# Inequality and Total Effect Summary Measures for Nominal and Ordinal Variables

## Introduction

### Abstract

Many of the topics most central to the social sciences involve nominal groupings or ordinal rankings. There are many cases in which a summary of a nominal or ordinal variable’s effect, or the effect on a nominal or ordinal outcome, is needed and useful for interpretation. For example, for nominal or ordinal independent variables a single summary measure is useful to compare effect sizes of different variables in a single model or to compare effect sizes across multiple models, as with mediation. For nominal or ordinal dependent variables, there are often an overwhelming number of effects to examine and understanding the holistic effect of an independent variable, or how effect sizes compare within or across models is difficult. In this project, we propose two new summary measures using marginal effects. For nominal and ordinal independent variables, we propose |inequality| as a summary measure of a nominal or ordinal independent variable’s holistic effect. For nominal and ordinal outcome models, we propose a total ME (marginal effect) measure which quantifies the comprehensive effect of each independent variable across all outcome categories. The added benefits of our methods are both intuitive effect size metrics and approaches that can be applied across a wide range of models, including linear, nonlinear, categorical, multilevel, longitudinal, and more.

### Example

For an example of the approach, see the slides and example code from a recent presentation:

### Citation

For now, please cite our presentation at the 2024 Sociological Science conference:

Mize, Trenton D. and Bing Han. 2024. "Inequality As a Summary Measure for the Effect of Nominal Independent Variables." Paper presented at the Sociological Science conference, Duke University.

## Stata Commands

Two Stata command to automate the calculation of the statistics, nomineq and totalme, are coming soon and will be posted here.