Difference Between Factor Analysis and PCA (Principal Component Analysis)

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Questions and Answers

What is the main objective of Principal Components Analysis (PCA)?

Identify the dependent variable to be explained by independent variables

Select a number of components that explain as much of the total variance as possible (correct)

Create new, uncorrelated variables called factors

Explain the interrelationships among the original variables

What distinguishes PCA and FA from regression analysis?

PCA and FA have no limitations, unlike regression analysis

PCA and FA focus on understanding relationships among variables, whereas regression predicts outcomes (correct)

PCA and FA use linear combinations, but regression does not

PCA and FA involve dependent and independent variables, but regression does not

In PCA, what makes the computation and interpretation of Principal Components (PCs) relatively simple?

The transformation of original variables into factors

The focus on explaining interrelationships among variables

Selecting components based on total variance explained

The use of uncorrelated PCs as linear combinations of original variables (correct)

Which technique transforms the original variables into new, uncorrelated variables called principal components?

Principal Components Analysis Signup and view all the answers

What is the major objective of selecting factors in Factor Analysis (FA)?

Explaining interrelationships among the original variables Signup and view all the answers

What is the main purpose of principal components analysis?

To transform observed variables to principal components Signup and view all the answers

In PCA, how are the coefficients chosen for each new variable (principal component)?

To satisfy specific conditions related to variance and orthogonality Signup and view all the answers

What does it mean by 'Var (C1) ≥ Var (C2) ≥ ... ≥ Var (CP)' in principal components analysis?

The variance of each principal component decreases sequentially Signup and view all the answers

What is the condition for the sum of the squares of coefficients for any principal component in PCA?

The sum must be one Signup and view all the answers

How are C1, C2, C3, and further principal components defined in terms of their variance in PCA?

Each subsequent principal component has a decreasing variance compared to its predecessor Signup and view all the answers

How are the variances of individual principal components related to the original total variance in PCA?

The variances add up to form the original total variance Signup and view all the answers

Study Notes

Principal Components Analysis (PCA)

The main objective of PCA is to reduce the dimensionality of a dataset while retaining most of the information.

Comparison with Regression Analysis

PCA and Factor Analysis (FA) differ from regression analysis in that they are not used to predict a dependent variable, but rather to identify patterns and relationships in the data.

Characteristics of Principal Components

The computation and interpretation of Principal Components (PCs) are relatively simple in PCA because the PCs are orthogonal (perpendicular) and uncorrelated.

Technique of PCA

PCA is a technique that transforms the original variables into new, uncorrelated variables called principal components.

Objective of Factor Analysis (FA)

The major objective of selecting factors in FA is to identify the underlying factors that explain the patterns and relationships in the data.

Purpose of PCA

The main purpose of PCA is to identify the directions of maximum variance in the data and to reduce the dimensionality of the dataset.

Coefficients in PCA

The coefficients for each new variable (principal component) are chosen in such a way that the first principal component has the maximum variance, the second principal component has the second maximum variance, and so on.

Variance of Principal Components

The variance of the principal components is in descending order, meaning that Var(C1) ≥ Var(C2) ≥ ...≥ Var(CP), where C1, C2, ..., CP are the principal components.

Condition for Coefficients

The condition for the sum of the squares of coefficients for any principal component in PCA is that it equals 1.

Definition of Principal Components

C1, C2, C3, and further principal components are defined in terms of their variance, with C1 having the highest variance, C2 having the second highest variance, and so on.

Relationship with Original Variance

The variances of individual principal components are related to the original total variance in that the sum of the variances of all principal components equals the original total variance.

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Description

Explore the differences between Principal Components Analysis (PCA) and Factor Analysis (FA), two statistical techniques used to identify key factors representing relationships among interrelated variables. Learn about the applications, advantages, and considerations when using PCA and FA.

Principal Components Analysis vs Factor Analysis