -.041     -.046

      sd |  .2859547   .423202  .4512706  .3871198

variance |  .0817701  .1790999  .2036451  .1498617

     min |     -.599    -4.561    -1.033     -.958

     max |     3.251      .069     1.265     3.709

skewness |  1.619585 -5.125411  -.258883  1.436217

kurtosis |  12.51759  36.48764  2.289026  10.07998

 

Estimated factor scores by lavaan

   stats |     ctrll      khoe      know    decent

---------+----------------------------------------

    mean |  .0087576 -.0336394   .006804 -.0012661

     p50 |   .000234  .0551334 -.0603237 -.1009806

      sd |  .8529798  .5595305  1.347304  1.177778

variance |  .7275745  .3130744  1.815227  1.387161

     min | -2.607173 -6.312629 -3.291503 -2.920526

     max |  7.274452  2.248832  4.471202  9.173009

skewness |  .8928723 -4.762663 -.1173813  1.216637

kurtosis |  6.602086  38.59525  2.377692  7.957119

Thank you very much,

Dai 

[nick judd]

Does it fit? (chi, rmsea & cfi)

I personally would find the spread of loadings troubling, you have a .9 and a .2.

Lavaan has a mimic function if you would like Mplus estimates.

Negative loadings are fine, yet they can flip the sign of the factor. 

best,

nick

[Edward Rigdon]

Common factors are typically indeterminate, whixh means that there is no one best representation of the common factors as a function of the model's observed variables. So there is no one best set of scores. An infinity pof different scores can be equally correct given a particular model and data. Many packages actually report "factor score estimators" which are not really factor scores at all. You can easily generate your own factor scores, but, again, any one set will be only set out of an infinity of possibilities. See, e.g.:

Grice, J. W. (2001). Computing and evaluating factor scores. Psychological methods (Very readble)

Rigdon, E. E., Becker, J. M., & Sarstedt, M. (2019). Factor indeterminacy as metrological uncertainty: Implications for advancing psychological measurement. Multivariate behavioral research.

  

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[Dai Duong]

To nick Judd,
fit is acceptable. CFI .962, TLI .953, RMSEA .051, SRMR .087