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In: Statistics and Probability

# 1. What are the different types of factor analysis and what are they used for in...

1. What are the different types of factor analysis and what are they used for in statistics?

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Solution :-

Factor analysis is a technique that is used to reduce a large number of variables into fewer numbers of factors. This technique extracts maximum common variance from all variables and puts them into a common score. As an index of all variables, we can use this score for further analysis. Factor analysis is part of general linear model (GLM) and this method also assumes several assumptions: there is linear relationship, there is no multicollinearity, it includes relevant variables into analysis, and there is true correlation between variables and factors. Several methods are available, but principle component analysis is used most commonly.

Different Types of factor analysis :-

1. Principal component analysis

2. Common factor analysis

3. Image factoring

4. Maximum likelihood method

There are different types of methods used to extract the factor from the data set:

1. Principal component analysis: This is the most common method used by researchers. PCA starts extracting the maximum variance and puts them into the first factor. After that, it removes that variance explained by the first factors and then starts extracting maximum variance for the second factor. This process goes to the last factor.

2. Common factor analysis: The second most preferred method by researchers, it extracts the common variance and puts them into factors. This method does not include the unique variance of all variables. This method is used in SEM.

3. Image factoring: This method is based on correlation matrix. OLS Regression method is used to predict the factor in image factoring.

4. Maximum likelihood method: This method also works on correlation metric but it uses maximum likelihood method to factor.

5. Other methods of factor analysis: Alfa factoring outweighs least squares. Weight square is another regression based method which is used for factoring.

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