Message/Author 

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. 


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. 


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)? 


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. 


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 nonnormal 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? 


Q1: Yes. Q2: A nonnormal distribution for the ESTIMATED factor scores might indicate the need to specify a model which allows nonnormality, e.g. by using mixtures. 

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