# Am I using Goodman-Kruskal gamma or Somers D or Kendall tau correctly and what do they mean?

I am seemingly blindly following this publication that has done work very similar to what I need to accomplish (page 18-21). My analysis is a multinomial logistic regression where I have 3 possible outcomes 0, 1, or 2 offspring produced. In the publication, they have recommended a Hosmer-Lemshow and a Persons test for goodness-of-fit. I have only figured out how to do the Hosmer-Lemshow test and my results are not so good (i.e. P-val is 0.00002). I have no idea how to do the Pearsons test (suggestions are appreciated).

The paper I am following, of course their tests are "good" for model fit (page 21). But they then go onto suggest that Somers D, the Goodman-Kruskala gamma and the Kendall's tau-a all indicate that their models are a good fit. But the paper does not report any of the values for these indices or how they calculated them.

I have just found a package ryouready that runs all of these tests. However, I have been having difficulties finding any help explaining what the values mean, let alone knowing if I have input my variables correctly.

My response variable is number of offspring, most of my explanatory variables are continuous like age or risk. Do I need to calculate the mean of each explanatory variable within each response variable (get the mean risk for 1 offspring, mean risk for 2 offspring etc...)and then compare those? It also seems that these tests are for 2x2 tables. If I am just looking at risk, my table would be a 1x3. However, my complete model will have 4 variables (age, risk, bp, and #offspring year before).

As you can likely tell, I am in the dark here on where to start. I would appreciate suggested readings, pdf lectures or videos of lectures would even be better!

EDIT/UPDATE: I have run the tests over my counts - I have 2 time periods (before/after) and then the count of offspring in each class (0,1,2). I do not know how to interpret the values - what is "good". What should I be looking for? Any source that explains these values would be nice to see.

Kendall's (and Stuart's) Tau statistics
Tau-b: 0.143
Tau-c: 0.130
Somers' d:
Columns dependent: 0.151
Rows dependent: 0.136
Symmetric: 0.143
Goodman-Kruskal Gamma: 0.312
Warning message:
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