I am working with data on coastal landscapes and I am proposing the following model for the two-way ANOVA:
patch area ~ year + class
I have four years and five classes (land cover) and for each combination the area of each patch, so the experimental design is not balanced:
Year Class n
1 1 260
1 2 678
1 3 392
1 4 89
1 5 162
...
4 1 81
4 2 1225
....
In addition, the assumptions of the ANOVA are not met: there is a relationship between the residuals and and the fixed values and the residuals are not normally distributed. Is there a non-parametric alternative for this model and design? Regards
You might look into robust ANOVA methods. Here is a link to a vignette of the WRS2 R-package. https://cran.r-project.org/web/packages/WRS2/vignettes/WRS2.pdf
An example of using the WRS2 package for two factor ANOVA can be found here: https://rcompanion.org/rcompanion/d_08a.html
Caleb A. Aldridge , good suggestion. One challenge I have with robust methods is that it's not always obvious in what way they are robust (robust against what?) or to what extent they are robust. And there are different methods used in the WRS2 package. (For example, using medians, trimmed means, M-estimators, and so on). So, the upshot is that it takes some research and thoughtfulness to choose the most appropriate robust approach.
ART anova: When all your independent variables are categorical and your dependent variable can be considered at least interval, then aligned ranks transformation anova can be an appropriate nonparametric approach. ARTool is very flexible, including mixed effects models (http://depts.washington.edu/madlab/proj/art/). It's relatively easy to use in R. But be sure to read the documentation on how to do multiple comparisons if you are going to use them.
Sal Mangiafico, correct. It takes a little trial and error—it seems that Wilcox suggest running traditional parametric models for comparison to robust approaches to 'see' the robustness.
Thanks for mentioning ART ANOVA and ARTool. New to me, and is perhaps just what César Alejandro Berlanga-Robles needs!
Caleb A. Aldridge and Sal Mangiafico thank you for your answers. I executed the analysis with the aligned ranks transformation anova, considering that I have an unbalanced design, the model was Y (ln (area)) ~ year * class.
I am interested in the differences between years, rather than between classes, the p value for these factor was p > 0.05 so I no longer carry out the subsequent multiple comparison. The analysis I did with more than 6000 data, I guess that guarantees me a high power ¿No?.
Best Regards.
Sal Mangiafico wrote:
" When all your independent variables are categorical and your dependent variable can be considered at least interval, then aligned ranks transformation anova can be an appropriate nonparametric approach. ARTool is very flexible, including mixed effects models (http://depts.washington.edu/madlab/proj/art/)."
Salvatore, Jacob Wobbrock's web-page, which you link to there, uses Likert-type items as an example. Such items are generally assumed to have ordinal, but not necessarily interval scale properties. Did you mean to say "can be considered at least ordinal"? If not, why would one not just use ordinary ANOVA when the DV has interval scale properties? Thanks for clarifying.
Bruce Weaver , looking at this article by Wobbroc and others 2011 ( https://faculty.washington.edu/wobbrock/pubs/chi-11.06.pdf ), it looks like cell means and residuals are calculated before the ranks are assigned. If this is the case, the data would need to be interval to do the averaging and subtracting. I may be misunderstanding, though.
César Alejandro Berlanga-Robles , yes, I think you are thinking about this correctly. Addition: From what I'm reading, ART anova doesn't need a balanced design, but I wonder if a very unbalanced design might be problematic. Even if only out of curiosity, I would try using a general linear model (lm), or maybe preferably for your data Gamma regression (glm, family = Gamma(link = "identity"). And see if year is significant. If so, there might be a better approach than ART anova.
Hi Salvatore. Cell means & residuals certainly are calculated. But the following excerpt from p. 144 of that same document says that "the response variable may be continuous or ordinal."
--- start of excerpt ---
THE ALIGNED RANK TRANSFORM FOR N FACTORS
This section describes the Aligned Rank Transform, generalizing it to an arbitrary number of factors. The ART is for use in circumstances similar to the parametric ANOVA, except that the response variable may be continuous or ordinal, and is not required to be normally distributed.
--- end of excerpt ---
Cheers,
Bruce
Bruce Weaver , I'm not sure. The way I read what the procedure is, you'd have to assume that an ordinal dependent variable is interval to do the averaging and subtraction....
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