Repeated measures for ordinal categorical variable analysis in r

Question

I have some environmental monitoring data that I've collected over 4 different years. I'd like to analyses the trend in the condition over this time period.

	2010	2013	2017	2022
Very good	37	34	8	29
Good	42	43	16	7
Fair	41	44	22	1
Poor	60	26	21	1

• Each plot was assessed in each assessment year (repeated measures?)
• Each plot was given a condition score of very good, good, fair or poor (ordinal categorical variable?)
• I've excluded "unknown" as it's not really ordinal meaning that the number of responses can vary between years as the number of 'unknown' plots changes.

When comparing the two most recent years, I used a Mann-Whitney U test:

result_table <- table(lapply(unstack(data, Condition ~ Year), factor, levels = c("Very good", "Good", "Fair", "Poor")))
df <- as.data.frame.matrix(result_table)
score <- c("Very good", "Good", "Fair", "Poor")
mh_test(as.table(result_table), scores = list(response = 1:length(score)), distribution='exact')

How do I analyse the full data set with all four years?

Answer 1

Since this is ordinal (ranked) data and we are comparing >2 levels of an independent variable (years), the classic approach will be Friedman's test. You can think of this as a robust alternative to the parametric repeated measures ANOVA. Since you posted R code, I'll assume you are interested in using R to run this analysis. I prefer the rstatix package for this, with the friedman_test() fucntion, read a walkthrough here. If you prefer base R stats, you can see this function.

There are additional ranked based methods for >2 dependent groups. Wilcox (2021) has a really nice chapter highlighting a number of valid approaches. See his chapter 8, section 5 for further suggestions. He also has R code available for running these approaches. Let me know if you'd like more detail.

Answer 2

A comprehensive solution may be obtained by forming an ordinal semiparametric model such as the proportional odds (PO) model. The PO model is a full generalization of the Wilcoxon and Kruskal-Wallis tests and also can handle paired data.

Note that the Friedman test has low relative efficiency since it reduces to the sign test in its simplest form.