Updated: How to do a sensitivity analysis for an ordered logistic regression in R? 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?

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.
