Using polychoric from psych to get correlation from ordinal and nominal variables

In the realm of statistical analysis, it’s not uncommon to encounter datasets that contain a mix of different types of variables. Ordinal and nominal variables are two such examples. While Pearson correlation is often used for this purpose, polychoric regression offers an alternative approach using a specialized type of correlation coefficient known as the polychoric correlation.

In this article, we’ll delve into the world of polychoric regression, exploring its strengths, limitations, and potential applications in analyzing datasets containing both ordinal and nominal variables. We’ll also examine some common issues that can arise when working with polychoric regression, including the warning message you encountered earlier.

Background on Polychoric Regression

Polychoric regression is a type of regression analysis used to model the relationship between two or more categorical variables. The key innovation behind polychoric regression lies in its use of a non-parametric approach to estimate correlations between ordinal and nominal variables. This contrasts with traditional Pearson correlation, which relies on assumptions about normality and equal variances.

Polychoric regression is particularly useful when working with datasets that contain ordinal variables, where the data may not conform to the assumptions required for traditional methods. By leveraging a specialized type of correlation coefficient, polychoric regression can provide a more robust estimate of the relationship between these variables.

Installing psych Package

The psych package in R provides an implementation of polychoric regression and other statistical models specifically tailored for working with ordinal and nominal data. To install this package, you’ll need to download the latest version from CRAN (Comprehensive R Archive Network). Here’s a step-by-step guide:

# Install the psych package using source code
packageurl <- "https://cran.r-project.org/src/contrib/Archive/psych/psych_1.9.12.tar.gz"
install.packages(packageurl, repos=NULL, type="source")

Understanding Polychoric Correlation

Polychoric correlation is a specialized measure of association that combines elements from both chi-squared analysis and Pearson correlation. It’s calculated using a specific formula that takes into account the number of categories in each variable.

The polychoric correlation coefficient ranges between -1 (perfect negative association) and 1 (perfect positive association). This makes it easier to interpret the results compared to other types of correlation coefficients, which may not be directly comparable across different datasets.

Error Messages and Solutions

When working with polychoric regression, you may encounter warning messages that indicate issues with variable ranges or NaN values. These errors typically arise due to differences in scale between variables being used for analysis.

Warning: Items Do Not Have an Equal Number of Response Alternatives

The first warning message indicates that the items do not have an equal number of response alternatives. This can lead to discrepancies in the polychoric correlation coefficient, causing it to produce NaN values.

To resolve this issue, you’ll need to ensure that all variables used for analysis are scaled similarly. You can achieve this by using a global set option with the polychoric() function.

# Example usage of polychoric() with global set option
library(psych)
setOption("polychoric.global", TRUE)
polychoric(data$Var1, data$Var2)

Warning: NaNs Produced

The second warning message arises when the qnorm() function encounters NaN values. This can occur due to differences in scale between variables.

To mitigate this issue, you’ll need to use a more robust estimation method or modify your data preparation steps to ensure that all values are within a valid range.

Example Application: Correlation Between Ordinal and Nominal Variables

Let’s assume we have a dataset containing an ordinal variable (AgeGroup) and a nominal variable (FavoriteFood). We want to explore the relationship between these variables using polychoric regression.

# Load necessary libraries and datasets
library(psych)
data <- read.csv("your_data.csv")

# Prepare data for analysis
correlation_matrix <- polychoric(data$AgeGroup, data$FavoriteFood,
                                 global = TRUE)
print(correlation_matrix)

Conclusion

In this article, we’ve explored the world of polychoric regression and its application in analyzing datasets containing both ordinal and nominal variables. We discussed common issues that can arise when working with polychoric regression, including warning messages related to variable ranges.

By leveraging a specialized type of correlation coefficient and following best practices for data preparation and analysis, you can unlock the full potential of polychoric regression in your statistical modeling endeavors. Whether you’re exploring relationships between ordinal and nominal variables or tackling complex datasets, polychoric regression offers an innovative approach that’s worth considering.

Last modified on 2024-12-15