How to interpret -oparallel- and -brant- test results

[Irina Chukhray]

Hello,

QUESTION 1 (test output): I am seeking advice on how to interpret potentially contradictory results from -oparallel- and -brant- tests. I'm trying to determine if I should run an -ologit- or -gologit- model.

I am predicting postsecondary enrollment (p2status) based on foreign-born students' school level (schaaa) when they arrived in the US relative to US-born peers, where 1= US-born (reference), 2= elementary age at arrival, 3= middle school age at arrival, 4=high school age at arrival.

BRANT TEST: If I am interpreting correctly (please see attachment with Stata output), the -brant- test indicates that the parallel regression assumption is violated in level 1 of the schaaa variable because it is significant, which means I should use a -gologit- model

OPARALLEL TEST: If I am interpreting correctly, none of the test statistics are significant, suggesting I should use the -ologit- model

Can someone please help me understand if I am misinterpreting my output? How do I determine if I should use the -ologit- or -gologit- model?



QUESTION 2 (error messages): when I run the full -ologit- model with all controls and then the -brant- test, I get an error saying "not all independent variables can be retained in binary logins; brant test cannot be computed" but I am not sure what this means.

Also, when I run the same full -ologit- model and then run the -oparallel- test, I get another error saying, "full model cannot be estimated due to perfect prediction" but I am also not sure what this means.

Any suggestions on what I should do to be able to run the -oparallel- and -brant- tests on my full model?


Thank you,
Irina

P.S. I am not super Stata literate, so if you can be generously detailed in your suggested steps, I would be very grateful

[Maarten Buis]

Question 1) If you want to compare oparallel with brant you need to look at the All row in brant, but that is unnecessary as the Brant test is already included in the output of oparallel. So there is no contradiction between these two commands. It means that overall we cannot, at a 5% level, reject the hypothesis that the parallel lines assumption holds. This does not necessarily mean that the parallel lines assumption holds. After all, there are two ways in which we can fail to find any deviation: 1) there is no deviation, or 2) we did not look hard enough (i.e. are sample size is to small to detect it). We can be almost certain that it is 2); an assumption like the parallel lines assumption is never exactly true, so if we increase the sample size enough we will be able to find some deviation. The real question is whether that deviation is meaningful enough to change our model. Remember that a model is by definition a simplification of reality, and simplification is just another word for "wrong in some useful way". So a significant test result tells use nothing new: it tells us that the model is wrong, which we already knew from the very definition of model. The real question is whether the deviation from the assumption is large enough to make the model no longer useful. That is a subjective decision. You need to look at the parameters and see how they differ when you relax the assumption, and whether your conclusions change. If your conclusions don't change, then no worries.

Question 2) With your data it is impossible to estimate the fully relaxed version of your full model. So you cannot do a Brant, Maximum Likelihood, or wolfegould test in your data, as these require the estimation of (an approximation of) the fully relaxed version. The score test might be possible, but I don't know how reliable it would be.

[Endi Chelidze]

Hello!
I am currently doing statistical analysis where I am examining data with an ordinal outcome variable derived from an Exploratory Factor Analysis (EFA). The outcome variable is structured on a scale from 1 to 10, which combines two factors identified during the EFA process. Given the ordinal nature of the outcome variable, an Ordinal Logistic Regression (OLR) model seems most appropriate for the analysis.

The dataset encompasses 2,797 observations, but it's important to note that there are missing values present, which could potentially influence the robustness of the statistical models employed. In an attempt to accommodate for the ordinal characteristics of the outcome variable while also considering its continuous influence, I conducted an Ordinary Least Squares (OLS) regression analysis, incorporating a comprehensive hierarchical model approach. This model includes 6 main independent variables and 24 control variables, structured across 12 different model specifications.

Upon applying the OLR models, I observed that the results are meaningful and align with the theoretical expectations of the study. However, I have encountered significant challenges in testing the proportional odds assumption using the Brant test. The test executes without issue for the initial two models (where Model 1 includes the outcome and one independent variable, and Model 2 expands to include a second independent variable. Of course my purpose is to check one final Model, but it is not possible, which is why i am manipulating with data). Beyond these, I encounter errors indicating either "not all independent variables can be retained in binary logins; the Brant test cannot be computed" or a generic "Brant r(2000)" error message. Adjustments to the model and attempts to consolidate the outcome variable's scale from 1 to 10 down to a 1 to 5 scale did not fix these issues.

I am seeking guidance on how to test the proportional odds assumption in this context adequately. Specifically, I am interested in understanding:

• The potential reasons why the Brant test fails to compute beyond the initial models, and whether this issue could be attributed to the sample size or the distribution of observations across the outcome variable's levels.
• Alternative strategies or statistical tests can be employed to assess the proportional odds assumption under these circumstances.
• The extent to which the observed difficulties in testing this assumption might impact the reliability and validity of the OLR models used in my analysis.

Additionally, I have attempted to use the KHB method for comparison but encountered similar challenges at certain levels of the analysis.
Any insights, recommendations, or references to relevant literature that could assist in addressing these challenges would be highly appreciated.