Recently, Anna Welander Tärneberg and I were doing research with patient satisfaction as the outcome, and we checked how other researchers had estimated these equations in the past. Here is what we found, as documented in the appendix of our recently published paper in the journal Health Economics.
People use a lot of different methods, and many authors use multiple methods. But there is a rich history of using Ordinary Least Squares regressions to estimate impacts on patient satisfaction. In our paper, we used OLS but verified all the results with Probit and Logit regressions. To add to this list, Dunsch et al. (including me) have a new paper out last week on patient satisfaction in Nigeria, also using OLS as the main estimation method.