# Factor Analysis vs Principal Component Analysis

This article shows how to decide whether to use factor analysis or principal component analysis.

The content of the article is structured as follows:

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## Clearing Confusion

Both Principal Component Analysis (PCA) and Factor Analysis (FA) are advanced statistical techniques frequently employed in multivariate data analysis.

At first glance, they may seem similar due to certain shared characteristics: both techniques transform a set of observed variables into a smaller set of new variables, involve eigenvalue and eigenvector decomposition, and typically start with standardized data.

However, their purposes and interpretations are distinctly different. Letâ€™s delve into both methodologies one by one!

## Principal Component Analysis

PCA aims to reduce the number of observed variables in a dataset while retaining as much variance as possible. It does this by transforming the original variables into a new set of orthogonal variables known as principal components.

These components capture the maximum variance in the data in decreasing order. The first few components usually contain most of the useful information, allowing for data compression.

PCA is frequently used when thereâ€™s a need to condense data for 2D or 3D visual representations, when facing the challenge of applying other algorithms due to computational constraints, and when the primary interest lies in capturing the total variance in the data.

For further details, see What is Principal Component Analysis?.

## Factor Analysis

FA delves deeper, it tries to understand the latent structures, called factors, that give rise to the observed correlations among variables.

These factors can represent underlying traits or characteristics that arenâ€™t directly observed but influence the observed variables.

FA is often employed when exploring hidden factors causing observed correlations, when validating and confirming the hypotehsized structure of underlying factors that arenâ€™t directly observable.

For further information, see Introduction to Factor Analysis.

## Key Distinctions

To sum up, the fundamental difference lies in their core objectives:

• PCA is essentially about capturing variance and simplifying data. It doesnâ€™t consider or aim to uncover any underlying structure.
• FA is all about uncovering latent structures. It operates on the assumption that there are underlying factors causing the correlations observed among variables.

In conclusion, while PCA and FA might seem similar at the outset due to their shared mathematical characteristics, understanding their distinct purposes ensures that you choose the appropriate method for your analytical goals.

Always keep in mind the nature of your data and the specific insights you seek.

## Video & Further Resources

Do you need more explanations about PCA maybe? Then you might watch the following video on my YouTube channel.

In addition to the video, you might read some of the other tutorials on my homepage. I have released several articles already:

This page was created in collaboration with Cansu Kebabci. Have a look at Cansuâ€™s author page to get more information about her professional background, a list of all his tutorials, as well as an overview on her other tasks on Statistics Globe.

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