I'm doing education research and looking at the effect of a particular study tool. My treatment was applied at the single item response level (rather than to entire participants or to entire tests). So, for each test item completed by a single participant, I have a treatment variable of low, medium, or high (0, 1, or 2) and I have an outcome variable of wrong, partially correct, or correct (0, 1, or 2).

My study was done with a group of students who took a series of tests over the course of an academic term. As a result of the study design, each response is horizontally nested within a single participant, who is in turn nested within a section. And each response is also vertically nested within a single item, which is in turn nested within a test. But I'm not interested in these particular groups of students or test items and I want to generalize my findings to other students and tests. So I have a classic case of crossed random effects.

Here's an example of my data:
Code:
* Example generated by -dataex-. To install: ssc install dataex
clear
input byte Participant float Section int Item byte(Test Treatment Outcome)
 1 1  88  5 0 2
13 2 280 14 0 0
16 2 375 19 2 2
20 2 270 14 0 2
11 2 373 19 0 2
 1 1  20  1 0 0
 6 1 188 10 2 2
 5 1 190 10 0 0
 3 1 109  6 0 1
13 2 251 13 0 2
 8 1 155  8 2 2
20 2 216 11 0 2
10 1  68  4 0 2
 9 1   8  1 0 1
 1 1  46  3 0 2
 8 1  92  5 0 2
17 2 379 19 0 0
19 2 353 18 2 2
11 2 381 20 2 2
14 2 313 16 1 2
 2 1  78  4 0 2
 6 1 132  7 0 0
 3 1   9  1 0 2
 9 1  50  3 0 0
end
I've started trying to analyze my data using the meologit command with the following syntax:
Code:
meologit Outcome Treatment || _all: R.Participant || Item:
But I've also seen the 2017 paper by McNeish et al. about "the unnecessary ubiquity of hierarchical linear modeling." McNeish makes a strong case that when the random effects are just "nuisance effects" that we seek to control, rather than to explicitly model, it would be better to use Generalized Estimating Equations (GEE). I'm curious if there's a way to use GEE in my analysis, but I haven't been able to find any examples of it used with ordinal response data.

Questions:
  1. For the initial approach of GLM, is this the correct code for running my analysis in meologit?
  2. If I'm only interested in seeing the effect of the treatment and controlling for other random effects, is there any reason to address the higher-level nesting structures of my data (participant within section and item within test)?
  3. If I decide to follow McNeish's advice and use GEE instead of GLM, how would I first transform my ordinal data? Can anyone point me to a study that uses GEE with categorical outcomes?
Thanks for any help you can give me!