Skewed outcome variable, sem model: is it a problem?

My outcome variable is really skewed, and I want to include it in a SEM model (I am using lavaan - R). It is measured with a 7-points Likert scale (agreement) and consists of 5 items.

• If the model is identified, should I proceed anyway but using a robust estimator?

• Should I check for residuals distribution instead? If yes, any suggestion on how to do it within the R environment?

Edit - Clarification: I always worked with normally distributed data, this is the first time that I have to deal with very skewed indicators of an outcome variable within a sem model.

My questions are:

1) is there something I should, in particular, do before running the sem model when I have this very skewed indicators (e.g. check residuals distribution)?

2) if you have this kind of skewed indicators but the fit indices and regressions of your sem model are fine, can you trust your results? (or it could be a false positive for example?).

I think Noah gave me the answer I needed (and thank you again!) but I would like to also have other opinions. I have preliminary data, and I am still collecting data (the problem is that I will present these results next week in a conference and no time to study non-normal distributions in the next few days).

Here the distribution after taking the mean of each item, by subject (in the sem model it will be a latent variable).

Thank you for any help you would be able to provide.

• Are you saying that the latent outcome variable is skewed? How do you know it is if it's latent? You may have a normally distributed outcome variable but skewed indicators because of poor measurement.
– Noah
Aug 19, 2019 at 19:55
• Thank you, Noah. I can't say that the latent variable is skewed, what I know is about the observed indicators. What should I do in your opinion? Thank you again
– Fran
Aug 19, 2019 at 22:30

I would treat the indicators as ordinal. Traditional factor analysis only works with continuous indicators, and Lickert scales are not continuous. You can treat them as such when they are approximately normally distributed, but in this case, that's clearly not true. Use the ordered() function in R to turn the variables into ordered factors, and then run the SEM.

• Lavaan automatically switched to a DWLS estimator after fitting the model ordering the outcome var as you suggest: fit<- sem(mod, data=df, ordered=c("outcome_1", "outcome_2", "outcome_3", "outcome_4", "outcome_5")) If this is correct and if fit indexes and regressions are ok, should I don't care anymore about the skewed indicators (considering that I have strong theoretical reasons that support the skewness)? So, can I basically "trust" this result? Thank you again Noah!
– Fran
Aug 20, 2019 at 22:16
• I would say you can trust this result. It makes few assumptions and is valid for the analysis you're doing. DWLS is a robust estimator that is one way to fit ordinal indicator models and tends to be the most used in this context. The indicators are no longer "skewed"; they're ordinal categories, so you aren't making any specific distribution assumptions about the values (i.e., 1-7) of the scores. You should definitely read about this analysis before you commit to it though.
– Noah
Aug 20, 2019 at 22:22
• Thank you so much Noah! One last thing. Should all the variables in the model be ordered as well? Predictors are measured with the same Likert - scale. (I will carefully study this kind of analysis, I have a conference next week and I am trying to figure out if and how I can present these preliminary data).
– Fran
Aug 21, 2019 at 9:54
• It does make sense to treat all indicators as ordinal, but you don't have to do it if some of them are well behaved (reasonably bell-shaped, symmetrical distributions). If the model becomes hard to fit because you have too many categories and too many items and not enough participants, you can collapse some of the smaller categories into fewer.
– Noah
Aug 21, 2019 at 15:37