# How to perform relative importance analysis on ordinal logistic regression model?

relative importance analysis there is an package called "flipRegression" from github.com which can perform relative analysis/ relative weights to analyze the importance of each brand attribute in relation to the others. I cannot download this package from github, is there any other way to do this analysis?

• what do you get when you run require(devtools) install_github("Displayr/flipRegression", dependencies = NA) ? Nov 15, 2022 at 21:12

I have not seen a method published in the academic literature extending relative weights analysis to ordered logistic regression. That is, it is unclear how it is implemented in {displayr}; I suspect the method uses linear regression to decompose the $$R^2$$ however.

That said, there is a method using the dominance_analysis() function from the parameters {parameters} package that is designed to work with the proportional odds model/ordered logit model.

For example, the below uses the datasets::mtcars data to get a ordered logit model and then conduct a dominance analysis on it (based on an approach discussed by Luchman, 2014).

library(MASS)

mtcars |>
transform(gear = as.ordered(gear)) |>
polr(gear ~ mpg + qsec + wt, data = _) |>
parameters::dominance_analysis()

# Dominance Analysis Results

Model R2 Value:  0.530

General Dominance Statistics

Parameter      | General Dominance | Percent | Ranks |   Subset
---------------------------------------------------------------
Intercept: 3|4 |                   |         |       | constant
Intercept: 4|5 |                   |         |       | constant
mpg            |             0.177 |   0.335 |     2 |      mpg
qsec           |             0.075 |   0.142 |     3 |     qsec
wt             |             0.277 |   0.523 |     1 |       wt

Conditional Dominance Statistics

Subset | IVs: 1 | IVs: 2 | IVs: 3
---------------------------------
mpg    |  0.296 |  0.233 |  0.004
qsec   |  0.021 |  0.131 |  0.074
wt     |  0.440 |  0.333 |  0.058

Complete Dominance Designations

Subset | < mpg | < qsec | < wt
------------------------------
mpg    |       |        | TRUE
qsec   |       |        |
wt     | FALSE |        |


Depending on how large your model is, you might consider using the sets argument to group variables to speed along runtime.

Reference

Luchman, J. N. (2014). Relative importance analysis with multicategory dependent variables: An extension and review of best practices. Organizational Research Methods, 17(4), 452-471.

• Your 2014 paper is really excellent and also has a great literature survey of pseudo $R^2$ measures. I’m glad to know about it. I was also glad to see our (Peterson & Harrell 1990) work referenced. A less comprehensive but simpler measure of relative importance may be found at hbiostat.org/rmsc/validate.html#sec-val-rev . This is based on projecting a categorical dependent variable model onto a linear model. One advantage is that it admits bootstrap or Bayesian uncertainty intervals for relative importance. Dec 10, 2023 at 12:50
• Many thanks @FrankHarrell for the kind words. The dominance approach does struggle to scale up and is rather computationally involved to bootstrap. See the advantage of a streamlined method for interval estimates and appreciate the pointer to the linked methodology. Dec 11, 2023 at 16:03