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:

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.



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