Asymptotic distribution free method for SEM

[Nicki Nimlos]

Hi everyone,

I am running structural equation models in STATA. I have issues of nonnormality and missing values in my dataset. I was able to estimate a model using Maximum Likelihood of Missing Values, however, this method assumes joint normality. A colleague of mine suggested using weighted least squares, so I attempted to estimate my model using asymptotic distribution free (adf) method. However, my model would not converge. Does anyone know the best way to estimate SEM models with non-normal and missing data? If I use the adf method, how do I handle missing data without deleting those missing values?

Thank you for your help.

[Daniel Schaefer]

Welcome to the forum. According to the forum rules, you need to post here using your real name. You can change your username by contacting the admins using the CONTACT US link at the bottom of the page.

What about Multiple Imputation with Chained Equations (MICE)? MICE allows you to specify that some variables are (e.g.) binary.

[Nicki Nimlos]

Basically, I am trying to figure out the best estimation method for SEM with missing values and non-normal data. What's the best estimation method that doesn't delete missing values all together? I thought I could use Maximum Likelihood with Missing Values, but this estimation method assumes joint normality.

[Daniel Schaefer]

Okay, again, it sounds to me like MICE should fit the bill.

[Nicki Nimlos]

Thank you for your reply. I have never used MICE before, so bear with me. How can I use MICE to replace the missing values before estimating my SEM? I have 4 latent variables that were created using CFA with ordinal variables. I am examining if the latent variables predict a binary dependent variable. My dependent variable is normally distributed and has no missing values. It's the survey items measuring the latent variables that are nonnormal with missing values.

Here is my coding thus far for MICE:

mi set mlong
mi register impute varlist
set seed

What are the next steps in the coding to replace the missing values?

Thank you for your help!

[Leonardo Guizzetti]

I would agree with Daniel that multiple imputation is your best bet here. I don’t think you will get offers on code because the breadth of multiple imputation methods encompasses a large literature and we are not familiar with your data or domain. I would recommend picking up an introductory textbook on missing data method or imputation as a starting point.

[Daniel Schaefer]

Leonardo is quite right. It's difficult to suggest code without knowing quite a bit more about your data. A core problem with MICE is that you need to construct an imputation model, and how you do that will depend on your data, the pattern of missing information, and the variables that are important to you. A text book is a good idea, because there are other imputation techniques that may or may not be more appropriate (you might also consider hot-deck multiple imputation). You might also want to take a look at this paper.

[Nicki Nimlos]

Update: I ended up removing missing values from the analysis and ran maximum likelhood with the Satorra-Bentler estimation to deal with non-normality.