Principal Component and Factor Analysis

Principal component and factor analysis

Data is an  integral part of  data analysis.  There was a time when the main challenge in data analysis was the availability of the data.

During that time, data was scarce and acquiring such types of data proved cumbersome. However, in  the internet age, the challenge of data is  not a problem. Data is  readily available in large quantity.  As the saying goes “a coin has two sides”, we moved to the extreme end of the challenge of having large data sets and analyzing a large dataset with a lot of dimensions led to an issue known as the curse of dimensionality which occurs when analyzing data with high dimensions.  Dimensionality reduction techniques are the one employed to reduce the dimensions of these datasets and make them easy for analysis. In reality, there are different types of dimensionality reduction techniques, but here we focus on two of the common types – principal component and factor analysis.

Principal component analysis.

This is the most used dimensionality reduction technique.   It reduces the dimensions of the data by extracting the valuable ones from the data.

The main challenge with dimensional reduction is that we have to trade of reducing the dimensions with accuracy. The goal of the principal component analysis is to reduce the dimensions with a little sacrifice of accuracy. The question that we will address here is when you can use the principal component analysis on your dataset?  And how does this method work?

There are three instances that you should consider if you want to use the principal component analysis. The first instance, if you want to perform a dimensionality reduction and do not know which variables you want to remove. The Second instance, if you want to ensure that there is independence between all the variables. And finally, if you are satisfied with the independent variables being less interpretable.

How does principal component analysis work?

When performing the principal component analysis, it’s a rule of thumb to standardize the variables first before proceeding to any other step.  The aim of standardization is to ensure that there is a minimal variance between the variables.  PCA is quite sensitive to the variability of the variables.

The second step is to compute the covariance matrix.  The covariance matrix helps to explain the relationship between the variables. After that, we proceed to the calculations of the Eigenvalues and the Eigenvectors. We then order them in a descending order which will help us in finding the principal components. We then choose the principal components and then recast the components to their initial values.

In most statistical software, they have a function for principal components analysis. The process should be straightforward, and you won’t even have to go through this process of calculating the covariance matrix and Eigenvalues and vectors

Factor analysis.

This is a dimensionality reduction technique that you will often hear, it is mentioned along with principal components analysis.  However, unlike PCA, which is well known, a few know  about this dimension reduction technique. Factor analysis reduces the dimensions of high dimensional data by similar grouping cases.

Factor analysis is very common in survey research where the response variables are categorical.  It aims to give an insight, not the latent variables behind people’s behavior  and choices.

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