[Carlo Lazzaro]

Evie:
I would stick with #14 recommendations.
It's a pity that Steve Samuels decided to stop participating to this forum.

[Daniel Santos Torres]

Hi Evie,

Just to add to the useful comments by Carlo and Steve, I think that the reason why it is not possible to visualize the residuals by typing rvfplot when using svy command arises because rvfplot takes into account the residuals generated by a model-based approach, in which the uncertainty of the true value of the estimates comes from the joint distribution imposed to x_i and u_i (the explanatory variables and the residual of the model). Ultimately, when fitting a model by OLS, the residuals are the square difference between the true values and the fitted values, and the uncertainty of the point estimates will depend on the restrictions imposed to the joint distribution of x_i and u_i.

In contrast, when using svy to account for complex-survey design, the uncertainty of the value of the estimates comes from the unequal probability of being sampled from the population due to the complexity of the sampling design. A complex-survey design usually involves a two-stage—or multi-stage—stratified sampling design where cluster units, labeled as the primary sampling unit (PSU), are sampled with unequal probability within each strata, and then, within each cluster, individuals are sampled. Uncertainty with the design-based approach here does not depend on the restrictions imposed to the joint distribution of the explanatory variables and the residuals of the model, but on the uncertainty of being selected to the sample due to the complexity of the survey design.

Thus, I think that heteroscedasticity in the residuals due to the unequal probability of selection is fully mitigated by the design-based approach by using svy. However, other types of heteroscedasticity might arise as other types of uncertainty might be present in the model. For instance, if you are interested in estimating a treatment effect in which the probability of being treated varies at other level different from the PSU, then the svy estimate would not be accounting for that kind of heteroscedasticity.

In the end, I think that how you proceed is going to depend on your research question and at what level your variable of interest varies.

That has been my reasoning but of course I could be wrong. Any correction/comment/suggestion on this will be highly appreciated.

Thanks!