• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar
The Analysis Factor

The Analysis Factor

Statistical Consulting, Resources, and Statistics Workshops for Researchers

  • Home
  • Our Programs
    • Membership
    • Online Workshops
    • Free Webinars
    • Consulting Services
  • About
    • Our Team
    • Our Core Values
    • Our Privacy Policy
    • Employment
    • Collaborate with Us
  • Statistical Resources
  • Contact
  • Blog
  • Login

In Principal Component Analysis, Can Loadings Be Negative?

by Karen Grace-Martin 1 Comment

Here’s a question I get pretty often: In Principal Component Analysis, can loadings be negative and positive?

Answer: Yes.

Recall that in PCA, we are creating one index variable (or a few) from a set of variables. You can think of this index variable as a weighted average of the original variables.

The loadings are the correlations between the variables and the component. We compute the weights in the weighted average from these loadings.

The goal of the PCA is to come up with optimal weights. “Optimal” means we’re capturing as much information in the original variables as possible, based on the correlations among those variables.

So if all the variables in a component are positively correlated with each other, all the loadings will be positive.

But if there are some negative correlations among the variables, some of the loadings will be negative too.

An Example of Negative Loadings in Principal Component Analysis

Here’s a simple example that we used in our Principal Component Analysis webinar. We want to combine four variables about mammal species into a single component.

The variables are weight, a predation rating, amount of exposure while sleeping, and the total number of hours an animal sleeps each day.

If you look at the correlation matrix, total hours of sleep correlates negatively with the other 3 variables. Those other three are all positively correlated.

It makes sense — species that sleep more tend to be smaller, less exposed while sleeping, and less prone to predation. Species that are high on these three variables must not be able to afford much sleep.

Think bats vs. zebras.

Likewise, the PCA with one component has positive loadings for three of the variables and a negative loading for hours of sleep.

 

 

 

 

 

Species with a high component score will be those with high weight, high predation rating, high sleep exposure, and low hours of sleep.

Principal Component Analysis
Summarize common variation in many variables... into just a few. Learn the 5 steps to conduct a Principal Component Analysis and the ways it differs from Factor Analysis.

Tagged With: Interpreting Loadings, Negative Loadings, PCA, principal component analysis

Related Posts

  • Four Common Misconceptions in Exploratory Factor Analysis
  • In Factor Analysis, How Do We Decide Whether to Have Rotated or Unrotated Factors?
  • How To Calculate an Index Score from a Factor Analysis
  • Can You Use Principal Component Analysis with a Training Set Test Set Model?

Reader Interactions

Comments

  1. Namrata Gulati says

    August 21, 2020 at 1:16 pm

    I am really grateful for the excellent information. Can you please guide me on the STATA codes for generating the index using PCA.

    Reply

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Please note that, due to the large number of comments submitted, any questions on problems related to a personal study/project will not be answered. We suggest joining Statistically Speaking, where you have access to a private forum and more resources 24/7.

Primary Sidebar

This Month’s Statistically Speaking Live Training

  • Member Training: Introduction to SPSS Software Tutorial

Upcoming Free Webinars

Poisson and Negative Binomial Regression Models for Count Data

Upcoming Workshops

  • Analyzing Count Data: Poisson, Negative Binomial, and Other Essential Models (Jul 2022)
  • Introduction to Generalized Linear Mixed Models (Jul 2022)

Copyright © 2008–2022 The Analysis Factor, LLC. All rights reserved.
877-272-8096   Contact Us

The Analysis Factor uses cookies to ensure that we give you the best experience of our website. If you continue we assume that you consent to receive cookies on all websites from The Analysis Factor.
Continue Privacy Policy
Privacy & Cookies Policy

Privacy Overview

This website uses cookies to improve your experience while you navigate through the website. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may affect your browsing experience.
Necessary
Always Enabled
Necessary cookies are absolutely essential for the website to function properly. This category only includes cookies that ensures basic functionalities and security features of the website. These cookies do not store any personal information.
Non-necessary
Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. It is mandatory to procure user consent prior to running these cookies on your website.
SAVE & ACCEPT