An Introduction to Factor Analysis Factor Analysis

An Introduction to Factor Analysis

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What is Factor Analysis?

Factor analysis can be defined as a technique that is used to condense data of a large number of variables into a smaller number of variables, referred to as factors, so that they can be studied more easily. This technique is generally used to investigate variable relationships that are complex by collapsing several variables into a small number of interpretable factors. 

Within this article, we will explore the concept of factor analysis to understand how and when it is used in research. We will also take a look at the different types of factor analysis to understand their distinctions.   

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Understanding Factors

An Introduction to Factor Analysis Factor Analysis

Factors

Before we can delve into understanding factor analysis, we must first understand what a factor is. In research, a ‘factor’ refers to a set of observed variables that have similar response patterns. These variables are associated with a hidden variable known as a confounding variable. 

Factor Loadings

Not all factors are created equal, meaning that some have more weight than others. Therefore, some variables will have a stronger association with the underlying latent variables than others. To reflect the difference in the strength of associations, “weights” known as factor loadings are used. Factor loadings are similar to correlation coefficients as they too vary from -1 to +1. The closer the factors are to -1 or +1, the stronger is their association with the latent variable. A factor loading of zero would indicate that the factor has no association with the latent variable and therefore has no effect on it. 

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Types of Factor Analysis

An Introduction to Factor Analysis Factor Analysis

Let’s take a look at a few different methods that can be used to extract factors from a data set:

  • Principal Component Analysis: Principle component analysis, or PCA, is the most common method of factor analysis used by researchers. PCA involves extracting the maximum variance between the variables and then putting it into the first factor. Then, the variance explained by the first factor is removed after which the maximum variance for the second factor is extracted. This process is repeated until the last factor.  
  • Maximum Likelihood Method (ML): In the maximum likelihood method, researchers can test the statistical significance of factor loadings and calculate the correlations among different factors so that the confidence intervals for these parameters can be computed. ML is best suited when working with data that is normally distributed because it facilitates the computation of a wide range of indexes. 
  • Common Factor Analysis: After PCA, common factor analysis is the most preferred method used by researchers. It involves extracting the fewest factors that can account for the common variance within a set of variables. 

 

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FAQs on Factor Analysis

A ‘factor’ is a set of observed variables that have similar response patterns. These variables are associated with a hidden variable, known as a confounding variable, which is not identified or measured. 

A few commonly used types of factor analysis are;

  • Principal factor analysis
  • Maximum likelihood method
  • Common factor analysis

A factor loading is a weight attached to different factors to indicate the strength of their association with the latent variable. Factor loading values can range between -1 and +1. The closer the value is to -1 or +1, the more effect they have on the latent variable. A factor loading of zero would mean that the factor has so effect on the latent variable. 

Factor analysis is a data reduction technique that is used when researchers are trying to investigate concepts that are tedious to measure due to the large number of variables involved. This technique allows researchers to reduce the number of variables into a smaller amount of factors so that the data is easier to understand and analyse.

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Hindol Basu 
GM, Voxco Intelligence

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