Hello,
I am working with weighted linear regression for calibration curves (testing different weighting factors) and trying to understand what is the correct approach to check regression assumptions for model diagnostics. My questions are as follows:
- Should the residuals from a weighted linear regression follow a normal distribution, or do they tend to deviate from normality?
- What are the differences between raw, standardized and studentized weighted residuals? Which of these should I use to check linear regression assumptions and why? Would using one or another lead to different conclusions?
Regards
WLS model is transformed to OLS model under the transformation matrix L= S ^(-1/2), where S is the population covariance matrix of the errors.
The original model can therefore be transformed and the model parameters and residuals corresponding to the transformed model, can be handled using OLS framework under standard OLS model assumptions.
In weighted linear regression, you should use standardized (or studentized) residuals not raw residuals to check normality and homoscedasticity.
Hello,
Thank you very much for your answers. Regarding the use of standardized residuals, does it matter whether internally or externally standardized residuals are used? In R, internally and externally standardized residuals would correspond to rstandard(“wls model”) and studres(“wls model”), respectively, the latter being from the MASS package.
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