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How would you do an robustness or sensitivity analysis for an ordered logistic regression?

Can it be done by replacing the control variables with others that are similar in the model? For instance replace health with hampered in dayli life or replaceing the NA's with 0?

If you can also recommend any textbook, video, link.. any type of source I really appreciate!

I'm using the R program and the MASS::polr.

EDIT 1: More prcisely I want to check my models for robustness by doing a sensitivity analysis and reverse causality. Since my dependent variable is ordered an the variable of interest is a dummy I considered to do a binary logit, however I'm indoubt to use the ordered variable as independent in a binary logit. Will it be a good way to check for reverse causality?

rr19
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    Sensitivity to what? Robustness to what? And for related issues see my blog post. – Frank Harrell Dec 21 '22 at 21:29
  • @FrankHarrell the objective is to run an ordered logit regression to check the effect of work load on life satisfaction where I interpreted odds ratios. After this I runned brant test. So, now I want to check if this effect is sensitive or robust. – rr19 Dec 21 '22 at 22:08
  • The Brant test is anti conservative. See the blog article. – Frank Harrell Dec 22 '22 at 00:00
  • @FrankHarrell but do you have an answer to how I can do the sensitivity analysis? Can I do it in the way I described? – rr19 Dec 22 '22 at 16:37
  • Once you answer my 2 initial questions I may be able to help. And state the study's ultimate goal. – Frank Harrell Dec 23 '22 at 11:00
  • @FrankHarrell but isn't the objective of a sensitivity analysis for regression models to test the sensitivity to changes.. i.e. the appropriateness of the moels/ results? It's really hard for me to find some theory in a textbook about it. :/ – rr19 Dec 27 '22 at 00:51
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    Yes but you need to be specific. Sensitive to changes in what? Addition of variables you had hoped you didn't need? Linearity assumption? Additivity assumption? Choice of link functions? Proportional odds assumption? – Frank Harrell Dec 27 '22 at 10:06
  • @FrankHarrell Oh okay, so I actually need to specify if it's the sensitivity of the choice of link functions or for instance testing the sensitivity of the proportional odds assumption.. Did I understood your comment correct? – rr19 Dec 27 '22 at 12:33
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    Yes; be specific. And state your alternative if you find there is sensitivity to a model aspect. Sometimes alternatives are worse, as detailed in the link I provided up top. – Frank Harrell Dec 27 '22 at 14:26
  • @FrankHarrell is it possible that you can have a look at my two post.. maybe you would have an answer? (the topic is the same in both of them; about heteroskedasticity in ordered logit): link and link – rr19 Dec 29 '22 at 20:41
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    Cross-posting is not a good idea. I've added an answer below. – Frank Harrell Dec 30 '22 at 10:26

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Your question did not mention heteroscedasticity but you've made it clear now that is your main issue. There is no assumption of heteroscedasticity per se in ordinal logistic regression but there is an analogous assumption: the equal slopes assumption (over levels of Y). For the proportional odds model this is the proportional odds assumption. When there is only a grouping variable (and no continuous covariates) this can be checked by looking a parallelism in transformed empirical cumulative distribution functions. Better ways for the general case are given here. Extensive material is available in the nonparametrics chapter of BBR and in the chapters on ordinary regression in RMS.

Instead of thinking about sensitivity analysis think about lack of fit and of the cost of making the fit "better" by adding too many parameters to the model.

Frank Harrell
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  • Thanks for your comment and time. Accoring to heteroskedasticity for ordered logit/probit models this may be a reference (I just found it right now): link ch 18.3.1.. I just wanted to share with you maybe if you want to read it and have a look at it. I didn't understooth much right now but I will have a look at it. – rr19 Jan 02 '23 at 00:40
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    This paper is consistent with what I said earlier. Heteroscedasticity is analogous to non-proportional odds, and the authors' consideration of non-constant thresholds is exactly the same as non-PO. So stick to an assessment of the PO assumption using methods such as those I've suggested. – Frank Harrell Jan 02 '23 at 08:05
  • Many thanks for your answer.. I first need to findout and understand that analogous to non-proportional odds means then I will have a look at it. – rr19 Jan 06 '23 at 12:03