WLSMV without specifying indicators as ordered

[ahmad]

Hi,

I have a couple of latent factors with indicators that are parcelled (rather than individual items). Typically, parcelled indicators are treated as approximately continuous and normally distributed, and thus the MLR estimator is commonly used. However, upon examining the distributions of my indicators, I found them to be severely non-normal. This raises the question of whether I can instead use WLSMV, but without specifying the indicators as ordered (ordered = c("indicator1", "indicator2") in lavaan. The issue is that when I specify the indicators as ordered, I encounter errors related to empty frequencies for some categories in the measurement invariance analysis. Therefore, my question is: Is it correct to use WLSMV without specifying the indicators as ordered? If so, would this be more appropriate than using MLR in my case?
Another reason I am considering WLSMV is consistency since my mediation model includes a mixture of ordinal and continuous indicators, WLSMV would seem to provide a more coherent estimation strategy across the models.

Thank you for your help in advance,

A

[Shu Fai Cheung (張樹輝)]

Maybe the following discussion is relevant to your main question:

https://groups.google.com/g/lavaan/c/qfCEL5EJlqk/m/ZTye_CntAQAJ

- Shu Fai

[ahmad]

Thank you for your response. It was helpful. What I understand is that although we can use  WLSMV without specifying the indicators in the ordered function, for parcelled indicators that are severely non-normal, MLR is still the better choice than WLSMV without specifying ordered. I would like to have your opinion on this.

Thanks,

A

[Shu Fai Cheung (張樹輝)]

Strictly speaking, "WLSMV" is not an estimator in lavaan, but a shorthand for a set of options. See this thread for the details (you can also find the "real" differences between the shorthands WLSMV and MLR there):

https://groups.google.com/g/lavaan/c/6oLwoboi-vQ/m/IQLAXChPAwAJ

It is hard to determine precisely how effective MLR will be in your specific situation. There are many different ways for a distribution to be nonnormal, and MLR may not perform well when the sample size is not large enough. What is "large enough" also depends on the distribution. Nevertheless, if you have no intention to treat any of the variables as ordinal, then MLR is a better choice than WLSMV. As Terrence explained, WLSMV is not intended to be used for a model with all variables treated as continuous, though it "can" be used this way (https://groups.google.com/g/lavaan/c/qfCEL5EJlqk/m/AvpiElx4BAAJ), and so a warning has been added (https://github.com/yrosseel/lavaan/issues/303).

-- Shu Fai