Relying on statistical tests of the assumptions of some model is generally not a great idea, IMO. Those tests typically have too little power when n is small and too much power as n gets larger. Regarding the test of parallel lines for ordinal logit models, see the relevant section on this page:

https://www.restore.ac.uk/srme/www/fac/soc/wie/research-new/srme/modules/mod5/4/index.html

See especially this bit:

However the test of the proportional odds assumption has been described as anti-conservative, that is it nearly always results in rejection of the proportional odds assumption (O’Connell, 2006, p.29) particularly when the number of explanatory variables is large (Brant, 1990), the sample size is large (Allison, 1999; Clogg & Shihadeh, 1994) or there is a continuous explanatory variable in the model (Allison, 1999). It is advisable to examine the data using a set of separate logistic regression equations to explicitly see how the ORs vary at the different thresholds, as we have done in Figure 5.3.3. In this particular case it might be reasonable to conclude that the OR for gender from the PO model (0.53) - while it does underestimate the extent of the over-representation of boys at the lowest level - does not differ hugely from those of the separate logistic regressions (0.45-0.56) and so is a reasonable summary of the trend across the data. Here the statistical test that led to the rejection of the PO assumption probably reflects the large sample size in our LSYPE dataset.

HTH.

Do you have any data? You can use my method and need software to contact me.

Introduction: http://www.eaihua.com/drs-e.html

It is not clear to me, if you used multinominal or ordered regression, since both are mentioned. As far as I remember, there is no assumption of proportional odds in the multinominal case (someone may correct me here).

But your "more profound question" question may need some attention. If you really have ordered data, you cannot simply create a mean value, since these would need information about the distance between your ordered categories. This is a point which is overlooked in many publications and a lot of authors just treat ordered data as metric, which is not recommended (but I am sure I am guilty of this myself...). But as you already started to think about your measurement level to find an appropriate test, maybe you could go a little bit further, although this might not be recommended for a bachelor level. Instead of aggregating the data to a single measure (your mean value), you could use all the information and incorporate this into a multilevel model. This may be challenging and not something you should do in a BA thesis. In my opinion a BA thesis should show that you can work scientifically correct, but not that you can do everything on your own. So please talk to your supervisor, what you should do specifically and what may be left for your discussion and further analyses.

Multilevel models/mixed models analyze the data on several levels (as the name suggests), in your case 1. on the measurement level, your items (level 1) and 2. the subjects (level 2). The items are nested in your subjects an hence may be more correlated within each subject as between subjects (classical example are students (level 1) are nested in classes (level 2) which are nested in schools (level 3)). The multilevel model recognizes this nesting and handles it appropriately. It is a middle ground between complete pooling of the data (aggregating your itmes to a single mean value) and no pooling (ingnoring the subjects and taking all items as data), which is called partial pooling. Since this is a general approach (generalized linear mixed models), it can be applied to ordered analyses as well. Multilvel models themselves are challenging enough, so do not interpret as a recommendation for you that you should do this for your BA.

I double upvote Bruce Weaver 's response.

You probably don't want to use multinomial logistic regression. Practically speaking, even if your model doesn't quite meet the proportional odds assumption, for what you want to know, you probably want to treat your dependent variable as ordinal, even if the model is a little off.

I've been struggling for some time to come up with a simple approach to assess the proportional odds assumption. I thought the following link had a good description of the assumption for a simple case. But I don't how to generalize this to a general visual approach. (Analogous to plotting the residuals from Ordinary Least Squares).

https://www.restore.ac.uk/srme/www/fac/soc/wie/research-new/srme/modules/mod5/3/index.html

If anyone has an idea, let me know. (Or publish an example !)

Richard A Williams, I know you are very well-versed in ordinal logit models*, and I am curious to hear your thoughts on what I wrote above about the "test of parallel lines". I also wonder if you have any thoughts on Sal Mangiafico's question about graphical methods for assessing proportionality. Thanks.

* Readers who are not familiar with Richard's nice website can start with these notes, for example:

• https://www3.nd.edu/~rwilliam/stats3/Ologit01.pdf

Or, perhaps, if the test for parallel lines is a chi-square test, maybe there is like an effect size statistic related to it, like chi-square / sample size or something.... But I would love some kind of graphical method....

Bruce Weaver, I certainly agree that, If you always make decisions based on Brant tests using the .05 level of significance, you aren't going to be presenting many ordinal models.

I think that is unfortunate. I sort of hate mlogit models because of the huge numbers of parameters involved -- who can really make sense of them? Plus, it isn't really necessary to make such a jump, at least not immediately -- other, more parsimonious models are possible.

I personally am partial to the generalized ordered logit/ partial proportional odds model. With these, you relax proportionality constraints when they are violated, while leaving them in when they aren't. My papers on this are at

https://www.stata-journal.com/article.html?article=st0097

Article Understanding and interpreting generalized ordered logit models

But, there are other ordinal models too, some of which may work better in any given situation. Besides ologit and gologit models, these include interval regression, stage models, rank ordered logit models, and others. I discuss some of these in

https://methods.sagepub.com/foundations/srmpromo/2Xt6fM/ordinal-regression-models

But, as already mentioned, even if an ordinal model is a little off it may be worth using. There is a lot to be said for a parsimonious model that comes close to being right. All the additional detail you get with mlogit may just cause you to miss the forest for the trees.

Finally, I'll toss in one other paper of mine, which talks about whether or when you can treat ordinal independent variables as continuous:

https://methods.sagepub.com/foundations/srmpromo/dIXviz/ordinal-independent-variables

Thanks Richard A Williams. What about Sal Mangiafico's question:

Are you aware of any graphical methods for assessing (via the eyeball test) how well one is meeting the proportional odds (or parallel lines) assumption?

Thanks,

Bruce

Bruce Weaver Off the top of my head, no, I don't know of a good visual test, but there may be one.

Dear Lisa, if you have found a violation of parallel lines assumption, why don´t you try with an auto fit procedure by stata. Regards

Pfarr, Ch, Schmid, A. and U. Schneider (2010) Estimating ordered categorical variables using panel data: a generalized ordered probit model with an auto fit procedure. MPRA Paper No. 23203.

Rainer Duesing

Follow-up question because I have been thinking about this. I am using the ordinal regression model and for my B.a. I think I will pool the data although it is not the best method I think it will suffice. However, since it's pooled, does it still count as ordinal or is it continous now? Because now there are decimals.

I have two issues here:

#1 This might be too detailed, but I am using SPSS as a software tool and have to categorize my independent variables as either Covariates or Factors and have put them in covariates because otherwise it will look at each value (and due to the decimals there are a lot) seperately in the Parameter Estimates table.

#2 Due to taking the average there are many categories and some only have a few cases (like 2.5). Also it makes it harder to interpret.

So essentially, I was wondering if I am doing something wrong? I also thought about "grouping" the data (meaning I put values from e.g. 1-1.499 into the group "1", values from 1.5-2.499 into "2" etc. to have one clear value for each respondent). Does that make sense or how is this commonly treated?

Lisa Ss it doesn't make sense to pool the data that way, if you believe that you have ordinal data. You cannot simply calculate a mean or a sum score from the items, since ordinal data doesnt provide that information. This demands a metric scale. Therefore, your "average" score is not appropriate and hence the "grouping", too.

In my opinion you have several options:

1) Use an ordinal multilevel model to account for the repeated measures and the ordinality.

2) Conduct an ordinal confirmatory factor analysis, calculate the factor score for the latent variable and use this as a dependent variable in a OLS regression.

3) Do everything with an ordinal SEM, the structural and the measurement model.

4) Treat the oridinal items as metric (not recommended),

Maybe others have different approaches, please share.

You can use mode or median instead of mean. Since the dependent variable will change, your other problems may also disappear.

Hayri Abar can you elaborate what you mean? How does mode or median help to conduct a regression? Why is this a better approach than my suggestions 1)-3)?