Principle component analysis which can also be identified as PCA and factor analysis have so much similarities in them. Many people may get confused about the fact that whether PCA i.e. principle component analysis is same as Factor analysis or not. But despite of all the similarities that they tend to have there are certain fundamental differences between them which we will discuss here.
Principle component analysis (PCA)
Principle component analysis (PCA) is generally used to represent a data table which will be multivariate data table which is made up of as smaller set of variables as possible in order to observe trends, jumps, clusters, and much more. Principle component analysis (PCA) is also tends to known as the process which computes the principal components and use them to perform a change of basis on the data.
In simple language Principle component analysis (PCA) is just a collection of points in real space which can be seen in the sequence of p direction vectors. It is a dimensionality reduction method.
Factor analysis
Factor analysis is a technique of statistical method which is generally used to describe a variability among observed. Its main purpose is said to reduce to many individual items into fewer number of dimensions.  This is a major technique that provides us index of all the variable, we can usually use this score for the further analysis.
Factor analysis is said to be a technique which is mainly used to reduce a vast number of variables into fewer number of variables factors. This is the technique through which it extracts minimum common variance from all the variables that are provided and then put them into a common score, so that we can use this score in further analysis.
Similarity
Both Principle component analysis (PCA) and Factor analysis have tones of similarities that is why people often get confused about both of them. They often get it wrong that they both are the same but in reality they are not.
As we are talking about the similarities that they both hold, they both are data reduction techniques in which they both allow you to collect the variance in variables which are present in the smaller sets. It is similar in many ways and it’s not really hard to see the difference between them. Principle component analysis (PCA) is very similar to another multivariate procedure that we have discussed earlier which is also known as Factor analysis.
Both even use the same software which is stat software which also uses the same extraction, interpretation, plus rotation and also choosing the number of factors or components coincide with it. The procedure of the software implementation is same along with the same procedure that we have.
Differences
Despite of having many similarities, there is just a fundamental difference between them. The fundamental difference is that Principle component analysis (PCA) is the linear combination of the variables and also Factor Analysis is a measurement model of a latent variable. Factor Analysis is also just based on a formal model predicting that is observed by the variables given from the theoretical latent factors. Principle component analysis (PCA) is a mathematical procedure that trasforms a number of variables into various number of uncorrelated variables which are also known as principal components.
