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Mplus Discussion > Structural Equation Modeling >
 Abby Gray posted on Friday, January 24, 2014 - 10:28 am
Hello. Could someone please explain to me in plain English what a factor score in MPlus actually represents? I understand how to produce them, and a bit about how MPlus computes them, but I am struggling with the language for their interpretation.
Thanks very much.
 Linda K. Muthen posted on Friday, January 24, 2014 - 10:40 am
It is the most likely value of a factor for a person given the person's observed values on the factor indicators and the estimated model.
 Abby Gray posted on Friday, January 24, 2014 - 10:45 am
Thank you. That's very clear.
 Christoph Schaefer posted on Thursday, April 26, 2018 - 8:48 am
Dear Professors,

Is the estimation of a latent variable or the factor scores (within an SEM) based on the assumption that the factor scores are normally distributed? Does this mean that it is not informative to test whether factor scores are normally distributed (unless mixed modelling is used)?
 Bengt O. Muthen posted on Thursday, April 26, 2018 - 4:43 pm
Q1: The true factor scores are assumed to be normally distributed (that is part of the model specifications). The estimated factor scores may not be.

Q2: Right.
 Christoph Schaefer posted on Thursday, April 26, 2018 - 5:04 pm
My apologies, but that answer makes me wonder: Did I understand you correctly that you are confirming: It is NOT useful/informative to test whether estimated factor scores are normally distributed?

In other words: Does a non-normal distribution of factor scores indicate a problem with the model, or can it be ignored since that has no implications for the assumption concerning the true scores?
 Bengt O. Muthen posted on Friday, April 27, 2018 - 9:05 am
Q1: Yes.

Q2: A non-normal distribution for the ESTIMATED factor scores might indicate the need to specify a model which allows non-normality, e.g. by using mixtures.
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