Comment: Struggles with Survey Weighting and Regression Modeling

We congratulate the author on an informative and thought-provoking discussion on a topic of broad interest to the statistics community: the fitting of models to data collected through complex surveys. The number of papers written on this topic, whether from a model-based or design-based perspective, is substantial and goes back at least to Konijn (1962). This topic has led to some disagreements between those advocating that the design best be ignored when the primary interest is on the characteristics of the model, and those stating that the design cannot be ignored. More recently, both sides of this discussion have moved to something approaching a consensus, with those favoring a model-based approach acknowledging the need to account for nonignorable designs in the model fitting, while the traditional design-based view has been extended to explore certain circumstances under which it is appropriate to ignore the design. The current article is an excellent example of those recent discussions of why the design needs to be accounted for in modeling, and how this can be done in practice. The importance of fully accounting for the design by incorporating all relevant interactions provides a good motivation for the discussion of the range of methods in the article. It also stresses other aspects of importance to people working with survey data, in particular the desirability of maintaining scale/location invariance and linearity of the modelbased estimators. This ensures consistency of estimates for different variables in the survey, as well as