Hello,
I have a large non-balanced panel dataset regarding a company dealing with private lessons for students. My goal is to fit a lmer model which predicts the number of monthly hours taken by a student according to a pretty large set of variables, both categorical and quantitative - most of them are counts, or relative percentile of a certain factor.
The random effect is based on a dummy which separates students who had only one teacher during the t period (about 63% of the entire record) from students who had more than one.
I have attached a barplot showing the distribution of my dependent variable, so we see it's strongly asymmetrical and with a long right tail.
I have already tried to apply the log-transformation by studying a Box-cox fit and it does a really good job for the consistency of parameters and of the model itself, showing positive R2 values and a residuals QQplot apparently good but, having it tested with both K-S and Jacque-Bera, I get p-values near to zero. Is there anything proper i could do to fix this issue?
A gamma model should be appropriate or at least a good choice. A log-normal should also work, as you already found.
Your sample size seems rather large (>10000). With such a large sample size, any test will tell you that the sample is sufficient to demonstrate deviations from some theoretical ideal. This is why you get p-values close to zero for any test of a particular distribution model. The question is if these differences are relevant. They are likely not relevant, because of this large sample size! Another nice example why formal tests of error distributions to justify another analysis (or test) are nonsense.
Jochen Wilhelm I will also figure out tomorrow with my professor the following topic. Here's the Q-Q plot of the LMM residuals. p-values relative to every test I apply seem to be really too harsh with the actual distribution of the residuals. Thank you for the suggestion - could you address me any paper or publication where I can find further infos about non-relevance of tests for large samples?
The plot looks close to perfect.
The tests on assumptions are not only non-relevant (I say: non-sensical) for large samples, they are also non-relevant (non-sensical) for small samples!
But the question for papers about that matter is good... I actually don't have one, but I would also be interested in having some. However, this is what I found:
https://arxiv.org/pdf/1908.02218.pdf
https://www.casact.org/pubs/forum/13fforum/07-Curley.pdf
and a great discussion on stackexchange:
https://stats.stackexchange.com/questions/2492/is-normality-testing-essentially-useless
and a blog-post from the statistician Robert Greener:
https://towardsdatascience.com/stop-testing-for-normality-dba96bb73f90
Jochen Wilhelm
In search for even better fits for my residuals, I tried bootstrapping it; attached pic to see they have finally reached an optimal shape. I used the boot option from the package car, but I can't figure out how to test the normality of these residuals. KS test and JB test seem to not recognize the object from boot(), is there any simple package or method I could test the null hypothesis with?
Thanks in advance
Jochen Wilhelm yes, and it was very exhaustive - thank you again. Having tried new ways which seem to bring a heavy improvement in residuals' distribution, I'd like to have still a normality distribution test. If it won't bring the result I expect, I will "give up" - but still satisfied.
- Badges
- Science topic