# Factor Analysis

## Factor Analysis

Factor analysis is a technique in mathematics that we use to reduce a larger number into a smaller number. Moreover, in this topic, we will talk about it and its various aspects.

### What is Factor Analysis?

It refers to a method that reduces a large variable into a smaller variable factor. Furthermore, this technique takes out maximum ordinary variance from all the variables and put them in common score.

Moreover, it is a part of General Linear Model (GLM) and it believes several theories that contain no multicollinearity, linear relationship, true correlation, and relevant variables into the analysis among factors and variables.

### Types of Factor Analysis

There are different methods that we use in factor analysis from the data set:

#### 1. Principal component analysis

It is the most common method which the researchers use. Also, it extracts the maximum variance and put them into the first factor. Subsequently, it removes the variance explained by the first factor and extracts the second factor. Moreover, it goes on until the last factor.

#### 2. Common Factor Analysis

Itâ€™s the second most favoured technique by researchers. Also, it extracts common variance and put them into factors. Furthermore, this technique doesnâ€™t include the variance of all variables and is used in SEM.

#### 3. Image Factoring

It is on the basis of the correlation matrix and makes use of OLS regression technique in order to predict the factor in image factoring.

#### 4. Maximum likelihood method

It also works on the correlation matrix but uses a maximum likelihood method to factor.

#### 5. Other methods of factor analysis

Alfa factoring outweighs least squares. Weight square is another regression-based method that we use for factoring.

Factor loading- Basically it the correlation coefficient for the factors and variables. Also, it explains the variable on a particular factor shown by variance.

Eigenvalues- Characteristics roots are its other name. Moreover, it explains the variance shown by that particular factor out of the total variance. Furthermore, commonality column helps to know how much variance the first factor explained out of total variance.

Factor Score- Itâ€™s another name is the component score. Besides, itâ€™s the score of all rows and columns that we can use as an index for all variables and for further analysis. Moreover, we can standardize it by multiplying it with a common term.

Rotation method- This method makes it more reliable to understand the output. Also, it affects the eigenvalues method but the eigenvalues method doesnâ€™t affect it. Besides, there are 5 rotation methods: (1) No Rotation Method, (2) Varimax Rotation Method, (3) Quartimax Rotation Method, (4) Direct Oblimin Rotation Method, and (5) Promax Rotation Method.

### Assumptions of Factor Analysis

Factor analysis has several assumptions. These include:

1. There are no outliers in the data.
2. The sample size is supposed to be greater than the factor.
3. It is an interdependency method so there should be no perfect multicollinearity between the variables.
4. Factor analysis is a linear function thus it doesnâ€™t require homoscedasticity between variables.
5. It is also based on the linearity assumption. So, we can also use non-linear variables. However, after a transfer, they change into a linear variable.
6. Moreover, it assumes interval data.

### Key Concepts of Factor Analysis

It includes the following key concept:

Exploratory factor analysis- It assumes that any variable or indicator can be associated with any factor. Moreover, it is the most common method used by researchers. Furthermore, it isnâ€™t based on any prior theory.

Confirmatory Factor Analysis- It is used to determine the factors loading and factors of measured variables, and to confirm what it expects on the basis of pre-established assumption. Besides, it uses two approaches:

2. The SEM Approach

### Solved Question for You

Question. How many types of Factor analysis are there?

A. 5
B. 6
C. 4
D. 3

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