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When carrying out OLS multiple linear regression, rather than plot the residuals against fitted values, I plot the (internal) Studentized residuals against fitted values (ditto for covariates). These residuals are defined as:

\begin{equation} e^*_i = \frac{e_i}{\sqrt{s^2 (1-h_{ii})}} \end{equation}

where $e_i$ is the residual and $h_{ii}$ are the diagonal elements of the hat matrix. To get these studentized residuals in R, you can use the rstandard command.

What type of residuals do people routinely use in this context? For example, do you just stick with $e_i$ or do you use jackknife residuals, or something else entirely.

Note: I'm not that interested in papers that define a new type of residual that no-one ever uses.

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Your question strikes me as oddly worded. You don't "choose" residuals. Those are given / implied by a procedure / analysis. The underlying model implies certain (abstract) error terms, and the analysis produces residuals. In that sense you choose the analysis not the residuals. Maybe rephrasing to "what type of post-fit analysis of residuals do you use" may be better? You seem to be leaning that way asking the question in the context of a OLS model. And in that case, looking at influential observations ("hat matrix") is a good method. –  Dirk Eddelbuettel Aug 11 '10 at 12:16
    
Thanks. I completely agree with your point and changed my question. –  csgillespie Aug 11 '10 at 13:07
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There are various types of residual analyses you can carry out depending upon what you are checking for. Depending upon the analysis, you either use original residuals or standardized residuals. You need to specify what exactly you are tying to verify post fitting of your model (constant variance assumption, normality assumption, IID assumption, etc).

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