I am trying to adjust a hierarchical multiple regression model and no matter which transformations I use (z-transformation, sqrt, cuberoot, inv, inv sqrt …), I do not manage to get the residuals normally distributed. What can I do? Does anyone have any suggestions? I also checked out a related thread, the transformations suggested there did not help me. My residuals are normal according to D'Agostino Normality Test, but not according to Shapiro-Wilk (which is the crucial one according to my supervisor). I cannot use a non-parametric model. I would appreciate your help a lot!
Thanks,
brobdingnag!
Solved – How do i normalize residuals
generalized linear modelnormalizationqq-plotregressionresiduals
Related Solutions
One way you can add a "test-like flavour" to your graph is to add confidence bounds around them. In Stata I would do this like so:
sysuse nlsw88, clear
gen lnw = ln(wage)
reg lnw i.race grade c.ttl_exp##c.ttl_exp union
predict resid if e(sample), resid
qenvnormal resid, mean(0) sd(`e(rmse)') overall reps(20000) gen(lb ub)
qplot resid lb ub, ms(oh none ..) c(. l l) ///
lc(gs10 ..) legend(off) ytitle("residual") ///
trscale(`e(rmse)' * invnormal(@)) ///
xtitle(Normal quantiles)
Trying to get to normality is usually a means to an end. Understanding the end will really help in understanding what is the best path forward, and oftentimes whether or not transforming to get to normality is even needed. There are tons of natural distributions that are not normal and do not need to be transformed to normal.
The set upper limit of 60 is problematic because it creates a false upper end of the distribution. You may be getting a bad Shapiro-Wilk simply because there are too many 60's in your dataset. I would recommend bootstrapping a right-tail or concatenating the upper and lower ends of your dataset. These are not ideal methods and must all be put in context of what you're trying to do, so as to see if they make sense.
Best Answer
Why can't you use non-parametric tests? Depending on what you are trying to learn there is probably a meaningful permutation test that would give meaningful results without needing the normality assumption (and is more meaningful that rank based tests).
Also note that the normality tests are really answering the wrong question. If you residuals are near normal (how near depends on sample size and other factors) then the normal based tests may give results that are close enough even though the normality tests may reject the "exact normality" hypothesis.