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Mulitlevel model with ordinal data

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Picture of user. pehkawn Joined: 05/24/2020
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Mixed Effects and Nested Models
I've been trying to build a three-level analysis of student survey data on the relationships between teaching practices and cultural background (SES as covariate) on science achievement.

The response items in the dataset is inherently categorical and ordinal (Likert-scale items) in nature. After having run variables of each level to see how they will run independently, I just tried to combine the levels only to get the following error:

Error in runHelper(model, frontendStart, intervals, silent, suppressWarnings, :
MxExpectationRAM: Ordinal indicators are not supported in multilevel models

It hadn't occurred to me that this could be a problem, and it puts me in somewhat of a predicament about how to proceed. Searching through some old forum threads, I did find a [thread that discusses this topic](https://openmx.ssri.psu.edu/node/4536), with a [comment suggestion using `mxFitFunctionAlgebra()` and `mxEvaluateOnGrid()`](https://openmx.ssri.psu.edu/comment/8418#comment-8418). However, I would not know how to proceed with that.

Has there any more developments on this issue? If there's no direct solution, I would need to consider workarounds or alternative strategies. The simplest alternative for the ordinal level 2 and 3 variables would be to model them as continuous. However, this does not seem like a good idea for variables which do not have any semblance of a normal distribution.
***Any suggestions how to proceed, or any code examples or similar that addresses this issue, would be appreciated.***

Replied on Mon, 06/06/2022 - 01:13
Picture of user. mhunter Joined: 07/31/2009

As the error message states, ordinal indicators are not supported in multilevel models. That is accurate. There are a number of workarounds and approximations that you could try, but there is no direct solution. Moreover, I do not know of any software that allows a likelihood-based, three-level multilevel SEM with ordinal observed variables at every level. There might be a WLS solution, but even the ones I know about for that are only two-level, and WLS does a lot of approximation.
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Replied on Mon, 06/06/2022 - 12:59
Picture of user. pehkawn Joined: 05/24/2020

Thank you for prompt reply. With regards to the model, I am already using WLS estimation, as the number of variables already exceeds the possibility of using ML. If you could provide links to any sources, tutorials or examples of any WLS solutions, even if they are only two-level, it would be appreciated.

Another solution would be to be to model level two and three variables as continuous. However, I am uncertain how this might affect model fit and estimation. What would the major drawbacks and pitfalls to such an approach be?

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Replied on Mon, 06/06/2022 - 08:40
Picture of user. AdminRobK Joined: 01/24/2014

Like mhunter, I am not aware of any satisfactory general method of modeling multivariate multilevel ordinal data via maximum-likelihood. Your best bet is probably Markov-Chain Monte-Carlo Bayesian methods.
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Replied on Mon, 06/06/2022 - 13:33
Picture of user. pehkawn Joined: 05/24/2020

I've heard Bayesian can be used for this purpose. I haven't really gotten into Bayesian statistics at this point. Which software would be the best bet for applying MCMC Bayesian methods on multivariate multilevel ordinal data?

I guess I didn't specify in the OP, but I am already down to using WLS estimation if that changes the outlook somewhat.

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