QUESTION: Can you recommend a nonparametric version of a multiway ANOVA that is also robust in the absence of homogeneity of variances? So, this is what I am looking for:
(1) Nonparametric ANOVA (no normality assumption).
(2) Multiway, AKA $k$-way (several factors, crossed design, second-order interactions can be studied).
(3) Admits heterogeneous variances between groups (no homoscedasticity assumption).
(4) General purpose and state-of-the-art.
As far as I know, Kruskall-Wallis meets (1) and (2) but not (3).
I conducted a quick literature search, but I am not sure of whether the methods I found are relevant or, instead, secondary.
Some methods I've read about are these:
- Welch (1951).
- Brown and Forsythe (1974).
- Sarmad (2006) (introducing the so-called 'Robust ANOVA', implemented in R at https://www.researchgate.net/publication/237324878_'robande'_An_R_package_for_Robust_ANOVA; I was unable to find it at CRAN).
As far as I know, all of them either perform so-so under certain assumptions or are not fully tested. No clear 'winner' option, according to my quick analysis.
CONTEXT: By the way, in case it matters, the data I want to analyse come from a study with single measurements, AKA without replication —that is to say, I have one single observation of my (continuous) dependent variable for each combination of the $k$ factors being considered.